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Gate-defined single-electron transistors in twisted bilayer graphene
Authors:
Alexander Rothstein,
Ammon Fischer,
Anthony Achtermann,
Eike Icking,
Katrin Hecker,
Luca Banszerus,
Martin Otto,
Stefan Trellenkamp,
Florian Lentz,
Kenji Watanabe,
Takashi Taniguchi,
Bernd Beschoten,
Robin J. Dolleman,
Dante M. Kennes,
Christoph Stampfer
Abstract:
Twisted bilayer graphene (tBLG) near the magic angle is a unique platform where the combination of topology and strong correlations gives rise to exotic electronic phases. These phases are gate-tunable and related to the presence of flat electronic bands, isolated by single-particle band gaps. This enables gate-controlled charge confinement, essential for the operation of single-electron transisto…
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Twisted bilayer graphene (tBLG) near the magic angle is a unique platform where the combination of topology and strong correlations gives rise to exotic electronic phases. These phases are gate-tunable and related to the presence of flat electronic bands, isolated by single-particle band gaps. This enables gate-controlled charge confinement, essential for the operation of single-electron transistors (SETs), and allows to explore the interplay of confinement, electron interactions, band renormalisation and the moiré superlattice, potentially revealing key paradigms of strong correlations. Here, we present gate-defined SETs in near-magic-angle tBLG with well-tunable Coulomb blockade resonances. These SETs allow to study magnetic field-induced quantum oscillations in the density of states of the source-drain reservoirs, providing insight into gate-tunable Fermi surfaces of tBLG. Comparison with tight-binding calculations highlights the importance of displacement-field-induced band renormalisation crucial for future advanced gate-tunable quantum devices and circuits in tBLG including e.g. quantum dots and Josephson junction arrays.
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Submitted 11 December, 2024; v1 submitted 12 September, 2024;
originally announced September 2024.
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Tunable Doping and Mobility Enhancement in 2D Channel Field-Effect Transistors via Damage-Free Atomic Layer Deposition of AlOX Dielectrics
Authors:
Ardeshir Esteki,
Sarah Riazimehr,
Agata Piacentini,
Harm Knoops,
Bart Macco,
Martin Otto,
Gordon Rinke,
Zhenxing Wang,
Ke Ran,
Joachim Mayer,
Annika Grundmann,
Holger Kalisch,
Michael Heuken,
Andrei Vescan,
Daniel Neumaier,
Alwin Daus,
Max C. Lemme
Abstract:
Two-dimensional materials (2DMs) have been widely investigated because of their potential for heterogeneous integration with modern electronics. However, several major challenges remain, such as the deposition of high-quality dielectrics on 2DMs and the tuning of the 2DM doping levels. Here, we report a scalable plasma-enhanced atomic layer deposition (PEALD) process for direct deposition of a non…
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Two-dimensional materials (2DMs) have been widely investigated because of their potential for heterogeneous integration with modern electronics. However, several major challenges remain, such as the deposition of high-quality dielectrics on 2DMs and the tuning of the 2DM doping levels. Here, we report a scalable plasma-enhanced atomic layer deposition (PEALD) process for direct deposition of a nonstoichiometric aluminum oxide (AlOX) dielectric, overcoming the damage issues associated with conventional methods. Furthermore, we control the thickness of the dielectric layer to systematically tune the doping level of 2DMs. The experimental results demonstrate successful deposition without detectable damage, as confirmed by Raman spectroscopy and electrical measurements. Our method enables tuning of the Dirac and threshold voltages of back-gated graphene and MoS${_2}$ field-effect transistors (FETs), respectively, while also increasing the charge carrier mobility in both device types. We further demonstrate the method in top-gated MoS${_2}$ FETs with double-stack dielectric layers (AlOX+Al${_2}$O${_3}$), achieving critical breakdown field strengths of 7 MV/cm and improved mobility compared with the back gate configuration. In summary, we present a PEALD process that offers a scalable and low-damage solution for dielectric deposition on 2DMs, opening new possibilities for precise tuning of device characteristics in heterogeneous electronic circuits.
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Submitted 13 August, 2024;
originally announced August 2024.
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Plasma-enhanced atomic layer deposition of Al$_2$O$_3$ on graphene using monolayer hBN as interfacial layer
Authors:
Barbara Canto,
Martin Otto,
Michael J. Powell,
Vitaliy Babenko,
Aileen O Mahony,
Harm Knoops,
Ravi S. Sundaram,
Stephan Hofmann,
Max C. Lemme,
Daniel Neumaier
Abstract:
The deposition of dielectric materials on graphene is one of the bottlenecks for unlocking the potential of graphene in electronic applications. In this paper we demonstrate the plasma enhanced atomic layer deposition of 10 nm thin high quality Al$_2$O$_3$ on graphene using a monolayer of hBN as protection layer. Raman spectroscopy was performed to analyze possible structural changes of the graphe…
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The deposition of dielectric materials on graphene is one of the bottlenecks for unlocking the potential of graphene in electronic applications. In this paper we demonstrate the plasma enhanced atomic layer deposition of 10 nm thin high quality Al$_2$O$_3$ on graphene using a monolayer of hBN as protection layer. Raman spectroscopy was performed to analyze possible structural changes of the graphene lattice caused by the plasma deposition. The results show that a monolayer of hBN in combination with an optimized deposition process can effectively protect graphene from damage, while significant damage was observed without an hBN layer. Electrical characterization of double gated graphene field effect devices confirms that the graphene did not degrade during the plasma deposition of Al$_2$O$_3$. The leakage current densities were consistently below 1 nA/mm for electric fields across the insulators of up to 8 MV/cm, with irreversible breakdown happening above. Such breakdown electric fields are typical for Al$_2$O$_3$ and can be seen as an indicator for high quality dielectric films.
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Submitted 24 August, 2022;
originally announced August 2022.
