Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

Two-band model works well for Hall effect in topological insulators. It turns out to be non-Hermitian when the system is subjected to environments, and its topology characterized by Chern numbers has received extensive studies in the past decades. However, how a non-Hermitian system responses to an electric field and what is the connection of the response to the Chern number defined via the non-Hermitian Hamiltonian remains barely explored. In this paper, focusing on a k-dependent decay rate, we address this issue by studying the response of such a non-Hermitian Chern insulator to an external electric field. To this aim, we first derive an effective non-Hermitian Hamiltonian to describe the system and give a specific form of k-dependent decay rate. Then we calculate the response of the non-Hermitian system to a constant electric field.We observe that the environment leads the Hall conductance to be a weighted integration of curvature of the ground band and hence the conductance is no longer quantized in general. And the environment induces a delay in the response of the system to the electric field. A discussion on the validity of the non-Hermitian model compared with the master equation description is also presented.

On the half-quantized Hall conductance of massive surface electrons in magnetic topological insulator films

In topological insulators,massive surface states resulting from local symmetry breaking were thought to exhibit a half-quantized Hall conductance,obtained from the low-energy effective model in an infinite Brillouin zone.In a lattice model,the surface band is composed of a combination of surface states and bulk states.The massive surface states alone may not be enough to support an exact one-half quantized surface Hall conductance in a finite Brillouin zone and the whole surface band always gives an integer quantized Hall conductance as enforced by the TKNN theorem.To explore this,we investigate the band structures of a lattice model describing the magnetic topological insulator film that supports the axion insulator,Chern insulator,and semi-magnetic topological insulator phases.We reveal that the gapped and gapless surface bands in the three phases are characterized by an integer-quantized Hall conductance and a half-quantized Hall conductance,respectively.We propose an effective model to describe the three phases and show that the low-energy dispersion of the surface bands inherits from the surface Dirac fermions.The gapped surface band manifests a nearly half-quantized Hall conductance at low energy near the center of Brillouin zone,but is compensated by another nearly half-quantized Hall conductance at high energy near the boundary of Brillouin zone because a single band can only have an integer-quantized Hall conductance.The gapless band hosts a zero Hall conductance at low energy but is compensated by another half-quantized Hall conductance at high energy,and thus the half-quantized Hall conductance can only originate from the gapless band.Moreover,we calculate the layer-resolved Hall conductance of the system.The conclusion suggests that the individual gapped surface band alone does not support the half-quantized surface Hall effect in a lattice model.

Applications of Quantum Physics on Resistivity, Dielectricity, Giant Magneto Resistance, Hall Effect and Conductance

Quantum theory with conjecture of fractional charge quantization, eigenfunctions for fractional charge quantization, fractional Fourier transform, Hermite function for fractional charge quantization, and eigenfunction for a twisted and twigged electron quanta is developed and applied to resistivity, dielectricity, giant magneto resistance, Hall effect and conductance. Our theoretical relationship for quantum measurements is in good conformity and in agreement with most of the experimental results. These relationships will pave a new approach to quantum physics for deciphering measurements on single quantum particles without destroying them. Our results are in agreement with 2012 Physics Nobel Prize winning Scientists, Serge Haroche and David J. Wineland.

Spin-Orbit Scattering Effects on Hall Conductivity in a Layered Disordered Electron System

Spin-orbit scattering effects in a layered quasi-2D disordered electron system have been investigated by the diagrammatic techniques in perturbation theory. The expression of Cooperon (propagator in particle-particle channel) is obtained as the function of interlayer coupling. The analytical result for the quantum correction to Hall conductivity has been obtained as functions of elastic, inelastic and spin-orbit scattering times. It is shown that the strong and weak couplings correspond, respectively, to the 3D and 2D situations. The Hall coefficient is shown to vanish. The relevant dimensional crossover behavior from 3D to 2D with decreasing the interlayer coupling has been discussed, and the condition for the crossover has been obtained. The present theory is expected to apply for the electronic transport in tunneling superlattices.

Integer quantum Hall effect in Kekulé-patterned graphene

Y-shaped Kekulébond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed.In this paper,the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field.Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula.It is found that the Y-shaped Kekulébond texture lifts the valley degeneracy of all Landau levels except that of the zero mode,leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity.Consequently,the Hall conductivity is quantized as±ne^(2)/h for n=2,4,6,8,10,...,excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones.These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulébond texture amplitude.

