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Hybrid-functional electronic structure of multilayer graphene
Authors:
Marco Campetella,
Nguyen Minh Nguyen,
Jacopo Baima,
Lorenzo Maschio,
Francesco Mauri,
Matteo Calandra
Abstract:
Multilayer graphene with rhombohedral and Bernal stacking are supposed to be metallic, as predicted by density functional theory calculations using semi-local functionals. However recent angular resolved photoemission and transport data have questioned this point of view. In particular, rhombohedral flakes are suggested to be magnetic insulators. Bernal flakes composed of an even number of layers…
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Multilayer graphene with rhombohedral and Bernal stacking are supposed to be metallic, as predicted by density functional theory calculations using semi-local functionals. However recent angular resolved photoemission and transport data have questioned this point of view. In particular, rhombohedral flakes are suggested to be magnetic insulators. Bernal flakes composed of an even number of layers are insulating, while those composed of an odd number of layers are pseudogapped. Here, by systematically benchmarking with plane waves codes, we develop very accurate all-electron Gaussian basis sets for graphene multilayers. We find that, in agreement with our previous calculations, rhombohedral stacked multilayer graphene are gapped for and magnetic. However, the valence band curvature and the details of the electronic structure depend crucially on the basis set. Only substantially extended basis sets are able to correctly reproduce the effective mass of the valence band top at the K point, while the popular POB-TZVP basis set leads to a severe overestimation. In the case of Bernal stacking, we show that exact exchange gaps the flakes composed by four layers and opens pseudogaps for N = 3, 6, 7, 8. However, the gap or pseudogap size and its behaviour as a function of thickness are not compatible with experimental data. Moreover, hybrid functionals lead to a metallic solution for 5 layers and a magnetic ground state for 5, 6 and 8 layers. Magnetism is very weak with practically no effect on the electronic structure and the magnetic moments are mostly concentrated in the central layers. Our hybrid functional calculations on trilayer Bernal graphene multilayers are in excellent agreement with non-magnetic GW calculations. For thicker multilayers, our calculations are a benchmark for manybody theoretical modeling of the low energy electronic structure.
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Submitted 17 January, 2020;
originally announced January 2020.
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Gate Tunable Magnetism and Giant Magnetoresistance in ABC-stacked Few-Layer Graphene
Authors:
Yongjin Lee,
Shi Che,
Jairo Velasco Jr.,
David Tran,
Jacopo Baima,
Francesco Mauri,
Matteo Calandra,
Marc Bockrath,
Chun Ning Lau
Abstract:
Magnetism is a prototypical phenomenon of quantum collective state, and has found ubiquitous applications in semiconductor technologies such as dynamic random access memory (DRAM). In conventional materials, it typically arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. Magnetism, however, can also emerge in perfect lattices from non-magnetic elemen…
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Magnetism is a prototypical phenomenon of quantum collective state, and has found ubiquitous applications in semiconductor technologies such as dynamic random access memory (DRAM). In conventional materials, it typically arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. Magnetism, however, can also emerge in perfect lattices from non-magnetic elements. For instance, flat band systems with high density of states (DOS) may develop spontaneous magnetic ordering, as exemplified by the Stoner criterion. Here we report tunable magnetism in rhombohedral-stacked few-layer graphene (r-FLG). At small but finite doping (n~10^11 cm-2), we observe prominent conductance hysteresis and giant magnetoconductance that exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by density and temperature, and disappears for n>10^12 cm-2 or T>5K. These results are confirmed by first principles calculations, which indicate the formation of a half-metallic state in doped r-FLG, in which the magnetization is tunable by electric field. Our combined experimental and theoretical work demonstrate that magnetism and spin polarization, arising from the strong electronic interactions in flat bands, emerge in a system composed entirely of carbon atoms. The electric field tunability of magnetism provides promise for spintronics and low energy device engineering.
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Submitted 11 November, 2019;
originally announced November 2019.