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Ultrafast Electron Diffraction: Visualizing Dynamic States of Matter
Authors:
Daniele Filippetto,
Pietro Musumeci,
Renkai Li,
Bradley John Siwick,
Martin Otto,
Martin Centurion Joao Pedro Nunes
Abstract:
Since the discovery of electron-wave duality, electron scattering instrumentation has developed into a powerful array of techniques for revealing the atomic structure of matter. Beyond detecting local lattice variations in equilibrium structures, recent research efforts have been directed towards the long sought-after dream of visualizing the dynamic evolution of matter in real-time. The atomic be…
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Since the discovery of electron-wave duality, electron scattering instrumentation has developed into a powerful array of techniques for revealing the atomic structure of matter. Beyond detecting local lattice variations in equilibrium structures, recent research efforts have been directed towards the long sought-after dream of visualizing the dynamic evolution of matter in real-time. The atomic behavior at ultrafast timescales carries critical information on phase transition and chemical reaction dynamics, the coupling of electronic and nuclear degrees of freedom in materials and molecules, the correlation between structure, function and previously hidden metastable or nonequilibrium states of matter. Ultrafast electron pulses play an essential role in this scientific endeavor, and their generation has been facilitated by rapid technical advances in both ultrafast laser and particle accelerator technologies. This review presents a summary of the remarkable developments in this field over the last few decades. The physics and technology of ultrafast electron beams is presented with an emphasis on the figures of merit most relevant for ultrafast electron diffraction (UED) experiments. We discuss recent developments in the generation, manipulation and characterization of ultrashort electron beams aimed at improving the combined spatio-temporal resolution of these measurements. The fundamentals of electron scattering from atomic matter and the theoretical frameworks for retrieving dynamic structural information from solid-state and gas-phase samples are described, together with essential experimental techniques and several landmark works. Ultrafast electron probes with ever improving capabilities, combined with other complementary photon-based or spectroscopic approaches, hold tremendous potential for revolutionizing our ability to observe and understand energy and matter at atomic scales.
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Submitted 30 June, 2022;
originally announced July 2022.
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Direct view of phonon dynamics in atomically thin MoS$_{2}$
Authors:
Tristan L. Britt,
Qiuyang Li,
Laurent P. René de Cotret,
Nicholas Olsen,
Martin Otto,
Syed Ali Hassan,
Marios Zacharias,
Fabio Caruso,
Xiaoyang Zhu,
Bradley J. Siwick
Abstract:
Transition metal dichalcogenide monolayers and heterostructures are highly tunable material systems that provide excellent models for physical phenomena at the two-dimensional (2D) limit. While most studies to date have focused on electrons and electron-hole pairs, phonons also play essential roles. Here, we apply ultrafast electron diffraction and diffuse scattering to directly quantify, with tim…
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Transition metal dichalcogenide monolayers and heterostructures are highly tunable material systems that provide excellent models for physical phenomena at the two-dimensional (2D) limit. While most studies to date have focused on electrons and electron-hole pairs, phonons also play essential roles. Here, we apply ultrafast electron diffraction and diffuse scattering to directly quantify, with time and momentum resolution, electron-phonon coupling (EPC) in monolayer molybdenum disulfide (MoS$_{2}$) and phonon transport from the monolayer to a silicon nitride (Si$_3$N$_4$) substrate. Optically generated hot carriers result in a profoundly anisotropic distribution of phonons in the monolayer on the $\sim$ 5 ps time scale. A quantitative comparison with ab-initio ultrafast dynamics simulations reveals the essential role of dielectric screening in weakening EPC. Thermal transport from the monolayer to the substrate occurs with the phonon system far from equilibrium. While screening in 2D is known to strongly affect equilibrium properties, our findings extend this understanding to the dynamic regime.
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Submitted 16 May, 2022;
originally announced May 2022.
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Direct visualization of polaron formation in the thermoelectric SnSe
Authors:
Laurent P. René de Cotret,
Martin R. Otto,
Jan-Hendrick Pöhls,
Zhongzhen Luo,
Mercouri G. Kanatzidis,
Bradley J. Siwick
Abstract:
SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing…
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SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing polaron formation in the material. We employ ultrafast electron diffraction and diffuse scattering to track the response of phonons in both momentum and time to the photodoping of free carriers across the bandgap, observing the bimodal and anisotropic lattice distortions that drive carrier localization. Relatively large (\SI{18.7}{\angstrom}), quasi-1D polarons are formed on the \SI{300}{\femto\second} timescale with smaller (\SI{4.2}{\angstrom}) 3D polarons taking an order of magnitude longer (\SI{4}{\pico\second}) to form. This difference appears to be a consequence of the profoundly anisotropic electron-phonon coupling in SnSe, with strong Fröhlich coupling only to zone center polar optical phonons. These results demonstrate that carriers in SnSe at optimal doping levels results in a high polaron density and that strong electron-phonon coupling is also critical to the thermoelectric performance of this benchmark material and potentially high-performance thermoelectrics more generally.
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Submitted 21 November, 2021; v1 submitted 18 November, 2021;
originally announced November 2021.
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Optimizing the Stability of FETs Based on Two-Dimensional Materials by Fermi Level Tuning
Authors:
Theresia Knobloch,
Burkay Uzlu,
Yury Yu. Illarionov,
Zhenxing Wang,
Martin Otto,
Lado Filipovic,
Michael Waltl,
Daniel Neumaier,
Max C. Lemme,
Tibor Grasser
Abstract:
Despite the enormous progress achieved during the past decade, nanoelectronic devices based on two-dimensional (2D) semiconductors still suffer from a limited electrical stability. This limited stability has been shown to result from the interaction of charge carriers originating from the 2D semiconductors with defects in the surrounding insulating materials. The resulting dynamically trapped char…
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Despite the enormous progress achieved during the past decade, nanoelectronic devices based on two-dimensional (2D) semiconductors still suffer from a limited electrical stability. This limited stability has been shown to result from the interaction of charge carriers originating from the 2D semiconductors with defects in the surrounding insulating materials. The resulting dynamically trapped charges are particularly relevant in field effect transistors (FETs) and can lead to a large hysteresis, which endangers stable circuit operation. Based on the notion that charge trapping is highly sensitive to the energetic alignment of the channel Fermi-level with the defect band in the insulator, we propose to optimize device stability by deliberately tuning the channel Fermi-level. Our approach aims to minimize the amount of electrically active border traps without modifying the total number of traps in the insulator. We demonstrate the applicability of this idea by using two differently doped graphene layers in otherwise identical FETs with Al$_2$O$_3$ as a gate oxide mounted on a flexible substrate. Our results clearly show that by increasing the distance of the Fermi-level to the defect band, the hysteresis is significantly reduced. Furthermore, since long-term reliability is also very sensitive to trapped charges, a corresponding improvement in reliability is both expected theoretically and demonstrated experimentally. Our study paves the way for the construction of more stable and reliable 2D FETs in which the channel material is carefully chosen and tuned to maximize the energetic distance between charge carriers in the channel and the defect bands in the insulator employed.