Hall Conductivity in the Cosmic Defect and Dislocation Spacetime

Influences of topological defect and dislocation on conductivity behavior of charge carriers in external electromagnetic fields are studied. Particularly the quantum Hall effect is investigated in detail. It is found that the nontrivial deformations of spacetime due to topological defect and dislocation produce an electric current at the leading order of perturbation theory. This current then induces a deformation on the Hall conductivity. The corrections on the Hall conductivity depend on the external electric fields, the size of the sample and the momentum of the particle.

Hall Conductivity in a Quasi—Two—Dimensional disordered Electron System

By making use of the diagrammatic techniques in perturbation theory,we have investigated the Hall effect in a quasi-two-dimensional disordered electron system.In the weakly localized regime,the analytical expression for quantum correction to Hall conductivity has been obtained using the Kubo formalism and quasiclassical approximation.The relevant dimensional crossover behavior from three dimensions to two dimensions with decreasing the interlayer hopping energy is discussed.The quantum interference effect is shown to have a vanishing correction t,o the Hall coefficient.

Anomalous Hall Effect in Spin-Polarized Two-Dimensional Hole Gas with Cubic-Rashbsa Spin-Orbit Interaction

Based on the Kubo formalism, the anomalous Hall effect in a magnetic two-dimensional hole gas with cubic-Rashba spin-orbit coupling is studied in the presence of δ-function scattering potential. When the weak, shortranged disorder scattering is considered in the Born approximation, we find that the self-energy becomes diagonal in the helicity basis and its value is independent of the wave number, and the vertex correction to the anomalous Hall conductivity due to impurity scattering vanishes when both subbands are occupied. That is to say, the anomalous Hall effect is not vanishing or influenced by the vertex correction for two-dimensional heavy-hole system, which is in sharp contrast to the case of linear-Rashba spin-orbit coupling in the electron band when the short-range disorder scattering is considered and the extrinsic mechanism as well as the effect of external electric field on the SO interaction are ignored.

Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries,we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light,in a three-dimensional topological insulator,when the intensity of the incident light exceeds a critical value.The circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass,which are highly controllable.The phase transition can be exactly characterized by the first Chern number.A tunable anomalous Hall conductivity emerges,which is fully determined by the location of the Weyl nodes in momentum space,even in the doping regime.Our predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.

Adsorptions of metal adatoms on graphene-like BC3 and their rich electronic properties： A first-principles study

Density functional calculations have been performed to investigate the adsorption of twenty two different kinds of metal adatoms on graphene-like BC3. In contrast to the graphene adsorbed with adatoms, the BC3 with adatoms shows many interesting properties.（1） The interaction between the metal adatoms and the BC3 sheet is remarkably strong. The Li, Na, K, and Ca possess the binding energies larger than the cohesive energies of their corresponding bulk metals.（2）The Li, Na, and K adatoms form approximately ideal ionic bonds with BC3, while the Be, Mg, and Ca adatoms form ionic bonds with BC3 with slight hybridization of covalent bonds. The Al, Ga, In, Sn, and all transition metal adatoms form covalent bonds with BC3.（3） For all the structures studied, there exhibit metal, half-metal, semiconducting, and spin-semiconducting behaviors. Especially, the BC3 with Co adatom shows a quantum anomalous Hall（QAH） phase with a Chern number of -1 based on local density approximation calculations.（4） For Li, Na, K, Ca, Ga, In, Sn, Ti, V, Cr,Ni, Pd, and Pt, there exists a trend that the adatom species with lower ionization potential have lower work function. Our results indicate the potential applications of functionalization of BC3 with metal adatoms.

Thermal Hall conductivity with sign change in the Heisenberg–Kitaev kagome magnet

The Heisenberg-Kitaev(HK)model on various lattices has attracted a lot of attention because it may lead to exotic states such as quantum spin liquid and topological orders.The rare-earth-based kagome lattice(KL)compounds Mg_(2)RE_(3)Sb_(3)O_(14)(RE=Gd,Er)and(RE=Nd)have q=0,120°order and canted ferromagnetic(CFM)order,respectively.Interestingly,the HK model on the KL has the same ground state long-range orders.In the theoretical phase diagram,the CFM phase resides in a continuous parameter region and there is no phase change across special parameter points,such as the Kitaev ferromagnetic(KFM)point,the ferromagnetic(FM)point and its dual FM point.However,a ground state property cannot distinguish a system with or without topological nontrivial excitations and related phase transitions.Here,we study the topological magnon excitations and related thermal Hall conductivity in the HK model on the KL with CFM order.The CFM phase can be divided into two regions related by the Klein duality,with the self dual KFM point as their boundary.We find that the scalar spin chirality,which is intrinsic in the CFM order,changes sign across the KFM point.This leads to the opposite Chem numbers of corresponding magnon bands in the two regions,and also the sign change of the magnon thermal Hall conductivity.