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Unconventional superconductivity from crystal field fluctuations
Authors:
M. A. Zeb
Abstract:
We present a novel pairing mechanism for superconductivity in strongly correlated electron systems, which often have both localised and itinerant charge carriers. An effective anisotropic interaction between the itinerant particles originates from the fluctuations in the crystal field associated with virtual hopping of the localised particles, a process that is also responsible for the Kondo excha…
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We present a novel pairing mechanism for superconductivity in strongly correlated electron systems, which often have both localised and itinerant charge carriers. An effective anisotropic interaction between the itinerant particles originates from the fluctuations in the crystal field associated with virtual hopping of the localised particles, a process that is also responsible for the Kondo exchange. Interestingly, this interaction is \emph{attractive} for charge transfer insulators such as cuprates. Considering a simple toy model for cuprates, without the antiferromagnetic exchange, this interaction leads to the correct d-wave superconducting gap, thus demonstrating its relevance.
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Submitted 1 December, 2025;
originally announced December 2025.
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Analytical solution of the disordered Tavis-Cummings model and its Fano resonances
Authors:
M. Ahsan Zeb
Abstract:
$\mathcal{N}$ emitters collectively coupled to a quantised cavity mode are described by the Tavis-Cummings model. We present complete analytical solution of the model in the presence of inhomogeneous couplings and energetic disorder. We derive the exact expressions for the bright and the dark sectors that decouple the disordered model and find that, in the thermodynamic limit, the energetic disord…
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$\mathcal{N}$ emitters collectively coupled to a quantised cavity mode are described by the Tavis-Cummings model. We present complete analytical solution of the model in the presence of inhomogeneous couplings and energetic disorder. We derive the exact expressions for the bright and the dark sectors that decouple the disordered model and find that, in the thermodynamic limit, the energetic disorder transforms the bright sector to Fano's model that can be easily solved. We thoroughly explore the effects of energetic disorder assuming a Gaussian distribution of emitter transition energies. We compare the Fano resonances in optical absorption and inelastic electron scattering both in the weak and the strong coupling regimes. We study the evolution of the optical absorption with an increase in the disorder strength and find that it changes the lower and upper polaritons to their broadened resonances that finally transform to a single resonance at the bare cavity photon energy, thus taking the system from the strong to the weak coupling regime. Interestingly, we learn that the Rabi splitting can exist even in the weak coupling regime while the polaritonic peaks in the strong coupling regime can represent almost excitonic states at intermediate disorder strengths. We also calculate the photon Green's function to see the effect of cavity leakage and non-radiative emitter losses and find that the polariton linewidth exhibits a minimum as a function of detuning when the cavity leakage is comparable to the Fano broadening.
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Submitted 25 August, 2022;
originally announced August 2022.
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Spin-orbit coupling in organic microcavities: Lower polariton splitting, triplet polaritons, and disorder-induced dark-states relaxation
Authors:
M. Ahsan Zeb,
Shoaib Masood
Abstract:
Using an extended Tavis-Cummings model, we study the effect of the spin-orbit coupling between the singlet and the triplet molecular excitons in organic microcavities in the strong coupling regime. The model is solved in the single excitation space for polaritons, which contains the bright (permutation symmetric) singlet and triplet excitons, as well as the dark bands consisting of the nonsymmetri…
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Using an extended Tavis-Cummings model, we study the effect of the spin-orbit coupling between the singlet and the triplet molecular excitons in organic microcavities in the strong coupling regime. The model is solved in the single excitation space for polaritons, which contains the bright (permutation symmetric) singlet and triplet excitons, as well as the dark bands consisting of the nonsymmetric excitons of either type. We find that the spin-orbit coupling splits the lower polariton into two branches, and also creates a triplet polariton when the cavity mode is in resonance with the triplet excitons. The optical absorption spectrum of the system that can reveal this splitting in experiments is presented and the effect of disorder in exciton energies and couplings is explored. An important consequence of the disorder in the spin-orbit coupling -- a weak coupling between the otherwise decoupled bright and dark sectors -- is explored and detailed calculations of the squared transition matrix elements between the dark bands and polaritons are presented along with derivation of some approximate yet quite accurate analytical expressions. This relaxation channel for the dark states contains an interference between two transition paths that, for a given polariton state, suppresses the relaxation of one dark band and enhances it for the other.