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Submitted 26 April, 2021; v1 submitted 16 April, 2021;
originally announced April 2021.
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Dispersive sensing of charge states in a bilayer graphene quantum dot
Authors:
Luca Banszerus,
Samuel Möller,
Eike Icking,
Corinne Steiner,
Daniel Neumaier,
Martin Otto,
Kenji Watanabe,
Takashi Taniguchi,
Christian Volk,
Christoph Stampfer
Abstract:
We demonstrate dispersive readout of individual charge states in a gate-defined few-electron quantum dot in bilayer graphene. We employ a radio frequency reflectometry circuit, where an LC resonator with a resonance frequency close to 280 MHz is directly coupled to an ohmic contact of the quantum dot device. The detection scheme based on changes in the quantum capacitance operates over a wide gate…
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We demonstrate dispersive readout of individual charge states in a gate-defined few-electron quantum dot in bilayer graphene. We employ a radio frequency reflectometry circuit, where an LC resonator with a resonance frequency close to 280 MHz is directly coupled to an ohmic contact of the quantum dot device. The detection scheme based on changes in the quantum capacitance operates over a wide gate-voltage range and allows to probe excited states down to the single-electron regime. Crucially, the presented sensing technique avoids the use of an additional, capacitively coupled quantum device such as a quantum point contact or single electron transistor, making dispersive sensing particularly interesting for gate-defined graphene quantum dots.
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Submitted 13 February, 2021; v1 submitted 11 December, 2020;
originally announced December 2020.
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Oxidising and carburising catalyst conditioning for the controlled growth and transfer of large crystal monolayer hexagonal boron nitride
Authors:
Vitaliy Babenko,
Ye Fan,
Vlad-Petru Veigang-Radulescu,
Barry Brennan,
Andrew J. Pollard,
Oliver Burton,
Jack A. Alexander-Webber,
Robert S. Weatherup,
Barbara Canto,
Martin Otto,
Daniel Neumaier,
Stephan Hofmann
Abstract:
Hexagonal boron nitride (h-BN) is well-established as a requisite support, encapsulant and barrier for 2D material technologies, but also recently as an active material for applications ranging from hyperbolic metasurfaces to room temperature single-photon sources. Cost-effective, scalable and high quality growth techniques for h-BN layers are critically required. We utilise widely-available iron…
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Hexagonal boron nitride (h-BN) is well-established as a requisite support, encapsulant and barrier for 2D material technologies, but also recently as an active material for applications ranging from hyperbolic metasurfaces to room temperature single-photon sources. Cost-effective, scalable and high quality growth techniques for h-BN layers are critically required. We utilise widely-available iron foils for the catalytic chemical vapour deposition (CVD) of h BN and report on the significant role of bulk dissolved species in h-BN CVD, and specifically, the balance between dissolved oxygen and carbon. A simple pre-growth conditioning step of the iron foils enables us to tailor an error-tolerant scalable CVD process to give exceptionally large h-BN monolayer domains. We also develop a facile method for the improved transfer of as-grown h-BN away from the iron surface by means of the controlled humidity oxidation and subsequent rapid etching of a thin interfacial iron oxide; thus, avoiding the impurities from the bulk of the foil. We demonstrate wafer-scale (2 inch) production and utilise this h-BN as a protective layer for graphene towards integrated (opto) electronic device fabrication.
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Submitted 26 November, 2020;
originally announced November 2020.
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Electrostatic detection of Shubnikov-de-Haas oscillations in bilayer graphene by Coulomb resonances in gate-defined quantum dots
Authors:
Luca Banszerus,
Thomas Fabian,
Samuel Möller,
Eike Icking,
Henning Heiming,
Stefan Trellenkamp,
Florian Lentz,
Daniel Neumaier,
Martin Otto,
Kenji Watanabe,
Takashi Taniguchi,
Florian Libisch,
Christian Volk,
Christoph Stampfer
Abstract:
A gate-defined quantum dot in bilayer graphene is utilized as a sensitive electrometer for probing the charge density of its environment. Under the influence of a perpendicular magnetic field, the charge carrier density of the channel region next to the quantum dot oscillates due to the formation of Landau levels. This is experimentally observed as oscillations in the gate-voltage positions of the…
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A gate-defined quantum dot in bilayer graphene is utilized as a sensitive electrometer for probing the charge density of its environment. Under the influence of a perpendicular magnetic field, the charge carrier density of the channel region next to the quantum dot oscillates due to the formation of Landau levels. This is experimentally observed as oscillations in the gate-voltage positions of the Coulomb resonances of the nearby quantum dot. From the frequency of the oscillations, we extract the charge carrier density in the channel and from the amplitude the shift of the quantum dot potential. We compare these experimental results with an electrostatic simulation of the device and find good agreement.
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Submitted 9 September, 2020; v1 submitted 23 June, 2020;
originally announced June 2020.
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Graphene-Quantum Dots Hybrid Photodetectors with Low Dark-Current Readout
Authors:
D. De Fazio,
B. Uzlu,
I. Torre,
C. Monasterio,
S. Gupta,
T. Khodkov,
Y. Bi,
Z. Wang,
M. Otto,
M. C. Lemme,
S. Goossens,
D. Neumaier,
F. H. L. Koppens
Abstract:
Graphene-based photodetectors have shown responsivities up to 10$^8$A/W and photoconductive gains up to 10$^{8}$ electrons per photon. These photodetectors rely on a highly absorbing layer in close proximity of graphene, which induces a shift of the graphene chemical potential upon absorption, hence modifying its channel resistance. However, due to the semi-metallic nature of graphene, the readout…
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Graphene-based photodetectors have shown responsivities up to 10$^8$A/W and photoconductive gains up to 10$^{8}$ electrons per photon. These photodetectors rely on a highly absorbing layer in close proximity of graphene, which induces a shift of the graphene chemical potential upon absorption, hence modifying its channel resistance. However, due to the semi-metallic nature of graphene, the readout requires dark currents of hundreds of $μ$A up to mA, leading to high power consumption needed for the device operation. Here we propose a novel approach for highly responsive graphene-based photodetectors with orders of magnitude lower dark current levels. A shift of the graphene chemical potential caused by light absorption in a layer of colloidal quantum dots, induces a variation of the current flowing across a metal-insulator-graphene diode structure. Owing to the low density of states of graphene near the neutrality point, the light-induced shift in chemical potential can be relatively large, dramatically changing the amount of current flowing across the insulating barrier, and giving rise to a novel type of gain mechanism. This readout requires dark currents of hundreds of nA up to few $μ$A, orders of magnitude lower than other graphene-based photodetectors, while keeping responsivities of $\sim$70A/W in the infrared, almost two orders of magnitude higher compared to established germanium on silicon and indium gallium arsenide infrared photodetectors. This makes the device appealing for applications where high responsivity and low power consumption are required.
