Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1996-12-03
Physical Review B 55, 10593 (1997)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
10 pages, REVTeX, 2 eps figures
Scientific paper
10.1103/PhysRevB.55.10593
We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C. By mapping it to a ferromagnetic superspin chain, and using a scaling analysis, we show its equivalence to a one-dimensional supersymmetric nonlinear sigma model in the scaling limit, for any value of the ratio L/C, except for short systems where L is less than of order C^{1/2}. For the sigma model, the universal crossover functions for the conductance and its variance have been determined previously. We also show that the DN model can be mapped directly onto the random matrix (Fokker-Planck) approach to disordered quasi-one-dimensional wires, which implies that the entire distribution of the conductance is the same as in the latter system, for any value of L/C in the same scaling limit. The results of Chalker and Dohmen are explained quantitatively.
Gruzberg Ilya A.
Read Nicholas
Sachdev Subir
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