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Submitted 7 October, 2022; v1 submitted 14 April, 2021;
originally announced April 2021.
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Efficient linear scaling mapping for permutation symmetric Fock spaces
Authors:
M. Ahsan Zeb
Abstract:
Numerically solving a second quantised many-body model in the permutation symmetric Fock space can be challenging for two reasons: (i) an increased complication in the calculations of the matrix elements of various operators, and (ii) a poor scaling of the cost of these calculations with the Fock space size. We present a method that solves both these problems. We find a mapping that can be used to…
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Numerically solving a second quantised many-body model in the permutation symmetric Fock space can be challenging for two reasons: (i) an increased complication in the calculations of the matrix elements of various operators, and (ii) a poor scaling of the cost of these calculations with the Fock space size. We present a method that solves both these problems. We find a mapping that can be used to simplify the calculations of the matrix elements. The mapping is directly generated so its computational cost scales only linearly with the space size and is negligible even for large enough sizes that approach the thermodynamic limit. A fortran implementation of the method as a library - FockMap - is provided along with a test program.
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Submitted 21 May, 2021; v1 submitted 29 January, 2021;
originally announced February 2021.
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Incoherent charge transport in an organic polariton condensate
Authors:
M. Ahsan Zeb,
Peter G. Kirton,
Jonathan Keeling
Abstract:
We study how polariton condensation modifies charge transport in organic materials. In typical organic materials, charge transport proceeds via incoherent hopping. We therefore provide an approach to determine how the rate and final state of this hopping process is affected by strong matter-light coupling and polariton condensation. We show how the hopping process may create excitations when start…
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We study how polariton condensation modifies charge transport in organic materials. In typical organic materials, charge transport proceeds via incoherent hopping. We therefore provide an approach to determine how the rate and final state of this hopping process is affected by strong matter-light coupling and polariton condensation. We show how the hopping process may create excitations when starting from a state with a finite excitation density. That is, how hopping can change the state of a lower polariton condensate by creating upper polaritons, optically inactive excitonic dark states, or by exciting vibrational sidebands. While the matrix elements for these processes can be large, for typical materials at room temperature, such excitations are suppressed by thermal factors, and ground state processes dominate. We thus study how the ground state hopping rate depends on condensate density, matter-light coupling, and cavity photon detuning. All these factors change the vibrational configuration associated with the optically active molecules, which can enhance or suppress hopping by increasing or decreasing the vibrational overlap with the state of a charged molecule. We show that hopping rates can be exponentially sensitive to detuning and condensate density, allowing an increase or decrease of hopping rate by two orders of magnitude.
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Submitted 24 July, 2022; v1 submitted 21 April, 2020;
originally announced April 2020.
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Exact states and spectra of vibrationally dressed polaritons
Authors:
M. Ahsan Zeb,
Peter G. Kirton,
Jonathan Keeling
Abstract:
Strong coupling between light and matter is possible with a variety of organic materials. In contrast to the simpler inorganic case, organic materials often have a complicated spectrum, with vibrationally dressed electronic transitions. Strong coupling to light competes with this vibrational dressing, and if strong enough, can suppress the entanglement between electronic and vibrational degrees of…
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Strong coupling between light and matter is possible with a variety of organic materials. In contrast to the simpler inorganic case, organic materials often have a complicated spectrum, with vibrationally dressed electronic transitions. Strong coupling to light competes with this vibrational dressing, and if strong enough, can suppress the entanglement between electronic and vibrational degrees of freedom. By exploiting symmetries, we can perform exact numerical diagonalization to find the polaritonic states for intermediate numbers of molecules, and use these to define and validate accurate expressions for the lower polariton states and strong-coupling spectrum in the thermodynamic limit. Using this approach, we find that vibrational decoupling occurs as a sharp transition above a critical matter-light coupling strength. We also demonstrate how the polariton spectrum evolves with the number of molecules, recovering classical linear optics results only at large $N$.
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Submitted 28 November, 2017; v1 submitted 31 August, 2016;
originally announced August 2016.