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Submitted 21 May, 2020;
originally announced May 2020.
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Tracking ultrafast solid-state dynamics using high harmonic spectroscopy
Authors:
Mina R. Bionta,
Elissa Haddad,
Adrien Leblanc,
Vincent Gruson,
Philippe Lassonde,
Heide Ibrahim,
Jérémie Chaillou,
Nicolas Émond,
Martin R. Otto,
Bradley J. Siwick,
Mohamed Chaker,
François Légaré
Abstract:
We establish time-resolved high harmonic generation (tr-HHG) as a powerful spectroscopy for photoinduced dynamics in strongly correlated materials through a detailed investigation of the insulator-to-metal transitions in vanadium dioxide. We benchmark our technique by comparing our measurements to established momentum-resolved ultrafast electron diffraction, and theoretical density functional calc…
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We establish time-resolved high harmonic generation (tr-HHG) as a powerful spectroscopy for photoinduced dynamics in strongly correlated materials through a detailed investigation of the insulator-to-metal transitions in vanadium dioxide. We benchmark our technique by comparing our measurements to established momentum-resolved ultrafast electron diffraction, and theoretical density functional calculations. Tr-HHG allows distinguishing of individual dynamic channels, including a transition to a thermodynamically hidden phase. In addition, the HHG yield is shown to be modulated at a frequency characteristic of a coherent phonon in the equilibrium monoclinic phase over a wide range of excitation fluences. These results demonstrate that tr-HHG is capable of tracking complex dynamics in solids through its sensitivity to the band structure.
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Submitted 23 March, 2020;
originally announced March 2020.
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Mechanisms of electron-phonon coupling unraveled in momentum and time: The case of soft-phonons in TiSe$_2$
Authors:
Martin R. Otto,
Jan-Hendrik Pöhls,
Laurent P. René de Cotret,
Mark J. Stern,
Mark Sutton,
Bradley J. Siwick
Abstract:
The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe$_2$ in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, $\Re\left[χ_0(\mathbf{q})\right]$, from those…
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The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe$_2$ in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, $\Re\left[χ_0(\mathbf{q})\right]$, from those due to the electron-phonon coupling vertex, $g_{\mathbf{q}}$, by following the response of semi-metallic (normal phase) 1T-TiSe$_2$ to the selective photo-doping of carriers into the electron pocket at the Fermi level. Quasi-impulsive and wavevector-specific renormalization of soft zone-boundary phonon frequencies (stiffening) is observed, followed by wavevector-independent electron-phonon equilibration. These results unravel the underlying mechanisms driving the phonon softening that is associated with the charge density wave transition at lower temperatures.
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Submitted 24 August, 2020; v1 submitted 7 December, 2019;
originally announced December 2019.
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Gate-tunable graphene-based Hall sensors on flexible substrates with increased sensitivity
Authors:
Burkay Uzlu,
Zhenxing Wang,
Sebastian Lukas,
Martin Otto,
Max C. Lemme,
Daniel Neumaier
Abstract:
We demonstrate a novel concept for operating graphene-based Hall sensors using an alternating current (AC) modulated gate voltage, which provides three important advantages compared to Hall sensors under static operation: 1) The sensor sensitivity can be doubled by utilizing both n- and p-type conductance. 2) A static magnetic field can be read out at frequencies in the kHz range, where the 1/f no…
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We demonstrate a novel concept for operating graphene-based Hall sensors using an alternating current (AC) modulated gate voltage, which provides three important advantages compared to Hall sensors under static operation: 1) The sensor sensitivity can be doubled by utilizing both n- and p-type conductance. 2) A static magnetic field can be read out at frequencies in the kHz range, where the 1/f noise is lower compared to the static case. 3) The off-set voltage in the Hall signal can be reduced. This significantly increases the signal-to-noise ratio compared to Hall sensors without a gate electrode. A minimal detectable magnetic field Bmin down to 290 nT/sqrt(Hz) and sensitivity up to 0.55 V/VT was found for Hall sensors fabricated on flexible foil. This clearly outperforms state-of-the-art flexible Hall sensors and is comparable to the values obtained by the best rigid III/V semiconductor Hall sensors.
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Submitted 16 September, 2019;
originally announced September 2019.
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Time- and momentum-resolved phonon population dynamics with ultrafast electron diffuse scattering
Authors:
Laurent P. René de Cotret,
Jan-Hendrik Pöhls,
Mark J. Stern,
Martin R. Otto,
Mark Sutton,
Bradley J. Siwick
Abstract:
Interactions between the lattice and charge carriers can drive the formation of phases and ordering phenomena that give rise to conventional superconductivity, insulator-to-metal transitions, and charge-density waves. These couplings also play a determining role in properties that include electric and thermal conductivity. Ultrafast electron diffuse scattering (UEDS) has recently become a viable l…
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Interactions between the lattice and charge carriers can drive the formation of phases and ordering phenomena that give rise to conventional superconductivity, insulator-to-metal transitions, and charge-density waves. These couplings also play a determining role in properties that include electric and thermal conductivity. Ultrafast electron diffuse scattering (UEDS) has recently become a viable laboratory-scale tool to track energy flow into and within the lattice system across the entire Brillouin zone, and deconvolves interactions in the time domain. Here, we present a detailed quantitative framework for the interpretation of UEDS signals, ultimately extracting the phonon mode occupancies across the entire Brillouin zone. These transient populations are then used to extract momentum- and mode-dependent electron-phonon and phonon-phonon coupling constants. Results of this analysis are presented for graphite, which provides complete information on the phonon-branch occupations and a determination of the $A_1'$ phonon mode-projected electron-phonon coupling strength $\langle g_{e,A_1'}^2 \rangle = 0.035 \pm 0.001$ eV$^2$ that is in agreement with other measurement techniques and simulations.
