Breakdown of the quantum Hall effect

Abstract The quantum Hall effect (QHE) is one of the most prominent effects in modern solid state physics. Since its discovery, the effect has been attracting interest by a steadily increasing community of researchers. The research activities have been focussed on both application aspects and the basic physics of the effect. The limits of the QHE, in particular its persistence at higher currents, are of crucial importance for the application of the effect as a resistance standard. The observation of the current-induced breakdown of the QHE initiated a variety of experimental and also theoretical work. In this article, the experiments related to the breakdown of the QHE are reviewed. Some current theories are discussed in conjunction with the experiments. Although no comprehensive theory of the breakdown is available yet, an at least qualitatively conclusive picture can be provided on the basis of the present knowledge.

[1]  B. Halperin.  Quantized Hall conductance, current carrying edge states, and the existence of extended states in a two-dimensional disordered potential , 1982 .

[2]  M. E. Cage,et al.  Temperature dependence of the quantum Hall resistance , 1984 .

[3]  G. Hein,et al.  Bistability in the current-induced breakdown of the quantum Hall effect , 1993 .

[4]  T. Klapwijk,et al.  Intrinsic sequence in the breakdown of the quantum Hall effect , 1990 .

[5]  Disappearance of the Breakdown of Quantum Hall Effects in Short Devices. , 1995 .

[6]  S. Hiyamizu,et al.  Effect of finite electric field on the quantum Hall effect , 1986 .

[7]  Inductive probing of the integer quantum Hall effect. , 1996, Physical review letters.

[8]  D. Chklovskii,et al.  Electrostatics of edge channels. , 1992, Physical review. B, Condensed matter.

[9]  J. Wolter,et al.  Contactless measurement of the spatial potential distribution in the quantum hall effect , 1990 .

[10]  G. Weimann,et al.  Quantum Hall effect in devices with an inner boundary , 1990 .

[11]  S. Trugman.  Localization, percolation, and the quantum Hall effect , 1983 .

[12]  G. Nachtwei,et al.  Breakdown of the quantum Hall effect as a function of the filling factor and the contact configuration , 1992 .

[13]  Moore,et al.  Evidence for an inhomogeneity size effect in narrow GaAs/ AlxGa1-xAs constrictions. , 1989, Physical review. B, Condensed matter.

[14]  Shinji Kawaji,et al.  Device-width dependence of plateau width in quantum Hall states , 1993 .

[15]  G. Weimann,et al.  Non-equilibrium behaviour of the two-dimensional electron gas in the quantized Hall resistance regime of GaAs/Al0.3Ga0.7As , 1984 .

[16]  Tsui,et al.  Distribution of the quantized Hall potential in GaAs-AlxGa1-xAs heterostructures. , 1985, Physical Review B (Condensed Matter).

[17]  W. Brinkman,et al.  Hall voltage and current distributions in an ideal two-dimensional system , 1983 .

[18]  Wright,et al.  Voltage-controlled dissipation in the quantum Hall effect in a laterally constricted two-dimensional electron gas. , 1986, Physical review. B, Condensed matter.

[19]  Komiyama,et al.  Evidence of Nonlocal Breakdown of the Integer Quantum Hall Effect. , 1996, Physical review letters.

[20]  T. Ando.  Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. III. Many-Site Approximation , 1974 .

[21]  Gerhardts,et al.  Self-consistent calculations of edge channels in laterally confined two-dimensional electron systems. , 1994, Physical review. B, Condensed matter.

[22]  Two-dimensional systems: A method for the determination of the fine structure constant , 1982 .

[23]  Polyakov,et al.  Conductivity-peak broadening in the quantum Hall regime. , 1993, Physical review. B, Condensed matter.

[24]  Thouless Dj.  Edge voltages and distributed currents in the quantum Hall effect , 1993 .

[25]  F. Ahlers,et al.  Potential distribution on multiple bridge devices in quantizing magnetic fields , 1995 .

[26]  D. C. Tsui,et al.  Dissipation and Dynamic Nonlinear Behavior in the Quantum Hall Regime , 1983 .

[27]  T. Ando,et al.  Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. I. Characteristics of Level Broadening and Transport under Strong Fields , 1974 .

[28]  R. Landauer,et al.  Electrical transport in open and closed systems , 1987 .