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Interplay between spin-orbit coupling and Hubbard interaction in SrIrO3 and related Pbnm perovskites
Authors:
M. Ahsan Zeb,
Hae-Young Kee
Abstract:
There has been a rapidly growing interest on the interplay between spin-orbit coupling (SOC) and Hubbard interaction U in correlated materials. A current consensus is that the stronger the SOC, the smaller is the critical interaction Uc required for a spin-orbit Mott insulator, because the atomic SOC splits a band into different total angular momentum bands narrowing the effective bandwidth. It wa…
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There has been a rapidly growing interest on the interplay between spin-orbit coupling (SOC) and Hubbard interaction U in correlated materials. A current consensus is that the stronger the SOC, the smaller is the critical interaction Uc required for a spin-orbit Mott insulator, because the atomic SOC splits a band into different total angular momentum bands narrowing the effective bandwidth. It was further claimed that at large enough SOC, the stronger the SOC, the weaker the Uc because in general the effective SOC is enhanced with increasing electron-electron interaction strength. Contrary to this expectation, we find that, in orthorhombic perovskite oxides (Pbnm), the stronger the SOC, the bigger the Uc. This is originated from a line of Dirac node in Jeff=1/2 bands near the Fermi level inherited from a combination of the lattice structure and a large SOC. Due to this protected line of nodes, there are small hole and electron pockets in SrIrO3, and such a small density of states makes Hubbard interaction less efficient in building a magnetic insulator. The full phase diagram in U vs. SOC is obtained, where non-magnetic semimetal, magnetic metal, and magnetic insulator are found. Magnetic ordering patterns beyond Uc are also presented. We further discuss implications of our finding in relation to other perovskites such as SrRhO3 and SrRuO3.
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Submitted 23 August, 2012; v1 submitted 25 June, 2012;
originally announced June 2012.
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Electronic stopping power in gold: The role of d electrons and the H/He anomaly
Authors:
M. Ahsan Zeb,
J. Kohanoff,
D. Sanchez-Portal,
A. Arnau,
J. I. Juaristi,
Emilio Artacho
Abstract:
The electronic stopping power of H and He moving through gold is obtained to high accuracy using time-evolving density-functional theory, thereby bringing usual first-principles accuracies into this kind of strongly coupled, continuum non-adiabatic processes in condensed matter. The two key unexplained features of what observed experimentally have been reproduced and understood: (i) The non-linear…
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The electronic stopping power of H and He moving through gold is obtained to high accuracy using time-evolving density-functional theory, thereby bringing usual first-principles accuracies into this kind of strongly coupled, continuum non-adiabatic processes in condensed matter. The two key unexplained features of what observed experimentally have been reproduced and understood: (i) The non-linear behaviour of stopping power versus velocity is a gradual crossover as excitations tail into the d-electron spectrum; and (ii) the low-velocity H/He anomaly (the relative stopping powers are contrary to established theory) is explained by the substantial involvement of the d electrons in the screening of the projectile even at the lowest velocities where the energy loss is generated by s-like electron-hole pair formation only.
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Submitted 8 May, 2012;
originally announced May 2012.
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Semimetal and Topological Insulator in Perovskite Iridates
Authors:
Jean-Michel Carter,
V. Vijay Shankar,
M. Ahsan Zeb,
Hae-Young Kee
Abstract:
The two-dimensional layered perovskite Sr2IrO4 was proposed to be a spin-orbit Mott insulator, where the effect of Hubbard interaction is amplified on a narrow J_{eff} = 1/2 band due to strong spin-orbit coupling. On the other hand, the three-dimensional orthorhombic perovskite (Pbnm) SrIrO3 remains metallic. To understand the physical origin of the metallic state and possible transitions to insul…
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The two-dimensional layered perovskite Sr2IrO4 was proposed to be a spin-orbit Mott insulator, where the effect of Hubbard interaction is amplified on a narrow J_{eff} = 1/2 band due to strong spin-orbit coupling. On the other hand, the three-dimensional orthorhombic perovskite (Pbnm) SrIrO3 remains metallic. To understand the physical origin of the metallic state and possible transitions to insulating phases, we construct a tight-binding model for SrIrO3. The band structure possesses a line node made of J_{eff} = 1/2 bands below the Fermi level. As a consequence, instability towards magnetic ordering is suppressed and the system remains metallic. This line node, originating from the underlying crystal structure, turns into a pair of three-dimensional nodal points on the introduction of a staggered potential or spin-orbit coupling strength between alternating layers. Increasing this potential beyond a critical strength induces a transition to a strong topological insulator, followed by another transition to a normal band insulator. We propose that materials constructed with alternating Ir- and Rh-oxide layers along the (001) direction, such as Sr2IrRhO6, are candidates for a strong topological insulator.