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Submitted 9 November, 2019; v1 submitted 7 August, 2019;
originally announced August 2019.
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How optical excitation controls the structure and properties of vanadium dioxide
Authors:
Martin R. Otto,
Laurent P. René de Cotret,
David A. Valverde-Chavez,
Kunal L. Tiwari,
Nicolas Émond,
Mohamed Chaker,
David G. Cooke,
Bradley J. Siwick
Abstract:
We combine ultrafast electron diffraction and time-resolved terahertz spectroscopy measurements to unravel the connection between structure and electronic transport properties during the photoinduced insulator-metal transitions in vanadium dioxide. We determine the structure of the metastable monoclinic metal phase, which exhibits anti-ferroelectric charge order arising from a thermally activated,…
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We combine ultrafast electron diffraction and time-resolved terahertz spectroscopy measurements to unravel the connection between structure and electronic transport properties during the photoinduced insulator-metal transitions in vanadium dioxide. We determine the structure of the metastable monoclinic metal phase, which exhibits anti-ferroelectric charge order arising from a thermally activated, orbital-selective phase transition in the electron system. The relative contribution of this photoinduced monoclinic metal (which has no equilibrium analog) and the photoinduced rutile metal (known from the equilibrium phase diagram) to the time and pump-fluence dependent multi-phase character of the film is established, as is the respective impact of these two distinct phase transitions on the observed changes in terahertz conductivity. Our results represent an important new example of how light can control the properties of strongly correlated materials and elucidate that multi-modal experiements are essential when seeking a detailed connection between ultrafast changes in optical-electronic properties and lattice structure in complex materials.
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Submitted 3 May, 2018;
originally announced May 2018.
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Mapping momentum-dependent electron-phonon coupling and non-equilibrium phonon dynamics with ultrafast electron diffuse scattering
Authors:
Mark J. Stern,
Laurent P. René de Cotret,
Martin R. Otto,
Robert P. Chatelain,
Jean-Philippe Boisvert,
Mark Sutton,
Bradley J. Siwick
Abstract:
Despite their fundamental role in determining material properties, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling (EPC and PPC, respectively) across the entire Brillouin zone (BZ) has proved difficult to obtain. Here we demonstrate that ultrafast electron diffuse scattering (UEDS) directly provides such information. By exploiting symmetry-base…
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Despite their fundamental role in determining material properties, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling (EPC and PPC, respectively) across the entire Brillouin zone (BZ) has proved difficult to obtain. Here we demonstrate that ultrafast electron diffuse scattering (UEDS) directly provides such information. By exploiting symmetry-based selection rules and time-resolution, scattering from different phonon branches can be distinguished even without energy resolution. Using graphite as a model system, we show that UEDS patterns map the relative EPC and PPC strength through their profound sensitivity to photoinduced changes in phonon populations. We measure strong EPC to the $K$-point transverse optical phonon of $A_1'$ symmetry ($K-A_1'$) and along the entire longitudinal optical branch between $Γ-K$, not only to the $Γ-E_{2g}$ phonon as previously emphasized. We also determine that the subsequent phonon relaxation pathway involves three stages; decay via several identifiable channels to transverse acoustic (TA) and longitudinal acoustic (LA) phonons (1-2 ps), intraband thermalization of the non-equilibrium TA/LA phonon populations (30-40 ps) and interband relaxation of the LA/TA modes (115 ps). Combining UEDS with ultrafast angle-resolved photoelectron spectroscopy will yield a complete picture of the dynamics within and between electron and phonon subsystems, helping to unravel complex phases in which the intertwined nature of these systems have a strong influence on emergent properties.
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Submitted 25 August, 2017; v1 submitted 3 August, 2017;
originally announced August 2017.
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Encapsulated graphene based Hall sensors on foil with increased sensitivity
Authors:
Zhenxing Wang,
Luca Banszerus,
Martin Otto,
Kenji Watanabe,
Takashi Taniguchi,
Christoph Stampfer,
Daniel Neumaier
Abstract:
The encapsulation of graphene based Hall sensors on foil is shown to be an effective method for improving the performance in terms of higher sensitivity for magnetic field detection. Two types of encapsulation were investigated: a simple encapsulation of graphene with polymethyl methacrylate (PMMA) as a proof of concept and an encapsulation with mechanically exfoliated hexagonal boron nitride (hBN…
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The encapsulation of graphene based Hall sensors on foil is shown to be an effective method for improving the performance in terms of higher sensitivity for magnetic field detection. Two types of encapsulation were investigated: a simple encapsulation of graphene with polymethyl methacrylate (PMMA) as a proof of concept and an encapsulation with mechanically exfoliated hexagonal boron nitride (hBN). The Hall sensor with PMMA encapsulation already shows higher sensitivity compared to the one without encapsulation. However, the Hall sensor with graphene encapsulated between two stacks of hBN shows a current and a voltage normalized sensitivity of up to 2270 V/AT and 0.68 V/VT respectively, which are the highest reported sensitivity values for Hall sensors on foil so far.
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Submitted 27 July, 2017;
originally announced July 2017.
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Flexible Hall Sensors Based on Graphene
Authors:
Zhenxing Wang,
Mehrdad Shaygan,
Martin Otto,
Daniel Schall,
Daniel Neumaier
Abstract:
The excellent electronic and mechanical properties of graphene provide a perfect basis for high performance flexible electronic and sensor devices. Here, we present the fabrication and characterization of flexible graphene based Hall sensors. The Hall sensors are fabricated on 50 um thick flexible Kapton foil using large scale graphene grown by chemical vapor deposition technique on copper foil. V…
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The excellent electronic and mechanical properties of graphene provide a perfect basis for high performance flexible electronic and sensor devices. Here, we present the fabrication and characterization of flexible graphene based Hall sensors. The Hall sensors are fabricated on 50 um thick flexible Kapton foil using large scale graphene grown by chemical vapor deposition technique on copper foil. Voltage and current normalized sensitivities of up to 0.096 V/VT and 79 V/AT were measured, respectively. These values are comparable to the sensitivity of rigid silicon based Hall sensors and are the highest values reported so far for any flexible Hall sensor devices. The sensitivity of the Hall sensor shows no degradation after being bent to a minimum radius of 4 mm, which corresponds to a tensile strain of 0.6%, and after 1,000 bending cycles to a radius of 5 mm.
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Submitted 27 July, 2017;
originally announced July 2017.
