CHERN NUMBER AND EDGE STATES IN THE INTEGER QUANTUM HALL-EFFECT

被引:1144
作者
HATSUGAI, Y [1 ]
机构
[1] UNIV TOKYO,INST SOLID STATE PHYS,MINATO KU,TOKYO 106,JAPAN
关键词
D O I
10.1103/PhysRevLett.71.3697
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider the integer quantum Hall effect on a square lattice in a uniform rational magnetic field. The relation between two different interpretations of the Hall conductance as topological invariants is clarified. One is the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) integer in the infinite system and the other is a winding number of the edge state. In the TKNN form of the Hall conductance, a phase of the Bloch wave function defines U(1) vortices on the magnetic Brillouin zone and the total vorticity gives sigma(xy). We find that these vortices are given by the edge states when they are degenerate with the bulk states.
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页码:3697 / 3700
页数:4
相关论文
共 10 条
[1]   HOMOTOPY AND QUANTIZATION IN CONDENSED MATTER PHYSICS [J].
AVRON, JE ;
SEILER, R ;
SIMON, B .
PHYSICAL REVIEW LETTERS, 1983, 51 (01) :51-53
[2]   QUANTIZED HALL CONDUCTANCE, CURRENT-CARRYING EDGE STATES, AND THE EXISTENCE OF EXTENDED STATES IN A TWO-DIMENSIONAL DISORDERED POTENTIAL [J].
HALPERIN, BI .
PHYSICAL REVIEW B, 1982, 25 (04) :2185-2190
[3]   EDGE STATES IN THE INTEGER QUANTUM HALL-EFFECT AND THE RIEMANN SURFACE OF THE BLOCH FUNCTION [J].
HATSUGAI, Y .
PHYSICAL REVIEW B, 1993, 48 (16) :11851-11862
[4]  
HATSUGAI Y, 1993, B AM PHYS SOC, V38, P397
[5]   ZERO MODES AND THE QUANTIZED HALL CONDUCTANCE OF THE TWO-DIMENSIONAL LATTICE IN A MAGNETIC-FIELD [J].
KOHMOTO, M .
PHYSICAL REVIEW B, 1989, 39 (16) :11943-11949
[6]  
KOHMOTO M, 1985, ANN PHYS-NEW YORK, V160, P355
[7]  
LAUGHLIN RB, 1981, PHYS REV B, V23, P5632, DOI 10.1103/PhysRevB.23.5632
[8]   QUANTIZED HALL CONDUCTANCE IN A TWO-DIMENSIONAL PERIODIC POTENTIAL [J].
THOULESS, DJ ;
KOHMOTO, M ;
NIGHTINGALE, MP ;
DENNIJS, M .
PHYSICAL REVIEW LETTERS, 1982, 49 (06) :405-408
[9]  
Toda M., 1981, THEORY NONLINEAR LAT, DOI [10.1007/978-3-642-96585-2, DOI 10.1007/978-3-642-96585-2]
[10]   WINDING NUMBER, FAMILY INDEX THEOREM, AND ELECTRON HOPPING IN A MAGNETIC-FIELD [J].
WEN, XG ;
ZEE, A .
NUCLEAR PHYSICS B, 1989, 316 (03) :641-662