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Submitted 7 March, 2012; v1 submitted 30 November, 2011;
originally announced December 2011.
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Interface states in bilayer graphene and valleytronics
Authors:
M. Ahsan Zeb
Abstract:
We study the states localized near an interface between conducting and insulating bilayer graphene (BLG) and show that they have highly unusual properties that have no analog in conventional systems. Moreover, the states belonging to the two independent valleys in the Brillouin zone of BLG show contrasting properties that allows a relatively easier experimental realization of various valley based…
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We study the states localized near an interface between conducting and insulating bilayer graphene (BLG) and show that they have highly unusual properties that have no analog in conventional systems. Moreover, the states belonging to the two independent valleys in the Brillouin zone of BLG show contrasting properties that allows a relatively easier experimental realization of various valley based functionalities desired in valleytronics without requiring any sophisticated techniques.
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Submitted 19 April, 2011;
originally announced April 2011.
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Comment on "Chiral tunnelling and the Klein paradox in graphene"
Authors:
M. Ahsan Zeb
Abstract:
Arising from the Article: Nature Phys. 2, 620-625 (2006), By M. I. Katsnelson, K. S. Novoselov, and A. K. Geim.
Arising from the Article: Nature Phys. 2, 620-625 (2006), By M. I. Katsnelson, K. S. Novoselov, and A. K. Geim.
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Submitted 12 October, 2010;
originally announced October 2010.
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Comment on "Photon-assisted electron transport in graphene: Scattering theory analysis"
Authors:
M. Ahsan Zeb
Abstract:
It is argued that Trauzettel et al. [Phys. Rev. B 75, 035305 (2007)] made some mistakes in their calculations regarding the photon-assisted transport in graphene that lead to uncoupled sidebands and emergence of step-like features in dG/dV (G is differential conductance and V is the bias voltage). We discuss the relevant corrections and explain in detail how the correct results are expected to be…
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It is argued that Trauzettel et al. [Phys. Rev. B 75, 035305 (2007)] made some mistakes in their calculations regarding the photon-assisted transport in graphene that lead to uncoupled sidebands and emergence of step-like features in dG/dV (G is differential conductance and V is the bias voltage). We discuss the relevant corrections and explain in detail how the correct results are expected to be quite different than the incorrect ones.
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Submitted 24 October, 2010; v1 submitted 11 October, 2010;
originally announced October 2010.
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Chiral tunneling through time-periodic potential in graphene
Authors:
M. Ahsan Zeb,
K. Sabeeh,
M. Tahir
Abstract:
Chiral tunneling through a harmonically driven potential barrier in graphene monolayer is considered in this work. Since the quasiparticles in this system are chiral in nature, tunneling is highly anisotropic, we determine the transmission probabilities for the central and sidebands as the incident angle of the electron beam is changed . Furthermore, we investigate how the transmission probabili…
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Chiral tunneling through a harmonically driven potential barrier in graphene monolayer is considered in this work. Since the quasiparticles in this system are chiral in nature, tunneling is highly anisotropic, we determine the transmission probabilities for the central and sidebands as the incident angle of the electron beam is changed . Furthermore, we investigate how the transmission probabilities change as the width, amplitude and frequency of the oscillating barrier is changed. An interesting result of our study is that perfect transmission for normal incidence that has been reported for a static barrier persists for the oscillating barrier, manifestation of Klein tunneling in a time harmonic potential.
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Submitted 23 August, 2008; v1 submitted 13 April, 2008;
originally announced April 2008.