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Exciton-Peierls mechanism and universal many-body gaps in carbon nanotubes
Authors:
Maria Hellgren,
Jacopo Baima,
Anissa Acheche
Abstract:
"Metallic" carbon nanotubes exhibit quasiparticle gaps when isolated from a screening environment. The gap-opening mechanism is expected to be of electronic origin, but the precise nature is debated. In this work, we show that hybrid density functional theory predicts a set of excitonic instabilities capable of opening gaps of the size found in experiment. The excitonic instabilities are coupled t…
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"Metallic" carbon nanotubes exhibit quasiparticle gaps when isolated from a screening environment. The gap-opening mechanism is expected to be of electronic origin, but the precise nature is debated. In this work, we show that hybrid density functional theory predicts a set of excitonic instabilities capable of opening gaps of the size found in experiment. The excitonic instabilities are coupled to vibrational modes and, in particular, the modes associated with the ${\bf Γ}-E_{2g}$ and ${\bf K}-A'_1$ Kohn anomalies of graphene, inducing Peierls lattice distortions with a strong electron-phonon coupling. In the larger tubes, the longitudinal optical phonon mode becomes a purely electronic dimerization that is fully symmetry conserving in the zigzag and chiral tubes, but breaks the symmetry in the armchair tubes. The resulting gaps are universal (i.e., independent of chirality) and scale as 1/R with tube radius.
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Submitted 8 November, 2018; v1 submitted 15 July, 2018;
originally announced July 2018.
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Field-effect-driven half-metallic multilayer graphene
Authors:
Jacopo Baima,
Francesco Mauri,
Matteo Calandra
Abstract:
Rhombohedral stacked multilayer graphene displays the occurrence of a magnetic surface state at low temperatures. Recent angular resolved photoemission experiments demonstrate the robustness of the magnetic state in long sequences of ABC graphene. Here, by using first-principles calculations, we show that field-effect doping of these graphene multilayers induces a perfect half-metallic behaviour w…
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Rhombohedral stacked multilayer graphene displays the occurrence of a magnetic surface state at low temperatures. Recent angular resolved photoemission experiments demonstrate the robustness of the magnetic state in long sequences of ABC graphene. Here, by using first-principles calculations, we show that field-effect doping of these graphene multilayers induces a perfect half-metallic behaviour with 100% of spin current polarization already at dopings attainable in conventional field effect transistors with solid state dielectrics. Our work demonstrates the realisability of a new kind of spintronic devices where the transition between the low resistance and the high resistance state is driven only by electric fields.
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Submitted 25 February, 2018;
originally announced February 2018.
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Exchange Enhancement of the Electron-Phonon Interaction: the Case of Weakly Doped Two-Dimensional Multivalley Semiconductors
Authors:
Betul Pamuk,
Paolo Zoccante,
Jacopo Baima,
Francesco Mauri,
Matteo Calandra
Abstract:
The effect of the exchange interaction on the vibrational properties and on the electron-phonon coupling were investigated in several recent works. In most of the case, exchange tends to enhance the electron-phonon interaction, although the motivations for such behaviour are not completely understood. Here we consider the class of weakly doped two-dimensional multivalley semiconductors and we demo…
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The effect of the exchange interaction on the vibrational properties and on the electron-phonon coupling were investigated in several recent works. In most of the case, exchange tends to enhance the electron-phonon interaction, although the motivations for such behaviour are not completely understood. Here we consider the class of weakly doped two-dimensional multivalley semiconductors and we demonstrate that a more global picture emerges. In particular we show that in these systems, at low enough doping, even a moderate electron-electron interaction enhances the response to any perturbation inducing a valley polarization. If the valley polarization is due to the electron-phonon coupling, the electron-electron interaction results in an enhancement of the superconducting critical temperature. We demonstrate the applicability of the theory by performing random phase approximation and first principles calculations in transition metal chloronitrides. We find that exchange is responsible for the enhancement of the superconducting critical temperature in Li$_x$ZrNCl and that much larger T$_c$s could be obtained in intercalated HfNCl if the synthesis of cleaner samples could remove the Anderson insulating state competing with superconductivity.
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Submitted 1 December, 2017;
originally announced December 2017.