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Low resistive edge contacts to CVD-grown graphene using a CMOS compatible metal
Authors:
Mehrdad Shaygan,
Martin Otto,
Abhay A. Sagade,
Carlos A. Chavarin,
Gerd Bacher,
Wolfgang Mertin,
Daniel Neumaier
Abstract:
The exploitation of the excellent intrinsic electronic properties of graphene for device applications is hampered by a large contact resistance between the metal and graphene. The formation of edge contacts rather than top contacts is one of the most promising solutions for realizing low ohmic contacts. In this paper the fabrication and characterization of edge contacts to large area CVD-grown mon…
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The exploitation of the excellent intrinsic electronic properties of graphene for device applications is hampered by a large contact resistance between the metal and graphene. The formation of edge contacts rather than top contacts is one of the most promising solutions for realizing low ohmic contacts. In this paper the fabrication and characterization of edge contacts to large area CVD-grown monolayer graphene by means of optical lithography using CMOS compatible metals, i.e. Nickel and Aluminum is reported. Extraction of the contact resistance by Transfer Line Method (TLM) as well as the direct measurement using Kelvin Probe Force Microscopy demonstrates a very low width specific contact resistance.
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Submitted 1 June, 2017;
originally announced June 2017.
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Graphene photodetectors with a bandwidth larger than 76 GHz fabricated in a 6 inch wafer process line
Authors:
Daniel Schall,
Caroline Porschatis,
Martin Otto,
Daniel Neumaier
Abstract:
In recent years, the data traffic has grown exponentially and the forecasts indicate a huge market that could be addressed by communication infrastructure and service providers. However, the processing capacity, space, and energy consumption of the available technology is a serious bottleneck for the exploitation of these markets. Chip-integrated optical communication systems hold the promise of s…
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In recent years, the data traffic has grown exponentially and the forecasts indicate a huge market that could be addressed by communication infrastructure and service providers. However, the processing capacity, space, and energy consumption of the available technology is a serious bottleneck for the exploitation of these markets. Chip-integrated optical communication systems hold the promise of significantly improving these issues related to the current technology. At the moment, the answer to the question which material is best suited for ultrafast chip integrated communication systems is still open. In this manuscript we report on ultrafast graphene photodetectors with a bandwidth of more than 76 GHz well suitable for communication links faster than 100 GBit/s per channel. We extract an upper value of 7.2 ps for the timescale in which the bolometric photoresponse in graphene is generated. The photodetectors were fabricated on 6 inch silicon-on-insulator wafers in a semiconductor pilot line, demonstrating the scalable fabrication of high-performance graphene based devices.
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Submitted 16 March, 2017;
originally announced March 2017.
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Identifying suitable substrates for high-quality graphene-based heterostructures
Authors:
Luca Banszerus,
Hendrik Janssen,
Martin Otto,
Alexander Epping,
Takashi Taniguchi,
Kenji Watanabe,
Bernd Beschoten,
Daniel Neumaier,
Christoph Stampfer
Abstract:
We report on a scanning confocal Raman spectroscopy study investigating the strain-uniformity and the overall strain and doping of high-quality chemical vapour deposited (CVD) graphene-based heterostuctures on a large number of different substrate materials, including hexagonal boron nitride (hBN), transition metal dichalcogenides, silicon, different oxides and nitrides, as well as polymers. By ap…
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We report on a scanning confocal Raman spectroscopy study investigating the strain-uniformity and the overall strain and doping of high-quality chemical vapour deposited (CVD) graphene-based heterostuctures on a large number of different substrate materials, including hexagonal boron nitride (hBN), transition metal dichalcogenides, silicon, different oxides and nitrides, as well as polymers. By applying a hBN-assisted, contamination free, dry transfer process for CVD graphene, high-quality heterostructures with low doping densities and low strain variations are assembled. The Raman spectra of these pristine heterostructures are sensitive to substrate-induced doping and strain variations and are thus used to probe the suitability of the substrate material for potential high-quality graphene devices. We find that the flatness of the substrate material is a key figure for gaining, or preserving high-quality graphene.
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Submitted 27 October, 2016;
originally announced October 2016.
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Experimental verification of electro-refractive phase modulation in graphene
Authors:
Muhammad Mohsin,
Daniel Neumaier,
Daniel Schall,
Martin Otto,
Christopher Matheisen,
Anna Lena Giesecke,
Abhay A. Sagade,
Heinrich Kurz
Abstract:
Graphene has been considered as a promising material for opto-electronic devices, because of its tunable and wideband optical properties. In this work, we demonstrate electro-refractive phase modulation in graphene at wavelengths from 1530 to 1570 nm. By integrating a gated graphene layer in a silicon-waveguide based Mach-Zehnder interferometer, the key parameters of a phase modulator like change…
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Graphene has been considered as a promising material for opto-electronic devices, because of its tunable and wideband optical properties. In this work, we demonstrate electro-refractive phase modulation in graphene at wavelengths from 1530 to 1570 nm. By integrating a gated graphene layer in a silicon-waveguide based Mach-Zehnder interferometer, the key parameters of a phase modulator like change in effective refractive index, insertion loss and absorption change are extracted. These experimentally obtained values are well reproduced by simulations and design guidelines are provided to make graphene devices competitive to contemporary silicon based phase modulators for on-chip applications.
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Submitted 17 March, 2015;
originally announced March 2015.
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Characterization of low-temperature microwave loss of thin aluminum oxide formed by plasma oxidation
Authors:
Chunqing Deng,
Martin Otto,
Adrian Lupascu
Abstract:
We report on the characterization of microwave loss of thin aluminum oxide films at low temperatures using superconducting lumped resonators. The oxide films are fabricated using plasma oxidation of aluminum and have a thickness of 5 nm. We measure the dielectric loss versus microwave power for resonators with frequencies in the GHz range at temperatures from 54 to 303 mK. The power and temperatur…
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We report on the characterization of microwave loss of thin aluminum oxide films at low temperatures using superconducting lumped resonators. The oxide films are fabricated using plasma oxidation of aluminum and have a thickness of 5 nm. We measure the dielectric loss versus microwave power for resonators with frequencies in the GHz range at temperatures from 54 to 303 mK. The power and temperature dependence of the loss is consistent with the tunneling two-level system theory. These results are relevant to understanding decoherence in superconducting quantum devices. The obtained oxide films are thin and robust, making them suitable for capacitors in compact microwave resonators.
