In computing electric conductivity based on the Kubo formula, the vertex corrections describe such effects as anisotropic scattering and quantum interference and are important to quantum transport properties. These vertex corrections are obtained by solving Bethe-Salpeter equations, which can become numerically intractable when a large number of k-points and multiple bands are involved. We introduce a non-iterative approach to the vertex correction based on rank factorization of the impurity vertices, which significantly alleviate the computational burden. We demonstrate that this method can be implemented along with effective Hamiltonians extracted from electronic structure calculations on perfect crystals, thereby enabling quantitative analysis of quantum effects in electron conduction for real materials.
Here we introduce a numerical method for computing conductivity via the Kubo Formula for incommensurate 2D bilayer heterostructures using a tight-binding framework. We begin with deriving the momentum space formulation and Kubo Formula from the real space tight-binding model using the appropriate Bloch transformation operator. We further discuss the resulting algorithm along with its convergence rate and computation cost in terms of parameters such as relaxation time and temperature. In particular, we show that for low frequencies, low temperature, and long relaxation times conductivity can be…
The closely related Green-Kubo and Helfand moment approaches are applied to obtain the thermal conductivity tensor of $β$-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane ($β$-HMX) at $T=300$ K and $P=1$ atm from equilibrium molecular dynamics (MD) simulations. Direct application of the Green-Kubo formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) simulation times. To partially mitigate this slow convergence we developed a numerical procedure that involves filtering of the MD-calculated heat current. The filtering is accomplished by physically justifi…
We herein present a first-principles formulation of the Green-Kubo method that allows the accurate assessment of the non-radiative thermal conductivity of solid semiconductors and insulators in equilibrium ab initio molecular dynamics calculations. Using the virial for the nuclei, we propose a unique ab initio definition of the heat flux. Accurate size- and time convergence are achieved within moderate computational effort by a robust, asymptotically exact extrapolation scheme. We demonstrate the capabilities of the technique by investigating the thermal conductivity of extreme high and low he…
In this letter we derive a new method for direct calculation of the modal contributions to thermal conductivity, which is termed Green-Kubo modal analysis (GKMA). The GKMA method combines the lattice dynamics formalism with the Green-Kubo formula for thermal conductivity, such that the thermal conductivity becomes a direct summation of modal contributions, where one need not define the phonon velocity. As a result the GKMA method can be applied to any material/group of atoms where the atoms vibrate around stable equilibrium positions, which includes not only crystalline line compounds, but als…
Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"
Universität Leipzig（莱比锡大学）；Joint Institute for Nuclear Research（联合核研究所）；Universidade Federal do ABC（ABC联邦大学）；Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences（俄罗斯科学院普尔科沃中央天文台）；Peter the Great Saint Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. Firstly, we derive an expression for the large-body limit of Kubo-Greenwood conductivity in terms of an integral of the conductivity function with respect to a current-current correlation measure. We then observe that the incommensurate structure can be exploited to decompose the current-current correlation measure into local contribution and deduce an approximation scheme which is exponentially convergent in terms of domain size. Sec…
Given the unique optical properties of LiF, it is often used as an observation window in high-temperature and pressure experiments; and, hence, estimates of its transmission properties are necessary to interpret observations. Since direct measurements of the thermal conductivity of LiF at the appropriate conditions are difficult, we resort to molecular simulation methods. Using the Belonoshko et al. (2000) empirical potential validated against ab initio phonon density of states, we estimate the thermal conductivity of LiF at high temperatures (1000-4000K) and pressures (100-400 GPa) with the G…
Different molecular dynamics methods like the direct method, the Green-Kubo (GK) method and homogeneous non-equilibrium molecular dynamics (HNEMD) method have been widely used to calculate lattice thermal conductivity ($κ_\ell$). While the first two methods have been used and compared quite extensively, there is a lack of comparison of these methods with the HNEMD method. Focusing on the underlying computational parameters, we present a detailed comparison of the GK and HNEMD methods for both bulk and vacancy Si using the Stillinger-Weber potential. For the bulk calculations, we find both meth…
Reply to "Comment on "Electric conductivity in graphene: Kubo model versus a nonlocal quantum field theory model"" (ArXiv:2506.10792v2)
Universidad Rey Juan Carlos（雷伊胡安卡洛斯大学）；CNRS-University of Montpellier（法国国家科学研究中心-蒙彼利埃大学）；National University of Singapore（新加坡国立大学）；Institut Universitaire de France, Ministère de l’Enseignement Supérieur et de la Recherche（法国高等教育与研究部下属法兰西学院）
In equilibrium molecular dynamics, Einstein relation can be used to calculate the thermal conductivity. This method is equivalent to Green-Kubo relation and it does not require a derivation of an analytical form for the heat current. However, it is not commonly used as Green-Kubo relationship. Its wide use is hindered by the lack of a proper definition for integrated heat current (energy moment) under periodic boundary conditions. In this paper, we developed an appropriate definition for integrated heat current to calculate thermal conductivity of solids under periodic conditions. We applied t…
The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense mater. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT (sDFT) framework, which requires knowledge only of the KS Hamiltonian but not…
We derive a formula for the electrical conductivity of solids that includes relaxation, dissipation, and quantum coherence. The derivation is based on the Kubo formula, with a Mori memory function approach to include dissipation effects at all orders in the relaxation interaction. It offers a practical method to evaluate the conductivity with electronic-structure codes and avoids the complications and limitations of the Kubo formula in the thermodynamic limit. The derivation of our formula provides a method applicable to other transport coefficients and correlation functions.
