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Register a new userA non-iterative method for the vertex corrections of the Kubo formula for electric conductivity
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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.
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Linear response theory plays a prominent role in various fields of physics and provides us with extensive information about the thermodynamics and dynamics of quantum and classical systems. Here we develop a general theory for the linear response in non-Hermitian systems with non-unitary dynamics and derive a modified Kubo formula for the generalized susceptibility for arbitrary (Hermitian and non-Hermitian) system and perturbation. As an application, we evaluate the dynamical response of a non-Hermitian, one-dimensional Dirac model with imaginary and real masses, perturbed by a time-dependent electric field. The model has a rich phase diagram, and in particular, features a tachyon phase, where excitations travel faster than an effective speed of light. Surprisingly, we find that the dc conductivity of tachyons is finite, and the optical sum rule is exactly satisfied for all masses. Our results highlight the peculiar properties of the Kubo formula for non-Hermitian systems and are applicable for a large variety of settings.
We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems.The dynamical DMRG is used to compute the linear response of a finite system to an applied AC source-drain voltage, then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the DC conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in an homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.
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 heat conducting materials, namely diamond Si and tetragonal ZrO$_2$.
Planar electrodes patterned on a ferroelectric substrate are shown to provide lateral control of the conductive state of a two-terminal graphene stripe. A multi-level and on-demand memory control of the graphene resistance state is demonstrated under low sub-coercive electric fields, with a susceptibility exceeding by more than two orders of magnitude those reported in a vertical gating geometry. Our example of reversible and low-power lateral control over 11 memory states in the graphene conductivity illustrates the possibility of multimemory and multifunctional applications, as top and bottom inputs remain accessible.
In a recent paper by Neupert, Santos, Chamon, and Mudry [Phys. Rev. B 86, 165133 (2012)] it is claimed that there is an elementary formula for the Hall conductivity of fractional Chern insulators. We show that the proposed formula cannot generally be correct, and we suggest one possible source of the error. Our reasoning can be generalized to show no quantity (such as Hall conductivity) expected to be constant throughout an entire phase of matter can possibly be given as the expectation of any time independent short ranged operator.
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