Kubo Conductivity Research Articles

Remarkable thermopower property enhancement in two-dimensional SiC via B and N doping and magnetic field

DFT-based tight binding theory calculations and the Kubo conductivity formula were used to investigate the thermopower properties of 2D SiC with different impurity concentrations and magnetic field. The electronic and thermal properties were studied for cases that a carbon replaced with B (BC) and N (NC) atoms. The impurity concentration has been controlled by varying the number of cells from n2 [two unit cells] to n5 [five unit cells]. The electronic structure of the doped SiC has been strongly modified with the impurity type and the created band gap is sensitive to impurity concentration and field strength. In all selected structures, regardless of the impurity type, the subband splitting and the band gap reduction are caused by the magnetic field. Selective doped structures have thermal properties that are dependent on the type and concentration of impurity and the strength of the magnetic field. As a result of the investigations, we are able to conclude (i) structures that contain lower impurity concentrations have larger thermal properties, (ii) doped structures containing BC impurities exhibit higher thermal properties than doped structures containing NC impurities and (iii) magnetic fields have a stronger influence on structures with lower impurity concentrations.

Kubo conductivity in phosphorene

Electrical conductivity in phosphorene is investigated within the linear response theory. We find that phosphorene shows signatures of asymmetry in its transport properties, inherited from the anisotropic band structure of that system. It is shown that the Dirac fermions in phosphorene exhibit enhanced electrical conductivity around the edges of conduction and valence bands, where the conductivity peak corresponding to the conduction band is larger than the one associated with the valence band, hallmark of anisotropic band structure of phosphorene. The separation between the two conductivity peaks is on the order of the band gap. In addition, the electrical conductivity shifts in the negative region of the chemical potential, reflecting anisotropy in the energy spectrum inherited from the lack of chiral symmetry in the Hamiltonian of the system. We also find that the electrical conductivity strongly depends on temperature of the system. Interestingly, the separation between the conductivity peaks can be tuned by an applied electric field which can vary the band gap induced by spin–orbit interaction.

Unexpected nontriviality of inter-band contribution and huge anisotropy of conductivity in tilted Weyl semimetals

For tilted type-I Weyl semimetals, our theoretical study indicates that the Kubo conductivity parallel to cone tilt direction increases rapidly with the Fermi energy. Hence it deviates from its Boltzmann counterpart sizably even though the electronic wavelength is so short that the quantum interference is seemingly trivial. As a result, such a system shows huge anisotropy of the conductivity. By means of the diagrammatic expansion technique, we find that the absence of backscattering and the breakdown of the time reversal symmetry in tilted Weyl semimetals are two crucial factors which bring about the nontrivial inter-band contribution to the Kubo conductivity. Our findings indicate that Boltzmann theory fails to describe reasonably the electronic transport of a tilted Weyl cone, even in the case of weak scattering and short Fermi wavelength. Though in this regime such a semiclassical transport theory is believed to be valid according to conventional arguments. This situation should be paid attention. • Via SCBA, the high order quantum corrections to conductivity are considered and it makes huge enhancement to diagonal conductivity σ z z , which is missed by the Boltzmann transport equation with the lowest order Born approximation. • The huge anisotropy of diagonal conductivity in tilted WSMs origin from the nature of the absence of backscattering and breakdown of TRS. • The interaction range of impurity potential affects the extent of anisotropy.

Graphene plasmonic nano-antenna for terahertz communication

In this manuscript, plasmonic nano patch antenna on the graphene material is designed and analyzed. The conductivity of the graphene material is modeled using Kubo conductivity formula and it is tuned using chemical potential of graphene. Further, analysis of Drude dispersive model for the graphene matrial exhibits negative real permittivity which is the required criterion for the plasmonic resonance. The designed graphene nano patch antenna provides a gain of 3.52 dB at 30 THz frequency which is suitable for terahertz communication. It is demonstrated that the graphene nano patch antenna resonates at multiple frequencies by varying the chemical potential and three resonating frequencies 30, 115, 176 THz with good characteristics are observed at 1.3 eV chemical potential. The gain of the graphene nano patch antenna is enhanced approximately three times by changing the shape of the patch from square to L-shape.

