Anomalies of higher conductance steps in quantum point contacts - fRG applied to a 2D Hubbard model -

Nikolai Ufer

12.01.2011 at 16:00 

Low-temperature transport experiments on quantum point contact geometries show besides the well-known conductance quantization G = n G_Q, in units of G_Q = 2 e^2/h, additional shoulder-like steps at non-integer multiples of the conductance quantum. Further investigations showed that these conductance anomalies are a generic phenomena [1]. But despite a lot of experimental and theoretical effort, there is still no microscopic model, that adequately explains all occurring features of these anomalies. In the scientific community there is at least the agreement, that this must be some many-body phenomena. Within the scope of a former thesis of Florian Bauer [2], it was possible to reproduce a promising magnetic field dependence of the first conduction anomaly, the "0.7 anomaly", in the limit of vanishing temperature and linear-conductance. This was achieved by applying the functional Renormalization Group (fRG) to an one-dimensional extended Hubbard model with a smooth potential barrier. In this talk we will show, how this approach can be extended to higher conductance anomalies by applying fRG to a two dimensional Hubbard model. This includes among others the question of how to solve numerically the fRG flow-equations and hence the need of an efficient way to compute certain elements of the Green functions. We do this by introducing the Recursive Green Function (RGF) algorithm, which is an efficient method to compute the inverse of sparse matrices of a quasi-one-dimensional systems.

[1] K.J. Thomas, J.T. Nicholls, M.Y. Simmons, M. Pepper, D.R. Mace and D.A. Ritchie: Possible spin polarization in a one-dimensional electron gas. Physical Review Letters 77 (1996), 135.
[2] F. Bauer: 0.7 Anomaly of Quantum Point Contacts. Treatment of Interaction with functional Renormalization Group. Ludwig-Maximilians Universit\"at, diploma thesis, 2008