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DY: Fachverband Dynamik und Statistische Physik

DY 24: Poster I

DY 24.24: Poster

Wednesday, March 28, 2007, 16:00–18:00, Poster D

Current instabilities in resonant tunneling quantum dot structures — •Kathy Lüdge and Eckehard Schöll — Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin

In this work we investigate the current transport through quantum dots (QDs) embedded in a double barrier structure that is operated in an external circuit with a dc bias voltage Uo and a series resistance R and a parallel capacitance C. We show that the performance of such nonlinear devices is crucially depending on the chosen external circuit parameters, so that they can be used either as switches or as self-sustained current oscillators.

For analyzing the dynamics of the QD system a Master equation approach for sequential tunneling through two parallel, electrostatically coupled quantum dots has been used, followed by a linear stability analysis of the fixed points of the five dimensional system, taking into account also the dynamic degree of freedom of the voltage drop across the QD structure due to Kirchhoff's circuit equation. Interesting effects are found if the nullclines of the external circuit and of the QD system intersect such that three operating points exist. For the usual case of a positive capacitance C we show that oscillatory instabilities caused by a Hopf bifurcation cannot occur. For negative capacitance, which can easily be realized by an active circuit consisting of operation amplifiers, a Hopf bifurcation leading to uniform limit cycle oscillations can be found. At a certain value of C the limit cycle collides with the saddle-point on the low current branch and disappears which represents a global homoclinic bifurcation (or blue-sky catastrophe).