An edge index for the Quantum Spin-Hall effect

Details An edge index for the Quantum Spin-Hall effect An edge index for the Quantum Spin-Hall effect

2008-09-25

arxiv.org/abs/0809.4511v3

J. Phys. A: Math. Theor. 42 (2009) 082001

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures

Scientific paper

10.1088/1751-8113/42/8/082001

Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number previously introduced in the literature. The result gives an effective tool for the investigation of the edge channels' structure in Quantum Spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge.

Affiliated with

Also associated with

No associations

Rating

An edge index for the Quantum Spin-Hall effect does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An edge index for the Quantum Spin-Hall effect, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An edge index for the Quantum Spin-Hall effect will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712544