DIOPHANTINE EQUATION FOR THE 3-DIMENSIONAL QUANTUM HALL-EFFECT

被引：128

作者：

KOHMOTO, M

HALPERIN, BI

WU, YS

机构：

[1] HARVARD UNIV, LYMAN LAB PHYS, CAMBRIDGE, MA 02138 USA

[2] UNIV UTAH, DEPT PHYS, SALT LAKE CITY, UT 84112 USA

来源：

PHYSICAL REVIEW B | 1992年 / 45卷 / 23期

关键词：

D O I：

10.1103/PhysRevB.45.13488

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

When the Fermi level lies in a gap, the Hall conductivity of three-dimensional electrons in a periodic potential is expressed in a topologically invariant form with a set of three integers. If the magnetic fluxes through the three independent areas of the periodic lattice are rational numbers, one obtains a Diophantine equation relating these numbers and the integers which characterize the Hall conductivity.

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页码：13488 / 13493

页数：6

相关论文

共 33 条

[1]

Aubry S., 1980, Annals of the Israel Physical Society, V3, P133

[2] STABILITY OF GAPS FOR PERIODIC POTENTIALS UNDER VARIATION OF A MAGNETIC-FIELD [J].

AVRON, J ;

SIMON, B .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1985, 18 (12) :2199-2205

[3] HOMOTOPY AND QUANTIZATION IN CONDENSED MATTER PHYSICS [J].

AVRON, JE ;

SEILER, R ;

SIMON, B .

PHYSICAL REVIEW LETTERS, 1983, 51 (01) :51-53

[4]

Azbel M. Ya, 1964, ZH EKSP TEOR FIZ, V46, P929

[5] QUANTIZED HALL CONDUCTANCE IN A PERFECT CRYSTAL [J].

DANA, I ;

AVRON, Y ;

ZAK, J .

JOURNAL OF PHYSICS C-SOLID STATE PHYSICS, 1985, 18 (22) :L679-L683

[6] POSSIBLE STATES FOR A 3-DIMENSIONAL ELECTRON-GAS IN A STRONG MAGNETIC-FIELD [J].

HALPERIN, BI .

JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS SHORT NOTES & REVIEW PAPERS, 1987, 26 :1913-1919

[7] 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

[8] GENERALIZED FLUX STATES ON 3-DIMENSIONAL LATTICE [J].

HASEGAWA, Y .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1990, 59 (12) :4384-4393

[9] ENERGY-LEVELS AND WAVE-FUNCTIONS OF BLOCH ELECTRONS IN RATIONAL AND IRRATIONAL MAGNETIC-FIELDS [J].

HOFSTADTER, DR .

PHYSICAL REVIEW B, 1976, 14 (06) :2239-2249

[10] THE ROTATION NUMBER FOR ALMOST PERIODIC POTENTIALS [J].

JOHNSON, R ;

MOSER, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 84 (03) :403-438

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