Time-dependent current through a quantum dot in the presence of a voltage probe
Current density evolution as measured behind a quantum dotAbstract
This thesis examines the effects of a Büttiker voltage probe on the time-dependent current through an idealized resonant quantum dot. The system is described by a tight binding Schrödinger equation which is then integrated numerically to obtain the time-dependent current. Correct probe behavior is provided by a time-dependent voltage profile that is obtained numerically via an iterative scheme. The stationary current values are found to be in agreement with predictions derived from the Landauer-Büttiker formalism. The time-dependent current characteristics are significantly affected by the probe-introduced decoherence, as is evident by a shortened time it takes for the current to reach its stationary value. This effect is approximated by a model whose parameter describes the time it takes for the current to reach its stationary value. Examining the data, the parameter values are found to be roughly proportional to the total resonance width of the system.
This is the thesis for my Diploma (Master’s and Bachelor’s combined) in Mathematical Physics at the University of Ljubljana. It was advised by dr. Tomaž Rejec from the Department of Theoretical Physics, Jožef Stefan Institute.
The work is an original examination of the effects that a coupled voltage probe has on the current flowing through a quantum dot, specifically its temporal properties. This was done by numerically simulating the problem from first principles (i.e. from a version of Schrödinger’s equation). The main challenge was to ensure that the voltage on the probe was set just so there was no current flowing in or out of it, while the system was being integrated - i.e. without knowing what the actual currents at that step were.
The document attached significantly compresses the theoretical background of the thesis (based on the Non-Equilibrium Green’s Functions formalism - NEGF), which is to be found in the referenced works since it falls outside of the Diploma program and the recommended Diploma thesis format.
References: University of Ljubljana Repository reference page.
