A linear-scaling source-sink algorithm for simulating time-resolved quantum transport and superconductivity

Abstract

We report on a "source-sink" algorithm which allows one to calculate time-resolved physical quantities from a general nanoelectronic quantum system (described by an arbitrary time-dependent quadratic Hamiltonian) connected to infinite electrodes. Although mathematically equivalent to the non equilibrium Green's function formalism, the approach is based on the scattering wave functions of the system. It amounts to solving a set of generalized Schrödinger equations which include an additional "source" term (coming from the time dependent perturbation) and an absorbing "sink" term (the electrodes). The algorithm execution time scales linearly with both system size and simulation time allowing one to simulate large systems (currently around $10^6$ degrees of freedom) and/or large times (currently around $10^5$ times the smallest time scale of the system). As an application we calculate the current-voltage characteristics of a Josephson junction for both short and long junctions, and recover the multiple Andreev reflexion (MAR) physics. We also discuss two intrinsically time-dependent situations: the relaxation time of a Josephson junction after a quench of the voltage bias, and the propagation of voltage pulses through a Josephson junction. In the case of a ballistic, long Josephson junction, we predict that a fast voltage pulse creates an oscillatory current whose frequency is controlled by the Thouless energy of the normal part. A similar effect is found for short junctions, a voltage pulse produces an oscillating current which, in the absence of electromagnetic environment, does not relax.

13 pages, 12 figures

References in corpus (8)

• An On-Demand Coherent Single Electron Source
• A time-dependent approach to electron pumping in open quantum systems
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Transient regime in non-linear transport through many-level quantum dots
• Stroboscopic wavepacket description of non-equilibrium many-electron problems
• AC Josephson effect without superconductivity
• Stopping electrons with radio-frequency pulses in the quantum Hall regime
• A computational approach to quantum noise in time-dependent nanoelectronic devices

Cited by in corpus (22)

• Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions
• Spin and charge pumping by steady or pulse current-driven magnetic domain wall: A self-consistent multiscale time-dependent-quantum/time-dependent-classical approach
• Tkwant: a software package for time-dependent quantum transport
• Quench dynamics in superconducting nanojunctions: metastability and dynamical Yang-Lee zeros
• A many-body approach to transport in quantum systems: From the transient regime to the stationary state
• Transport through correlated systems with density functional theory
• Andreev bound states formation and quasiparticle trapping in quench dynamics revealed by time-dependent counting statistics
• Towards Realistic Time-Resolved Simulations of Quantum Devices
• Spin-orbit coupling induced ultra-high harmonic generation from magnetic dynamics
• Simulating time-dependent thermoelectric transport in quantum systems
• Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems
• Role of the quasi-particles in an electric circuit with Josephson junctions
• Transient and Sharvin resistances of Luttinger liquids
• Toward flying qubit spectroscopy
• Cooperative Charge Pumping and Enhanced Skyrmion Mobility
• Order O(1) algorithm for first-principles transient current through open quantum systems
• On Landauer--Büttiker formalism from a quantum quench
• Atomistic modeling of a superconductor-transition-metal dichalcogenide-superconductor Josephson junction
• Birth and Early Growth of Entanglement by sd Exchange with Gate-Voltage-Controllable Destiny
• Thermoelectric study of the time-dependent Resonant Level Model
• Quantum nonlinear ac transport theory at low frequency
• Impact of spin-orbit coupling and Zeeman interaction on the multiple Andreev reflections subharmonic gap structure in nanoscopic Josephson junctions