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Submitted 27 December, 2013;
originally announced December 2013.
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An analysis method for transmission measurements of superconducting resonators with applications to quantum-regime dielectric-loss measurements
Authors:
Chunqing Deng,
Martin Otto,
Adrian Lupascu
Abstract:
Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator cou…
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Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator coupled to a transmission line. We first derive an approximate expression for the transmission S-parameter $S_{21}$ based on a complete circuit model. In the weak coupling limit, we show that the internal quality factor is reliably determined by fitting the approximate form of $S_{21}$. Since the voltage $V$ of the capacitor of the LC circuit is required to determine the energy stored in the resonator, we next calculate the relation between $V$ and the forward propagating wave voltage $V_{in}^+$. Due to the dependence of the quality factor on voltage, $V$ is not simply proportional to $V_{in}^+$. We find a self-consistent way to determine the relation between $V$ and $V_{in}^+$, which employs only the fitting parameters for $S_{21}$ and a linear scaling factor. We then examine the resonator transmission in the cases of port reflection and impedance mismatch. We find that resonator transmission asymmetry is primarily due to the reflection from discontinuity in transmission lines. We show that our analysis method to extract the internal quality factor is robust in the non-ideal cases above. Finally, we show that the analysis method on LC resonator can be generalize to arbitrary weakly coupled lumped and distributed resonators. The generalization uses a systematic approximation on the response function based on the pole and zero which are the closest to the resonance frequency. This Closest Pole and Zero Method (CPZM) is a valuable tool for analyzing physical measurements of high-Q resonators.
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Submitted 8 August, 2013; v1 submitted 16 April, 2013;
originally announced April 2013.
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High On/Off Ratios in Bilayer Graphene Field Effect Transistors Realized by Surface Dopants
Authors:
Bartholomaeus N. Szafranek,
Daniel Schall,
Martin Otto,
Daniel Neumaier,
Heinrich Kurz
Abstract:
The unique property of bilayer graphene to show a band gap tunable by external electrical fields enables a variety of different device concepts with novel functionalities for electronic, optoelectronic and sensor applications. So far the operation of bilayer graphene based field effect transistors requires two individual gates to vary the channel's conductance and to create a band gap. In this pap…
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The unique property of bilayer graphene to show a band gap tunable by external electrical fields enables a variety of different device concepts with novel functionalities for electronic, optoelectronic and sensor applications. So far the operation of bilayer graphene based field effect transistors requires two individual gates to vary the channel's conductance and to create a band gap. In this paper we report on a method to increase the on/off ratio in single gated bilayer graphene field effect transistors by adsorbate doping. The adsorbate dopants on the upper side of the graphene establish a displacement field perpendicular to the graphene surface breaking the inversion symmetry of the two graphene layers. Low temperature measurements indicate, that the increased on/off ratio is caused by the opening of a mobility gap. Beside field effect transistors the presented approach can also be employed for other bilayer graphene based devices like photodetectors for THz to infrared radiation, chemical sensors and in more sophisticated structures such as antidot- or superlattices where an artificial potential landscape has to be created.
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Submitted 24 February, 2011;
originally announced February 2011.
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Electrical observation of a tunable band gap in bilayer graphene nanoribbons at room temperature
Authors:
Bartholomaeus N. Szafranek,
Daniel Schall,
Martin Otto,
Daniel Neumaier,
Heinrich Kurz
Abstract:
We investigate the transport properties of double-gated bilayer graphene nanoribbons at room temperature. The devices were fabricated using conventional CMOS-compatible processes. By analyzing the dependence of the resistance at the charge neutrality point as a function of the electric field applied perpendicular to the graphene surface, we show that a band gap in the density of states opens, re…
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We investigate the transport properties of double-gated bilayer graphene nanoribbons at room temperature. The devices were fabricated using conventional CMOS-compatible processes. By analyzing the dependence of the resistance at the charge neutrality point as a function of the electric field applied perpendicular to the graphene surface, we show that a band gap in the density of states opens, reaching an effective value of ~sim50 meV. This demonstrates the potential of bilayer graphene as FET channel material in a conventional CMOS environment.
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Submitted 28 January, 2010;
originally announced January 2010.
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Microscopic dynamics of thin hard rods
Authors:
Matthias Otto,
Timo Aspelmeier,
Annette Zippelius
Abstract:
Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlatio…
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Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalised Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualtitative agreement for higher densities.
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Submitted 11 October, 2006; v1 submitted 18 October, 2005;
originally announced October 2005.
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Local Equation of State and Velocity Distributions of a Driven Granular Gas
Authors:
Olaf Herbst,
Peter Müller,
Matthias Otto,
Annette Zippelius
Abstract:
We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local…
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We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local constitutive equation. For strong inelasticities the local constitutive relation depends on global system parameters, like the volume fraction and the aspect ratio. For moderate inelasticities the constitutive relation is approximately independent of the system parameters and can hence be regarded as a local equation of state, even though the system is highly inhomogeneous with heterogeneous temperature and density profiles arising as a consequence of the energy injection. Concerning the local velocity distributions we find that they do not scale with the square root of the local granular temperature. Moreover the high-velocity tails are different for the distribution of the x- and the y-component of the velocity, and even depend on the position in the sample, the global volume fraction, and the coefficient of restitution.
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Submitted 6 July, 2004; v1 submitted 4 February, 2004;
originally announced February 2004.
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Topological interactions in systems of mutually interlinked polymer rings
Authors:
Matthias Otto
Abstract:
The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Ph…
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The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined in several ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$ where $R_G$ is average size of single random walk ring, the effective topological interaction (free energy) scales $\propto R^4$.
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Submitted 8 September, 2003;
originally announced September 2003.
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Anisotropy in granular media: classical elasticity and directed force chain network
Authors:
M. Otto,
J. -P. Bouchaud,
P. Claudin,
J. E. S. Socolar
Abstract:
A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular n…
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A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.
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Submitted 7 January, 2003; v1 submitted 1 November, 2002;
originally announced November 2002.