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Flat Electronic Bands in Long Sequences of Rhombohedral-stacked Multilayer Graphene
Authors:
Hugo Henck,
Jose Avila,
Zeineb Ben Aziza,
Debora Pierucci,
Jacopo Baima,
Betül Pamuk,
Julien Chaste,
Daniel Utt,
Miroslav Bartos,
Karol Nogajewski,
Benjamin A. Piot,
Milan Orlita,
Marek Potemski,
Matteo Calandra,
Maria C. Asensio,
Francesco Mauri,
Clément Faugeras,
Abdelkarim Ouerghi
Abstract:
The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic properties. It has been predicted that a rhombohedral (ABC) stacking displays a conducting surface state with flat electronic dispersion. In such a flat band, the role of electron-electron correlation is enhanced possibly resulting in high Tc superconductivity, charge density wave or ma…
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The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic properties. It has been predicted that a rhombohedral (ABC) stacking displays a conducting surface state with flat electronic dispersion. In such a flat band, the role of electron-electron correlation is enhanced possibly resulting in high Tc superconductivity, charge density wave or magnetic orders. Clean experimental band structure measurements of ABC stacked specimens are missing because the samples are usually too small in size. Here, we directly image the band structure of large multilayer graphene flake containing approximately 14 consecutive ABC layers. Angle-resolved photoemission spectroscopy experiments reveal the flat electronic bands near the K point extends by 0.13 Å-1 at the Fermi level at liquid nitrogen temperature. First-principle calculations identify the electronic ground state as an antiferromagnetic state with a band gap of about 40 meV.
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Submitted 25 June, 2018; v1 submitted 10 August, 2017;
originally announced August 2017.
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Critical role of the exchange interaction for the electronic structure and charge-density-wave formation in TiSe2
Authors:
Maria Hellgren,
Jacopo Baima,
Raffaello Bianco,
Matteo Calandra,
Francesco Mauri,
Ludger Wirtz
Abstract:
We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe2. In contrast to local approximations in density functional theory, the explicit inclusion of exact, non-local exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and st…
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We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe2. In contrast to local approximations in density functional theory, the explicit inclusion of exact, non-local exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-density-wave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments.
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Submitted 18 October, 2017; v1 submitted 19 April, 2017;
originally announced April 2017.
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Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles
Authors:
Betül Pamuk,
Jacopo Baima,
Francesco Mauri,
Matteo Calandra
Abstract:
We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedral-stacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin-polarization, an extremely flat surface band centered at the special point ${\bf K}$ of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surfac…
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We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedral-stacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin-polarization, an extremely flat surface band centered at the special point ${\bf K}$ of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surface state by stabilizing an antiferromagnetic state. The top and the bottom surface layers are weakly ferrimagnetic in-plane (net magnetization smaller than $10^{-3}μ_B$), and are antiferromagnetic coupled to each other. This coupling is propagated by the out-of-plane antiferromagnetic coupling between the nearest neighbors. The gap is very small in a spin-polarized generalized gradient approximation, while it is proportional to the amount of exact exchange in hybrid functionals. For trilayer rhombohedral graphene it is $38.6$ meV in PBE0, in agreement with the $42$ meV gap found in experiments. We study the temperature and doping dependence of the magnetic gap. At electron doping of $n \sim 7 \times 10^{11}$ cm$^{-2}$ the gap closes. Charge density wave instabilities with $\sqrt{3}\times\sqrt{3}$ periodicity do not occur.
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Submitted 3 March, 2017; v1 submitted 11 October, 2016;
originally announced October 2016.
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Raman spectroscopic features of the neutral vacancy in diamond from ab initio quantum-mechanical calculations
Authors:
J. Baima,
A. Zelferino,
P. Olivero,
A. Erba,
R. Dovesi
Abstract:
Quantum-mechanical ab initio calculations are performed to elucidate the vibrational spectroscopic features of a common irradiation-induced defect in diamond, i.e. the neutral vacancy. Raman spectra are computed analytically through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach as a function of both different defect spin states and defect concentration. The experimental Raman features of def…
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Quantum-mechanical ab initio calculations are performed to elucidate the vibrational spectroscopic features of a common irradiation-induced defect in diamond, i.e. the neutral vacancy. Raman spectra are computed analytically through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach as a function of both different defect spin states and defect concentration. The experimental Raman features of defective diamond located in the 400-1300 cm-1 spectral range, i.e. below the first-order line of pristine diamond at 1332 cm-1 , are well reproduced, thus corroborating the picture according to which, at low damage densities, this spectral region is mostly affected by non-graphitic sp3 defects. No peaks above 1332 cm-1 are found, thus ruling out previous tentative assignments of different spectral features (at 1450 and 1490 cm-1) to the neutral vacancy. The perturbation introduced by the vacancy to the thermal nuclear motion of carbon atoms in the defective lattice is discussed in terms of atomic anisotropic displacement parameters (ADPs), computed from converged lattice dynamics calculations.
