Evidence of Hofstadter's fractal energy spectrum in the quantized Hall conductance

被引:219
作者
Albrecht, C [1 ]
Smet, JH
von Klitzing, K
Weiss, D
Umansky, V
Schweizer, H
机构
[1] Max Planck Inst Festkorperforsch, D-70569 Stuttgart, Germany
[2] Univ Regensburg, Inst Expt & Angew Phys, D-93040 Regensburg, Germany
[3] Weizmann Inst Sci, Braun Ctr Submicron Res, IL-76100 Rehovot, Israel
[4] Univ Stuttgart, Inst Phys 4, D-70550 Stuttgart, Germany
关键词
D O I
10.1103/PhysRevLett.86.147
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The energy spectrum of a two-dimensional electron system in a perpendicular homogeneous magnetic field and a weak lateral superlattice potential with square symmetry is composed of Landau bands with recursive internal subband structure. The Hall conductance in the minigaps is anticipated to be quantized in integer multiples of e(2)/h that vary erratically from minigap to minigap in accordance with a Diophan-time equation. Hall measurements on samples with the requisite properties uncover this long searched for evidence of Hofstadter's butterflylike energy spectrum.
引用
收藏
页码:147 / 150
页数:4
相关论文
共 18 条
[1]   Fermiology of two-dimensional lateral superlattices [J].
Albrecht, C ;
Smet, JH ;
Weiss, D ;
von Klitzing, K ;
Hennig, R ;
Langenbuch, M ;
Suhrke, M ;
Rössler, U ;
Umansky, V ;
Schweizer, H .
PHYSICAL REVIEW LETTERS, 1999, 83 (11) :2234-2237
[2]   NOVEL MAGNETORESISTANCE OSCILLATIONS IN A PERIODICALLY MODULATED TWO-DIMENSIONAL ELECTRON-GAS [J].
GERHARDTS, RR ;
WEISS, D ;
VONKLITZING, K .
PHYSICAL REVIEW LETTERS, 1989, 62 (10) :1173-1176
[3]   Effects of screening on the Hofstadter butterfly [J].
Gudmundsson, V ;
Gerhardts, RR .
PHYSICAL REVIEW B, 1995, 52 (23) :16744-16752
[4]   SINGLE BAND MOTION OF CONDUCTION ELECTRONS IN A UNIFORM MAGNETIC FIELD [J].
HARPER, PG .
PROCEEDINGS OF THE PHYSICAL SOCIETY OF LONDON SECTION A, 1955, 68 (10) :874-878
[5]   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
[6]   Microwave realization of the Hofstadter butterfly [J].
Kuhl, U ;
Stockmann, HJ .
PHYSICAL REVIEW LETTERS, 1998, 80 (15) :3232-3235
[7]   TIGHT-BINDING AND NEARLY-FREE-ELECTRON APPROACH TO LATTICE ELECTRONS IN EXTERNAL MAGNETIC FIELDS [J].
LANGBEIN, D .
PHYSICAL REVIEW, 1969, 180 (03) :633-&
[8]  
LAUGHLIN RB, 1981, PHYS REV B, V23, P5632, DOI 10.1103/PhysRevB.23.5632
[9]   THEORY OF MAGNETOTRANSPORT IN 2-DIMENSIONAL ELECTRON-SYSTEMS SUBJECTED TO WEAK 2-DIMENSIONAL SUPERLATTICE POTENTIALS [J].
PFANNKUCHE, D ;
GERHARDTS, RR .
PHYSICAL REVIEW B, 1992, 46 (19) :12606-12626
[10]   Internal structure of a Landau band induced by a lateral superlattice: A glimpse of Hofstadter's butterfly [J].
Schlosser, T ;
Ensslin, K ;
Kotthaus, JP ;
Holland, M .
EUROPHYSICS LETTERS, 1996, 33 (09) :683-688