Theory of Time-Dependent Transport and Levitons in Nanowires

Abstract: An interesting type of quasi-particles in solid-state materials are the so-called levitons. These are single- electron excitations above the Fermi-level that do not produce any hole states when carrying an integer multiple of the elementary charge. Levitons are produced when a quantum conductor is subjected to a time-dependent voltage pulse with a Lorentzian shape. The parameters of the voltage pulse determine the amount of charge carried by a leviton, meaning that single-electron excitations can be generated without the need for advanced nanofabrication. This makes levitons interesting for potential use in experiments and nanoelectronic devices involving single electrons. In this thesis, I simulate the transport of levitons through one-dimension tight-binding chains. The tight-binding chains consist of a scattering region with one or two barriers, connected to leads at both ends. The goal of these simulations is to study how the properties of a leviton, in particular its shape and the amount of charge transported through the system, is affected by quantum tunnelling through the barriers. The simulations are done using a Python package called Tkwant, aimed at calculating time-dependent transport through quantum systems. The levitons are generated by applying a time-dependent voltage pulse to the left lead of the system. The results are presented as the expectation values of the current, calculated after the scattering region. The amount of charge transported is then obtained by integrating the current with respect to time. Since the expectation value of the current is proportional to the absolute value squared of the wave function, the shape of the current corresponds to the shape of the absolute value squared of the wave function. The shape of the current after the scattering region is determined by fitting a Lorentzian function (or a sum of Lorentzian functions in the case of two barriers) to the result. This shows whether the transmitted part of the wave function still has a Lorentzian shape, and if so, how the parameters of the Lorentzian have changed compared to before entering the scattering region. The results of the simulations show that a leviton do seem to retain its shape after the tunnelling events and that the amount of charge transported through the system decrease exponentially with increased barrier height. When the barriers are much higher in energy than the leviton, the parameters of the Lorentzian curve are virtually unchanged by the tunnelling. This is likely because all energy components of the leviton transmit through the barriers with a similar probability. When the barrier height is at an energy comparable to that of the leviton, a narrowing of the Lorentzian is observed, probably due to a more prominent difference in transmittance between the high and low energy components of the leviton.