We propose a non-perturbative $ab$ $initio$ approach to calculate the electrical conductivity of a liquid metal. Our approach is based on the Kubo formula and the theory of electron-phonon coupling (EPC), and unlike the conventional empirical approach based on the Kubo-Greenwood formula, fully takes into account the effect of coupling between electrons and moving ions. We show that the electrical conductivity at high temperature is determined by an EPC parameter $λ_{\mathrm{tr}}$, which can be inferred, non-perturbatively, from the correlation of electron scattering matrices induced by ions. T…
We calculate the optical Hall conductivity within the Kubo formalism for systems with gapped spectral nodes, where the latter have a power-law dispersion with exponent n. The optical conductivity is proportional to n and there is a characteristic logarithmic singularity as the frequency approaches the gap energy. The optical Hall conductivity is almost unaffected by thermal fluctuations and disorder for n=1, whereas disorder has a stronger effect on transport properties if n=2.
We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector $q$ to order $q^2$, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tenso…
The calculations of thermal conductivity requires to know anharmonic properties of the crystal. For this purpose a non-perturbative anharmonic theory is applied, which do not make use of the potential energy expansion over atomic displacements, but instead, runs ab initio calculations of Hellmann-Feynman forces for atomic patterns of atoms with specific displacements to rebuild the anharmonic phonon frequencies, and group velocities. see [K.Parlinski, Phys.Rev. B 98, 054305 (2018),] The Green-Kubo equation for the thermal conductivity needs to know the above quantities and the phonon relaxatio…
The remarkable transport properties of graphene follow not only from the the Dirac-like energy dispersion, but also from the chiral nature of its excitations, which makes unclear the limits of applicability of the standard semiclassical Boltzmann approach. In this paper we provide a quantum derivation of the transport scattering time in graphene in the case of electron-phonon interaction. By using the Kubo formalism, we compute explicitly the vertex corrections to the dc conductivity by retaining the full chiral matrix structure of graphene. We show that at least in the regime of large chemica…
We study the optical conductivity of a doped graphene when a sublattice symmetry breaking is occurred in the presence of the electron-phonon interaction. Our study is based on the Kubo formula that is established upon the retarded self-energy. We report new features of both the real and imaginary parts of the quasiparticle self-energy in the presence of a gap opening. We find an analytical expression for the renormalized Fermi velocity of massive Dirac Fermions over broad ranges of electron densities, gap values and the electron-phonon coupling constants. Finally we conclude that the inclusion…
We have developed an efficient order-N real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illus…
Graphene's near-field radiative heat transfer is determined from its electrical conductivity, commonly modeled using the local Kubo and Drude formulas. In this letter, we analyze the non-locality of graphene's electrical conductivity using the Lindhard model combined with the Mermin relaxation time approximation. We also study how the variation of electrical conductivity with wavevector affects near-field radiative conductance between two graphene sheets separated by a vacuum gap. It is shown that the variation of electrical conductivity with wavevector, $k_ρ$, is appreciable for $k_ρ$s greate…
The first non-empirical computation of lattice thermal conductivity has been performed for MgO using molecular dynamics (MD), a non-empirical ionic model (the Variationally Induced Breathing (VIB) model), and Green-Kubo theory. The computation is first-principles in the sense that no parameters are fit to experiment. Results are presented at low pressure as a function of temperature, and for 2500K for pressures to 290 GPa. We find an unexpectedly small pressure effect at small compressions, perhaps due to saturation of thermal conductivity at the high temperatures due to the small mean free pa…
A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin current density a Kubo-Středa-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker (KKR) band structure method in combination with the Coherent Potential Approximation (CPA) allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-sc…
Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phonon branch and calculate its contribution to the thermal conductivity within the Kubo formalism. We find a low temperature power law dependence of the thermal conductivity as $T^α$, with $1 < α< 2$, (lower than $T^3$ behavior) due to optical phonons near the quantum critical point. This result is in accord with the experimental findings and indicates…
We compute the electrical conductivity for liquid hydrogen at high pressure using quantum Monte Carlo. The method uses Coupled Electron-Ion Monte Carlo to generate configurations of liquid hydrogen. For each configuration correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give AC electrical conductivity directly. The extrapolated DC conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transiti…
Liquid NaSn alloys in five different compositions (20, 40, 50, 57 and 80% sodium) are studied using density functional calculations combined with molecular dynamics(Car-Parrinello method). The frequency-dependent electric conductivities for the systems are calculated by means of the Kubo-Greenwood formula. The extrapolated DC conductivities are in good agreement with the experimental data and reproduce the strong variation with the concentration. The maximum of conductivity is obtained, in agreement with experiment, near the equimolar composition. The strong variation of conductivity, ranging …
We have performed quantum molecular dynamic simulations for warm dense polystyrene at high pressures. The principal Hugoniot up to 790 GPa is derived from wide range equation of states, where contributions from atomic ionizations are semiclassically determined. The optical conductivity is calculated via the Kubo-Greenwood formula, from which the dc electrical conductivity and optical reflectivity are determined. The nonmetal-to-metal transition is identified by gradual decomposition of the polymer. Our results show good agreement with recent high precision laser-driven experiments.