Anisotropic Kubo conductivity of electric field-induced monolayer β12-borophene.

In this paper, we used three monolayer β12-borophene Hamiltonian models to calculate the band structure, intra-band, and inter-band optical conductivity (IOC). Linear response theory and the Kubo formula are employed to calculate optical conductivity. We have shown that the band gap proportional to the inversion non-symmetric model increases by applying an external electric field (EEF), and for homogeneous and inversion-symmetric models, gap opening occurs. We found an anisotropic behavior in the IOC of β12-borophene for polarized light along x and y-directions. The peak of the real part of the IOC for polarized light along the x-direction (ℜσxx) locates at the energy equal to the band gap and by applying an EEF shifts to the higher energies and experiences a blue shift. Also, the electric field has little effect on the IOC along y-direction (σyy) and in contrast to σxx, by applying an electric field, the peak of the IOC shifts towards lower energies and a redshift occurs. In addition, unlike inter-band transitions, the intra-band optical conductivity of β12-borophene is isotropic in all three models, and an EEF can not shift plots to higher or lower energies and only reduces the height of both imaginary and real parts of the optical conductivity.

Systematic competition between strain and electric field stimuli in tuning EELS of phosphorene

The strongly anisotropic properties of phosphorene makes it an attractive material for applications in deciding the specific direction for different purposes. Here we have particularly reported the competition between strain and electric field stimuli in evaluating the band gap and electron energy loss spectrum (EELS) of single-layer black phosphorus using the tight-binding method and the Kubo conductivity. We construct possible configurations for this competition and evaluate the interband optical excitations considering the corresponding band gap variations. The band gap increases with the individual electric field, while it increases (decreases) with tensile (compressive) uniaxial in-plane strain. Contrary to the in-plane strains, the uniaxial out-of-plane strain shows a critical strain at which the system suffers from a phase transition. Furthermore, the presence of these stimuli simultaneously results in an extraordinary band gap engineering. Based on the EELS response in the electromagnetic spectrum, the armchair (zigzag) direction is classified into the infrared and visible (ultraviolet) region. We report that the electric field gives rise to the blue shift in the interband optical transitions along the armchair direction, while the compressive/tensile (tensile/compressive) in-plane/out-of-plane strain provides a red (blue) shift. Moreover, we observe an inverse behavior of EELS response to the individual and combined effects of electric field and strains compared to the band gap behavior except at critical out-of-plane strain for which the physical theory of interband excitation is simply violated. Our results provide a new perspective on the applicability of phosphorene in stimulated optical applications.

Modeling and Computation of Kubo Conductivity for Two-Dimensional Incommensurate Bilayers

This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. First, we derive an expression for ...

GPUQT: An efficient linear-scaling quantum transport code fully implemented on graphics processing units

We present GPUQT, a quantum transport code fully implemented on graphics processing units. Using this code, one can obtain intrinsic electronic transport properties of large systems described by a real-space tight-binding Hamiltonian together with one or more types of disorder. The DC Kubo conductivity is represented as a time integral of the velocity auto-correlation or a time derivative of the mean square displacement. Linear scaling (with respect to the total number of orbitals in the system) computation time and memory usage are achieved by using various numerical techniques, including sparse matrix–vector multiplication, random phase approximation of trace, Chebyshev expansion of quantum evolution operator, and kernel polynomial method for quantum resolution operator. We describe the inputs and outputs of GPUQT and give a few examples to demonstrate its usage, paying attention to the interpretations of the results. Program summaryProgram Title: GPUQTProgram Files doi:http://dx.doi.org/10.17632/xbf5kbkzx7.1Licensing provisions: GPLv3Programming language: CUDANature of problem: Obtain intrinsic electronic transport properties of large systems described by real-space tight-binding Hamiltonians.Solution method: The DC conductivity is represented as a time integral of the velocity auto-correlation (VAC) or a time derivative of the mean square displacement (MSD). The calculations achieve linear scaling (with respect to the number of orbitals in the system) computation time and memory usage by using various numerical techniques, including sparse matrix–vector multiplication, random phase approximation of trace, Chebyshev expansion of quantum evolution operator, and kernel polynomial method for quantum resolution operator.Restrictions: The number of orbitals is restricted to about 20 million due to the limited amount of device memory in current GPUs.

