Abstract

Quantum transport has far-reaching applications in modern electronics as it enables the control of currents in nanoscale systems such as quantum dots. In this paper we introduce tinie: a state-of-the-art quantum transport simulation framework, which can efficiently perform first-principle calculations based on the Landauer-Büttiker formalism. The computational repertoire of tinie includes calculations of transmission, conductivity, and currents running through arbitrary multi-terminal two-dimensional transport devices, with additional tools that enable the computation of the local density of states. The generality of tinie ranges from wide-band approximation calculations to investigating systems subject to an external magnetic field. The future prospects of tinie include the simulation of, e.g., two-dimensional cavities, quantum dots, or molecular junctions. The package is written in Python 3.6, and its well-documented modular structure is designed with an intent to create a platform suited for continuous expansion and development. With tinie it is possible to obtain specific information about the effects of impurities and imperfections in quantum devices, particularly between ballistic and diffusive transport regimes. Program summaryProgram title:tinieCPC Library link to program files:https://doi.org/10.17632/7487cpj9hm.1Developer's repository link:https://gitlab.com/compphys-public/tinieLicensing provisions: MIT LicenseProgramming language: Python 3.6Nature of problem: Numerical calculation of the properties of a two-dimensional nanoscale electron transport system in a uniform magnetic field (zero or non-zero), specifically the currents running through the reservoirs (leads) coupled to a quantum dot (central region) and the corresponding transmission coefficients.Solution method: The problem solution is split into two stages. The first stage (tinie_prepare stage) prepares the transport system data for the main transport calculation. This data comprise Hamiltonian matrices of the uncoupled reservoirs and quantum dot regions, their respective sets of eigenfunctions and the coupling matrices between the quantum dot and the reservoirs. The second stage (tinie stage) performs the transport calculation for the given system using the embedding self-energy technique.Additional comments including restrictions and unusual features: The code is restricted to the non-interacting equilibrium transport problems.The code is modular in structure, allowing for easy extension and introduction of different reservoir/quantum dot/coupling types. Additionally, tinie is compatible with systems in a non-zero uniform magnetic field.The source code is available at https://gitlab.com/compphys-public/tinie and Python package in https://pypi.org/project/tinie/. An extensive documentation of the code functionality can be found in the README.md file accompanying the code.

Highlights

  • Quantum transport is one of the most common – and at the same time most tedious – concepts in condensed matter physics dating back to the beginning of mesoscopic physics when the first transport algorithms were developed [1, 2, 3, 4, 5, 6, 7]

  • In this paper we present tinie: a modern, versatile implementation of the Green’s function method for solving the equilibrium quantum transport properties of a generic two-dimensional (2D) nanostructure. 2D systems are convenient theoretical models, but they are experimentally realizable in various settings including, e.g., semiconductor structures [8, 9, 10, 11], quantum Hall systems [12, 13], topological insulators [14, 15], quantum dots [9, 10, 11, 16, 17, 18, 19, 20, 21], graphene [22, 23, 24] and other single-layer atomic systems

  • The Green’s function formalism used in our program has been employed before [28, 29, Preprint submitted to Computer Physics Communications

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Summary

Introduction

Quantum transport is one of the most common – and at the same time most tedious – concepts in condensed matter physics dating back to the beginning of mesoscopic physics when the first transport algorithms were developed [1, 2, 3, 4, 5, 6, 7]. Solving a quantum transport problem provides access to currents, conductances, density of states, and other key properties of nanosystems including novel structures such as topological insulators, for example. In this paper we present tinie: a modern, versatile implementation of the Green’s function method for solving the equilibrium quantum transport properties of a generic two-dimensional (2D) nanostructure. Tinie is designed to be compatible with itp2d package [33] which is optimized for solving tens of thousands of eigenstates of the time-independent Schrodinger equation for an arbitrary external potential, allowing various experimentally relevant shapes for quantum dots, for example. After solving the given eigenvalue problem, the quantum transport properties of an open system can be determined by employing the versatile numerical environment given by tinie.

Theoretical background
Landauer-Buttiker formalism
Transport setup
Embedding self-energy technique
Gauge transformation for a magnetic field
Design of the program
Discretization of eigenfunctions, potentials and coupling
Discretization of Hamiltonians
Coupling matrix
Self-energy calculator
Overlap coupling
Tight-binding coupling
Green’s functions calculator
Transport properties calculator
Density of states calculator
Program structure tinie has been written in
Data files
Parallelization
Comparison with other transport software
One- and two-level systems
Potential barrier
Two-dimensional potential well in a magnetic field
Multi-terminal two-dimensional perturbed potential well in a magnetic field
Performance testing
Summary
Full Text
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