emil prodan- an edge index for the quantum spin-hall effect

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An edge index for the Quantum Spin-Hall effect Emil Prodan Department of Physics, Yeshiva University, New York, NY 10016 Abstract. Quan tum Spin- Hall syste ms are topological insulators displaying di ss i pa ti onl es s s pi n cu rrents flo wi ng at t he e dg es of t he sa mpl es . In cont radist inction to the Quantum Hall syste ms where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open probl em to find the obs erv abl e whose edg e cur ren t is quant ize d. In thi s 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 give n by the inde x of a cer tain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number pre viously introduced in the litera tur e. The result gives an effectiv e 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. P ACS numbers: 73.43.-f,7 2.25.Mk

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Page 1: Emil Prodan- An edge index for the Quantum Spin-Hall effect

8/3/2019 Emil Prodan- An edge index for the Quantum Spin-Hall e�ffect

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