Universality of the Hall Conductivity in Interacting Electron Systems

We prove the quantization of the Hall conductivity for general weakly interacting gapped fermionic systems on two-dimensional periodic lattices. The proof is based on fermionic cluster expansion techniques combined with lattice Ward identities, and on a reconstruction theorem that allows us to compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart.

Non-perturbative analysis of impurity effects on the Kubo conductivity of nano to macroscopic structures

ABSTRACTThe presence of impurities in solids is a source of many interesting effects, particularly relevant in the conductivity, optical properties and specific heat. For instance, in nano-electronics these effects could be useful to develop molecular devices such as novel computer architectures, chemical and biomedical sensors. However, the inclusion of impurities breaks the translational symmetry, restricting the systems that can be addressed theoretically in an exact way to those of few atoms. In this work, we present an alternative way to study the electrical conductance in real-space by means of a renormalization plus convolution method applied on the Kubo-Greenwood formula for multidimensional systems of macroscopic size with site and bond impurities. The results show that the spectral average of conductivity depends strongly on the location of site and bond impurities in periodic chains. Particularly, when the distance between impurities follows the Fibonacci sequence, we find that the spectral average falls following a power law as the number of atoms in the system grows. Finally, we analyze the impurity effects on the conductance spectra of periodic core-shell nanowires with a macroscopic length and periodic and quasiperiodically located impurities.

Real-space calculation of the conductivity tensor for disordered topological matter.

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.

Kubo conductivity tensor for two- and three-dimensional magnetic nulls.

The complete Kubo conductivity tensor is computed in two- and three-dimensional linear magnetic null systems using collisionless single-particle simulations. Regions of chaotic charged-particle dynamics are constructed for each case. It is found that stochastic frequency mixing of particle bounce motion, as well as gyromotion, contribute significantly to the conductivity. The conductivity curves are well approximated by power laws over a certain frequency range and the ac conductivity is found to be an order of magnitude smaller than the dc value, leading to enhanced resistivity, particularly near the cyclotron frequency. The ac conductivities must be accounted for in computation of the total dissipation.

Asymptotic Quantum Many-Body Localization from Thermal Disorder

We consider a quantum lattice system with infinite-dimensional on-site Hilbert space, very similar to the Bose–Hubbard model. We investigate many-body localization in this model, induced by thermal fluctuations rather than disorder in the Hamiltonian. We provide evidence that the Green–Kubo conductivity κ(β), defined as the time-integrated current autocorrelation function, decays faster than any polynomial in the inverse temperature β as \({\beta \to 0}\). More precisely, we define approximations \({\kappa_{\tau}(\beta)}\) to κ(β) by integrating the current-current autocorrelation function up to a large but finite time \({\tau}\) and we rigorously show that \({\beta^{-n}\kappa_{\beta^{-m}}(\beta)}\) vanishes as \({\beta \to 0}\), for any \({n,m \in \mathbb{N}}\) such that m−n is sufficiently large.

Optical conductivity of thet2gtwo-dimensional electron gas

Motivated by recent interest in perovskite surfaces and heterostructures, we present an analysis of the Kubo conductivity of a two-dimensional electron gas (2DEG) formed in the $t_{2g}$ bands of an oxide with perovskite structure. We find that when the electric field is polarized in the plane of the 2DEG, the optical conductivity is dominated by nearly independent Drude contributions from two-dimensional subband Fermi surfaces, whereas for perpendicular-to-plane polarization it has strong intersubband features. Our analysis suggests that perpendicular-to-plane optical conductivity studies may help advance understanding of the interplay between lattice distortions and electron-electron interactions in complex oxide 2DEG quantum confinement physics.

Non-perturbative study of impurity effects on the Kubo conductivity in macroscopic periodic and quasiperiodic lattices

In this paper, we analyze the effects of site and bond impurities on the electrical conductance of periodic and quasiperiodic systems with macroscopic length by means of a real-space renormalization plus a convolution method developed for the Kubo–Greenwood formula. All analyzed systems are connected to semi-infinite periodic leads. Analytical and numerical conductivity spectra are obtained for one and two site impurities in a periodic chain, where the separation between impurities determines the number of maximums in the spectra. We also found transparent states at the zero chemical potential in Fibonacci chains of every three generations with bond impurities, whose existence was confirmed by an analytical analysis within the Landauer formalism. For many impurities, the spectral average of the conductivity versus the system length reveals a power-law behavior, when the distance between impurities follows the Fibonacci sequence. Finally, we present an analysis of the conductance spectra of segmented periodic and Fibonacci chains and nanowires.

