Improvements on non-equilibrium and transport Green function techniques: The next-generation transiesta

Abstract

We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes (Ne ≥ 1) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour optimizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a generic NEGF "post-processing" code (tbtrans/phtrans) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, Ne ≥ 1 electrode capability, bond-currents, generalized interface for user-defined tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding 10 6 atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems. * The transport of charge, magnetic moments and, in general, any sort of excitation is a fascinating fundamental physical problem that has demanded attention for a long time [1]. Today, the interest is enhanced by the technological needs of an industry increasingly based on devices whose detailed atomistic structure matters [2], but the treatment of transport is still a formidable open task. Spurred by the fast developments of the microelectronic industry, the first attempts to understand electronic transport at the atomic scale where based on scattering theory [3]. The electron transmission between two semi-infinite reservoirs was treated in a time-independent fashion solving the scattering matrix connecting the reservoirs. At this stage, transport was described as one-electron scattering by a static contact region and this granted access to many concepts and to devising new experiments [4][5][6]. However, the problem is fundamentally a non-equilibrium one that requires evolving many-body states [7][8][9][10].Density functional theory (DFT) has been one method to address some aspects of this problem. Conceptually, DFT is a mean-field many-body theory of the ground state. As such, it can in principle give exact results for the linear conductance because the linear response is a property of the ground state [11]. Beyond linear conductance, not even ideal DFT works because of the need to describe excited states and dynamics of the system. Such limitations may be mitigated by using time-dependent DFT [12,13], but going beyond the linear regime is highly nontrivial. A main issue of a DFT description stems from the approximations made to compute the ground state. Indeed, it has been recently shown that cases where strong correlations rein, such as the Coulomb blockade regime, the commonly used exchange-and-correlation functionals fail and new ones have to be used [14].Probably the most significant conceptu...

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Current-induced atomic forces in gated graphene nanoconstrictions

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“…While the real-space Green function calculates spectral quantities in a pristine system it is rarely competitive with regular diagonalization methods in the 00 subspace and using Bloch's theorem. Our key mission in calculating the real-space Green function is that it holds the real-space self-energy, Σ R , which in turn allows truly single defects (bulk) and contacts (transport) using the Green function formalism [12,14].…”

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