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The direct link model for polymer rings as a topological field theory and the second topological moment in dense systems
Authors:
Matthias Otto
Abstract:
Polymer rings in solution are either permanently entangled or not. Permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume. Conversely, entangled polymer rings systems may be formed by closing randomly entangled flexible linear chains. The dependance of linking numbers between randomly entangled…
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Polymer rings in solution are either permanently entangled or not. Permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume. Conversely, entangled polymer rings systems may be formed by closing randomly entangled flexible linear chains. The dependance of linking numbers between randomly entangled rings on the chain length, more specifically the second topological moment $<n^2>$, i.e. the average squared linking number, may be determined. In this paper, an approach recently discussed in mathematical physics and called abelian BF theory, is presented which allows to express the linking constraint in its simplest form, the Gauss integral, in terms of two gauge fields. The model of Brereton and Shah for a single ring entangled with many other surrounding rings is rederived. The latter model is finally used to calculate the second topological moment, in agreement with a recent result by Ferrari, Kleinert, and Lazzizzera obtained by using ${\rm n}$-component $φ^4$ theory in the limit ${\rm n}\to 0$.
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Submitted 19 February, 2001; v1 submitted 23 November, 2000;
originally announced November 2000.
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Force chain splitting in granular materials: a mechanism for large scale pseudo-elastic behaviour
Authors:
J. -P. Bouchaud,
P. Claudin,
D. Levine,
M. Otto
Abstract:
We investigate both numerically and analytically the effect of strong disorder on the large scale properties of the hyperbolic equations for stresses proposed in \protect\cite{bcc,wcc}. The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid mediu…
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We investigate both numerically and analytically the effect of strong disorder on the large scale properties of the hyperbolic equations for stresses proposed in \protect\cite{bcc,wcc}. The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid medium, we propose a Boltzmann-like equation to describe these processes. We show that, for isotropic packings, the resulting large scale effective equations for the stresses have exactly the same structure as those of an elastic body, despite the fact that no displacement field needs to be introduced at all. Correspondingly, the response function evolves from a two peak structure at short scales to a broad hump at large scales. We find, however, that the Poisson ratio is anomalously large and incompatible with classical elasticity theory that requires the reference state to be thermodynamically stable.
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Submitted 27 November, 2000; v1 submitted 13 November, 2000;
originally announced November 2000.
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Stochastic relaxational dynamics applied to finance: towards non-equilibrium option pricing theory
Authors:
Matthias Otto
Abstract:
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et al.) considers fluctuations around this equilibrium state by introducing a relaxational dynamics with random noise for intermediate deviations called ``virtual''…
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Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et al.) considers fluctuations around this equilibrium state by introducing a relaxational dynamics with random noise for intermediate deviations called ``virtual'' arbitrage returns. In this work, the model is incorporated within a martingale pricing method for derivatives on securities (e.g. stocks) in incomplete markets using a mapping to option pricing theory with stochastic interest rates. Using a famous result by Merton and with some help from the path integral method, exact pricing formulas for European call and put options under the influence of virtual arbitrage returns (or intermediate deviations from economic equilibrium) are derived where only the final integration over initial arbitrage returns needs to be performed numerically. This result is complemented by a discussion of the hedging strategy associated to a derivative, which replicates the final payoff but turns out to be not self-financing in the real world, but self-financing {\it when summed over the derivative's remaining life time}. Numerical examples are given which underline the fact that an additional positive risk premium (with respect to the Black-Scholes values) is found reflecting extra hedging costs due to intermediate deviations from economic equilibrium.
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Submitted 14 October, 1999; v1 submitted 14 June, 1999;
originally announced June 1999.
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Using path integrals to price interest rate derivatives
Authors:
Matthias Otto
Abstract:
We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (Black-Scholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach is tested by rederiving the prices of a zero bond and a zero bond option for a short rate environment which…
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We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (Black-Scholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach is tested by rederiving the prices of a zero bond and a zero bond option for a short rate environment which is governed by Vasicek dynamics. Furthermore, a generalization of the method to general short rate models is outlined. In the case, where analytical solutions are not accessible, numerical implementations of the path integral method in terms of lattice calculations as well as path integral Monte Carlo simulations are possible.
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Submitted 14 June, 1999; v1 submitted 18 December, 1998;
originally announced December 1998.
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Topological interactions in DNA catenanes
Authors:
M. Otto,
T. A. Vilgis
Abstract:
The elasticity of DNA catenanes, i.e. multiply linked DNA rings, is investigated using the Gauss invariant as a minimal model for topology conservation. An effective elastic free energy as a function of the distance $R$ between segments located on different rings is obtained. An anharmonic part at large distances, growing as $R^{4}$, if $R\gg R_{G}$ ($R_{G}$ being the radius of gyration of a ran…
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The elasticity of DNA catenanes, i.e. multiply linked DNA rings, is investigated using the Gauss invariant as a minimal model for topology conservation. An effective elastic free energy as a function of the distance $R$ between segments located on different rings is obtained. An anharmonic part at large distances, growing as $R^{4}$, if $R\gg R_{G}$ ($R_{G}$ being the radius of gyration of a random walk ring) is found, while for $R\ll R_{G}$ the interaction is strongly repulsive. Treating the attractive interaction as the dominant one, distribution functions for the distance between segments located on different rings for several linking numbers are derived which are in qualitative agreement with distributions functions obtained experimentally from electron micrographs of DNA catenanes (S. D. Levene et al., Biophys.J. 69, 277, 1995).
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Submitted 26 November, 1997;
originally announced November 1997.
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Elasticity of entangled polymer loops: Olympic gels
Authors:
T. A. Vilgis,
M. Otto
Abstract:
In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto λ^{5/2}$ whe…
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In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto λ^{5/2}$ where $λ$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.
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Submitted 27 May, 1997;
originally announced May 1997.
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Entangled Polymer Rings in 2D and Confinement
Authors:
Matthias Otto,
Thomas A. Vilgis
Abstract:
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collaps…
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The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$.
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Submitted 17 April, 1996; v1 submitted 16 April, 1996;
originally announced April 1996.
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The conformation of conducting polymer chains: Hubbard polymers
Authors:
M. Otto,
T. A. Vilgis
Abstract:
The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are presented. One important result is that the electronic degrees of freedom greatly affect the conformational statistics of the walks and vice versa. The electronic de…
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The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are presented. One important result is that the electronic degrees of freedom greatly affect the conformational statistics of the walks and vice versa. The electronic degrees of freedom extend the size of the chain. The end-to-end distance behaves as $R\propto L^ν$ with $ν=(d+1)/(d+2)$, where $d$ is the spatial dimension.
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Submitted 14 October, 1994;
originally announced October 1994.