We present KITE, a general purpose open-source tight-binding software for accurate real-space simulations of electronic structure and quantum transport properties of large-scale molecular and condensed systems with tens of billions of atomic orbitals (N ∼ 10 10 ). KITE's core is written in C++, with a versatile Python-based interface, and is fully optimised for shared memory multi-node CPU architectures, thus scalable, efficient and fast. At the core of KITE is a seamless spectral expansion of lattice Green's functions, which enables large-scale calculations of generic target functions with uniform convergence and fine control over energy resolution. Several functionalities are demonstrated, ranging from simulations of local density of states and photo-emission spectroscopy of disordered materials to large-scale computations of optical conductivity tensors and real-space wave-packet propagation in the presence of magneto-static fields and spin-orbit coupling. On-the-fly calculations of real-space Green's functions are carried out with an efficient domain decomposition technique, allowing KITE to achieve nearly ideal linear scaling in its multi-threading performance. Crystalline defects and disorder, including vacancies, adsorbates and charged impurity centers, can be easily set up with KITE's intuitive interface, paving the way to user-friendly large-scale quantum simulations of equilibrium and nonequilibrium properties of molecules, disordered crystals and heterostructures subject to a variety of perturbations and external conditions. arXiv:1910.05194v1 [cond-mat.mes-hall] 11 Oct 2019 2 IntroductionComputational modelling has become an essential tool in both fundamental and applied research that has propelled the discovery of new materials and their translation into practical applications [1]. The study of condensed phases of matter has benefited from significant advances in electronic structure theory and simulation methodologies. Among these advances are: explicitly correlated wave-function-based techniques achieving sub-chemical accuracy [2], first-principles methods to tackling electronic excitations [3], charge-self-consistent atomistic models for accurate electronic structure calculations [4], and the use of machine learning as means to finding density functionals without solving the Khon-Sham equations [5,6].Semi-empirical atomistic methods are amongst the most simple and effective methods to calculate ground-and excited-state properties of materials [7][8][9][10]. The increasingly popular tight-binding approach [11] has been employed for accurate and fast calculations of total energies and electronic structure in complex materials, including semiconductors [12,13], quantum dots [14] and super-lattices [15,16], and is particularly well-suited for implementation of O(N ) (linear scaling) algorithms for efficient calculations of total energies and forces [17].Accurate tight-binding models have been devised for a plethora of model systems, ranging from metals to ionic materials [18], and shown to correctly p...
In this paper, we developed a basis-independent perturbative method for calculating the nonlinear optical response of arbitrary non-interacting tight-binding models. Our method is based on the non-equilibrium Keldysh formalism and allows an efficient numerical implementation within the framework of the kernel polynomial method for systems which are not required to be translation-invariant. Some proof-of-concept results of the second-order optical conductivity are presented for the special case of gapped graphene with vacancies and an on-site Anderson disordered potential.
How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound ∆ V > 5.0 on the scaling dimension of the lowest virial current candidate V , well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model. E. Heuristic optimization of boundary conditions 251 We would also like to point out a related lattice study of conformal invariance in 3d percolation [4].
The electronic structure of a cubic T -symmetric Weyl semimetal is analyzed in the presence of atomic-sized vacancy defects. Isolated vacancies are shown to generate nodal bound states with r −2 asymptotic tails, even when immersed in a weakly disordered environment. These states show up as a significantly enhanced nodal density of states which, as the concentration of defects is increased, reshapes into a nodal peak that is broadened by intervacancy hybridization into a comb of satellite resonances at finite energies. Our results establish point defects as a crucial source of elastic scattering that leads to nontrivial modifications in the electronic structure of Weyl semimetals.
In AA-stacked twisted bilayer graphene, the lower energy bands become completely flat when the twist angle passes through certain specific values: the so-called “magic angles”. The Dirac peak appears at zero energy due to the flattening of these bands when the twist angle is sufficiently small [1-3]. When a constant perpendicular magnetic field is applied, Landau levels start appearing as expected [5]. We used the Kernel Polynomial Method (KPM) [6] as implemented in KITE [7] to study the optical and electronic properties of these systems. The aim of this work is to analyze how the features of these quantities change with the twist angle in the presence of an uniform magnetic field.
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