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Submitted 26 August, 2016;
originally announced August 2016.
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Softening the ultra-stiff: controlled variation of Young's modulus in single crystal diamond
Authors:
A. Battiato,
M. Lorusso,
E. Bernardi,
F. Picollo,
F. Bosia,
D. Ugues,
A. Zelferino,
A. Damin,
J. Baima,
N. M. Pugno,
E. P. Ambrosio,
P. Olivero
Abstract:
A combined experimental and numerical study on the variation of the elastic properties of defective single-crystal diamond is presented for the first time, by comparing nano-indentation measurements on MeV-ion-implanted samples with multi-scale modeling consisting of both ab initio atomistic calculations and meso-scale Finite Element Method (FEM) simulations. It is found that by locally introducin…
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A combined experimental and numerical study on the variation of the elastic properties of defective single-crystal diamond is presented for the first time, by comparing nano-indentation measurements on MeV-ion-implanted samples with multi-scale modeling consisting of both ab initio atomistic calculations and meso-scale Finite Element Method (FEM) simulations. It is found that by locally introducing defects in the 2x10^18 - 5x10^21 cm-3 density range, a significant reduction of, as well as of density, can be induced in the diamond crystal structure without incurring in the graphitization of the material. Ab initio atomistic simulations confirm the experimental findings with a good degree of confidence. FEM simulations are further employed to verify the consistency of measured deformations with a stiffness reduction, and to derive strain and stress levels in the implanted region. Combining these experimental and numerical results, we also provide insight into the mechanism responsible for the depth dependence of the graphitization threshold in diamond. This work prospects the possibility of achieving accurate tunability of the mechanical properties of single-crystal diamond through defect engineering, with significant technological applications, i.e. the fabrication and control of the resonant frequency of diamond-based micromechanical resonators.
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Submitted 25 August, 2016;
originally announced August 2016.
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Spin susceptibility and electron-phonon coupling of two-dimensional materials by range-separated hybrid density functionals: Case study of Li$_x$ZrNCl
Authors:
Betül Pamuk,
Jacopo Baima,
Roberto Dovesi,
Matteo Calandra,
Francesco Mauri
Abstract:
We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, $χ_s$, and the intervalley electron-phonon coupling in Li$_x$ZrNCl. At low doping, Li$_x$ZrNCl behaves as a two-dimensional two-valley electron gas, with parabolic bands. In such a system, $χ_s$ increases with decreasing doping because of the electron-electron interaction. We show th…
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We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, $χ_s$, and the intervalley electron-phonon coupling in Li$_x$ZrNCl. At low doping, Li$_x$ZrNCl behaves as a two-dimensional two-valley electron gas, with parabolic bands. In such a system, $χ_s$ increases with decreasing doping because of the electron-electron interaction. We show that DFT with local functionals (LDA/GGA) is not capable of reproducing this behavior. The use of exact exchange in Hartree-Fock (HF) or in DFT hybrid functionals enhances $χ_s$. HF, B3LYP, and PBE0 approaches overestimate $χ_s$, whereas the range-separated HSE06 functional leads to results similar to those obtained in the random phase approximation (RPA) applied to a two-valley two-spin electron gas. Within HF, Li$_x$ZrNCl is even unstable towards a ferromagnetic state for $x<0.16$. The intervalley phonons induce an imbalance in the valley occupation that can be viewed as the effect of a pseudomagnetic field. Thus, similarly to what happens for $χ_s$, the electron-phonon coupling of intervalley phonons is enhanced by the electron-electron interaction. Only hybrid DFT functionals capture such an enhancement and the HSE06 functional reproduces the RPA results presented in M. Calandra {\it et al.} [Phys. Rev. Lett. {\bf 114}, 077001 (2015)]. These results imply that the description of the susceptibility and electron-phonon coupling with a range-separated hybrid functional would be important also in other two-dimensional weakly doped semiconductors, such as transition-metal dichalcogenides and graphene.
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Submitted 7 July, 2016; v1 submitted 16 February, 2016;
originally announced February 2016.