Theory of conductivity of chiral particles

In this methodology focused paper we scrutinize the application of the band-coherent Boltzmann equation approach to calculating the conductivity of chiral particles. As the ideal testing ground we use the two-band kinetic Hamiltonian with an N-fold chiral twist that arises in a low-energy description of charge carriers in rhombohedrally stacked multilayer graphene. To understand the role of chirality in the conductivity of such particles we also consider the artificial model with the chiral winding number decoupled from the power of the dispersion. We first utilize the approximate but analytically solvable band-coherent Boltzmann approach including the ill-understood principal value terms that are a byproduct of several quantum many-body theory derivations of Boltzmann collision integrals. Further on, we employ the finite-size Kubo formula with the exact diagonalization of the total Hamiltonian perturbed by disorder. Finally, we compare several choices of Ansatz in the derivation of the Boltzmann equation according to the qualitative agreement between the Boltzmann and Kubo conductivities. We find that the best agreement can be reached in the approach where the principal value terms in the collision integral are absent.

Kubo conductivity of macroscopic systems with Fano defects for periodic and quasiperiodic cases by means of renormalization methods in real space

In this paper, we investigate the effects on the electrical conductivity originated by the inclusion of Fano defects (FDs) for periodic and quasiperiodic systems of macroscopic size. This study is developed using the extension of the methods of renormalization for the Kubo–Greenwood formula in real space within the tight-binding formalism. Within this formalism, the conductivity is determined in an exact form, without any other approximation. For periodic systems, we find the zeros of conductivity located at the eigenenergies of the coupled chain of atoms, and transparent states at the eigenenergies of a chain of atoms. These results are shown in both numerical and analytical way. Moreover, the position of the FD in the system does not alter the conductivity spectrum. On the other hand, for quasiperiodic systems, only some coupled chains preserve the transparent state; this was found both numerically and analytically. The case of two FDs attached to the system is also analyzed, founding a high dependence of the electrical conductivity on the distance between the FDs. Finally, this study is extended to two dimensions.

Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene

We report on robust features of the longitudinal conductivity (σ(xx)) of the graphene zero-energy Landau level in the presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both σ(xx) and Hall σ(xy)). As long as valley degeneracy is maintained, the obtained critical conductivity σ(xx) =/~ 1.4e(2)/h is robust upon an increase in disorder (by almost 1 order of magnitude) and magnetic fields ranging from about 2 to 200 T. When the sublattice symmetry is broken, σ(xx) eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a σ(xy) = 0 plateau) change to σ(xx) =/~ e(2)/h, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the nondissipative nature of the quantum Hall effect in disordered graphene in the presence of Landau level splitting.

Charge Transport in Weyl Semimetals

We study transport in Weyl semimetals with N isotropic Weyl nodes in the presence of Coulomb interactions or disorder at temperature T. In the interacting clean limit, we determine the conductivity σ(ω,T) by solving a quantum Boltzmann equation within a "leading log" approximation and find it to be proportional to T, up to logarithmic factors arising from the flow of couplings. In the noninteracting disordered case, we compute the Kubo conductivity and show that it behaves differently for ω << T and ω >> T: in the former regime we recover a previous result, of a finite dc conductivity and a Drude width vanishing as NT(2); in the latter, we find that σ(ω,T) vanishes linearly with ω with a leading term as T → 0 equal to the clean, free-fermion result: σ(0)((N))(ω,T = 0) = Ne(2)/12h|ω|/v(F). We compare our results to transport data on Y(2)Ir(2)O(7) and comment on the possible relevance to recent experiments on Eu(2)Ir(2)O(7).

The Kubo conductivity tensor for 2- and 3-dimensional magnetic nulls

The Kubo conductivity tensor for 2- and 3-dimensional magnetic nulls