Optimal block-tridiagonalization of matrices for coherent charge transport

Abstract

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms requires the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrary complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green's function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.

28 pages, 14 figures; submitted to Journal of Computational Physics

References in corpus (7)

• The electronic properties of graphene
• Spin currents in rough graphene nanoribbons: Universal fluctuations and spin injection
• A knitting algorithm for calculating Green functions in quantum systems
• Effects of short-range interactions on transport through quantum point contacts: A numerical approach
• Ballistic quantum transport at high energies and high magnetic fields
• A variant transfer matrix method suitable for transport through multi-probe systems
• An efficient and accurate method to obtain the energy-dependent Green function for general potentials

Cited by in corpus (42)

• Kwant: a software package for quantum transport
• Quantized conductance at the Majorana phase transition in a disordered superconducting wire
• Quantum point contact as a probe of a topological superconductor
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Barrier transmission of Dirac-like pseudospin-one particles
• Direct determination of spin orbit interaction coefficients and realization of the persistent spin helix symmetry
• Graphene Rings in Magnetic Fields: Aharonov-Bohm Effect and Valley Splitting
• Spin Hall Effect and Origins of Nonlocal Resistance in Adatom-Decorated Graphene
• Charge impurity effects in hybrid Majorana nanowires
• Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing large number of atoms
• Coherent transport through graphene nanoribbons in the presence of edge disorder
• Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
• Random-matrix theory of Andreev reflection from a topological superconductor
• Symmetries and the conductance of graphene nanoribbons with long-range disorder
• Interfaces Within Graphene Nanoribbons
• Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
• Recursive Green's function method for multi-terminal nanostructures
• Towards superlattices: Lateral bipolar multibarriers in graphene
• Topological transitions in spin interferometers
• Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport
• Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction
• An efficient method for computing the electronic transport properties of a multi-terminal system
• Magnetotransport in disordered two-dimensional topological insulators: signatures of charge puddles
• Improved recursive Green's function formalism for quasi one-dimensional systems with realistic defects
• Quantum transport through resistive nanocontacts: Effective one-dimensional theory and conductance formulas for non-ballistic leads
• Revisiting Quasiparticle Scattering Interference in High-Temperature Superconductors: The Problem of Narrow Peaks
• Self-Energies and Quasiparticle Scattering Interference
• Using Topological Insulator Proximity to Generate Perfectly Conducting Channels in Materials without Topological Protection
• Signatures of spin-preserving symmetries in two-dimensional hole gases
• Quantum coherence and its dephasing in the giant spin Hall effect and nonlocal voltage generated by magnetotransport through multiterminal graphene bars
• Magnetotransport through graphene nanoribbons at high magnetic fields
• Spin transistor action from Onsager reciprocity and SU(2) gauge theory
• Spin Conductance of Diffusive Graphene Nanoribbons: a Probe of Zigzag Edge Magnetization
• A numerical method to efficiently calculate the transport properties of large systems: an algorithm optimized for sparse linear solvers
• Geometric Correlations and Breakdown of Mesoscopic Universality in Spin Transport
• Büttiker probes and the Recursive Green's Function; an efficient approach to include dissipation in general configurations
• Spin transmission control in helical magnetic fields
• Orbital Magnetism of Graphene Nanostructures: Bulk and Confinement Effects
• Conductance response of graphene nanoribbons and quantum point contacts in the scanning probe measurements
• Weak localization in mesoscopic hole transport: Berry phases and classical correlations
• NanoNET: an extendable Python framework for semi-empirical tight-binding models
• Spin-Orbit Based Coherent Spin Ratchets