Linear scaling quantum transport methodologies

DOI10.1016/j.physrep.2020.12.001zbMath1484.82053arXiv1811.07387OpenAlexW3116074372MaRDI QIDQ2231836

Ari Harju, Aron W. Cummings, Zheyong Fan, Michel Panhans, José H. Garcia, Stephan Roche, Jose Eduardo Barrios-Vargas, Frank G. Ortmann

Publication date: 30 September 2021

Published in: Physics Reports (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.07387

zbMATH Keywords

numerical methodstime-dependent Schrödinger equationquantum transporttopological materials2D materialskernel polynomials method

Mathematics Subject Classification ID

Transport processes in time-dependent statistical mechanics (82C70) Time-dependent Schrödinger equations and Dirac equations (35Q41) Basic methods in statistical mechanics (82M99) Statistical mechanics in condensed matter (general) (82D03)

Uses Software

• Kwant
• TBTK
• transiesta

Cites Work

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• Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene
• A comparison of different propagation schemes for the time dependent Schrödinger equation
• Solution of the Schrödinger equation by a spectral method
• Kernel polynomial approximations for densities of states and spectral functions
• An order \(N\) numerical method to efficiently calculate the transport properties of large systems: an algorithm optimized for sparse linear solvers
• Numerical approaches to time evolution of complex quantum systems
• Studies of polaron motion. I: The molecular-crystal model; II: The 'small' polaron
• Topological Bloch bands in graphene superlattices
• The kernel polynomial method
• The Boltzmann Equation in the Theory of Electrical Conduction in Metals
• On the Electrical Conductivity of Metals
• A dielectric formulation of the many body problem: Application to the free electron gas
• The Law of Wiedemann and Franz
• Evaluation of Kubo's Formula for the Impurity Resistance of an Interacting Electron Gas
• Quantum Field Theory of Non-equilibrium States
• Electronic transport properties of quasicrystals
• ELECTRONIC TRANSPORT IN GRAPHENE: QUANTUM EFFECTS AND ROLE OF LOCAL DEFECTS
• Modern Quantum Mechanics
• The Effect of a Magnetic Field on Electrons in a Periodic Potential
• Theory of the Effect of Spin-Orbit Coupling on Magnetic Resonance in Some Semiconductors
• On Quantum Theory of Transport Phenomena
• Theory of Superconductivity