[29]  Wolter,et al.  Spatial potential distribution in GaAs/AlxGa1-xAs heterostructures under quantum Hall conditions studied with the linear electro-optic effect. , 1991, Physical review. B, Condensed matter.

[30]  O. Hansen,et al.  The diagonal and off-diagonal AC conductivity of two-dimensional electron gases with contactless Corbino geometry in the quantum Hall regime , 1996 .

[31]  R. Woltjer.  Experiments and theory on the quantum hall effect with inhomogeneous electron density , 1988 .

[32]  Two-dimensional electron gases in the quantum hall regime : Analysis of the circulating current in contactless corbino geometry , 1996 .

[33]  Wright,et al.  Low-voltage breakdown of the quantum Hall state in a laterally constricted two-dimensional electron gas. , 1986, Physical review. B, Condensed matter.

[34]  Büttiker,et al.  Absence of backscattering in the quantum Hall effect in multiprobe conductors. , 1988, Physical review. B, Condensed matter.

[35]  Y. Ono.  Localization of Electrons under Strong Magnetic Fields in a Two-Dimensional System , 1982 .

[36]  J. Niemeyer,et al.  Critical current density for the dissipationless quantum Hall effect , 1986 .

[37]  Kristensen,et al.  Nonlinear current-voltage characteristics at quantum Hall resistance minima. , 1994, Physical review. B, Condensed matter.

[38]  Harrison,et al.  Edge channels and the quantum-Hall-effect breakdown. , 1994, Physical review. B, Condensed matter.

[39]  L. Challis,et al.  A search for asymmetry in the dissipation between the current entry and exit points in the quantum Hall regime of a silicon MOSFET , 1992 .

[40]  D. Thouless.  Field distribution in a quantum Hall device , 1985 .

[41]  S. Kawaji,et al.  Quantized hall and transverse resistivities in silicon MOS n-inversion layers , 1983 .

[42]  Jeanneret,et al.  Observation of the integer quantum Hall effect by magnetic coupling to a Corbino ring. , 1995, Physical review. B, Condensed matter.

[43]  Raymond,et al.  Heating of two-dimensional electrons by a high electric field in a quantizing magnetic field: Consequences in Landau emission and in the quantum Hall effect. , 1995, Physical review. B, Condensed matter.

[44]  F. Ahlers,et al.  Gate-controlled current distribution on double-bridge quantum Hall conductors , 1996 .

[45]  Shtrikman,et al.  Scaling of the critical current in the quantum Hall effect: A probe of current distribution. , 1993, Physical review letters.

[46]  J. Riess.  Electric field dependent mobility edge and theory of the breakdown of the integer quantum Hall effect , 1993 .

[47]  K. Klitzing,et al.  Potential drops across quantum Hall effect samples — in the bulk or near the edges? , 1996 .

[48]  Chang,et al.  Critical currents of the quantum Hall effect in the mesoscopic regime. , 1987, Physical review. B, Condensed matter.

[49]  M. E. Cage,et al.  Quantised dissipative states at breakdown of the quantum Hall effect , 1990 .

[50]  Thomas,et al.  Experimental study of the current flow in the quantum Hall regime. , 1986, Physical review. B, Condensed matter.

[51]  van Son PC,et al.  Current contacts and the breakdown of the quantum Hall effect. , 1990, Physical review. B, Condensed matter.

[52]  Theory of Hall Effect in a Two-Dimensional Electron System , 1975 .

[53]  C. E. Timmering,et al.  A New Approach to the Quantum Hall Effect , 1986 .

[54]  R. Haug.  Edge-state transport and its experimental consequences in high magnetic fields , 1993 .

[55]  L. Smrcka,et al.  Thermodynamic derivation of the Hall current and the thermopower in quantising magnetic field , 1983 .

[56]  S. Kawaji,et al.  Magnetic field dependence of the device-width-dependent breakdown current in the quantum Hall effect , 1994 .

[57]  S. Kawaji,et al.  Breakdown of the Quantum Hall Effect in GaAs/AlGaAs Heterostructures Due to Current , 1994 .

[58]  L. Challis,et al.  Studies of the asymmetry of phonon emission from hot carriers in the quantum Hall regime of GaAs , 1994 .

[59]  J. Killoran,et al.  Comparisons of edge state versus bulk conduction in the quantum Hall regime , 1990 .

[60]  K. Klitzing,et al.  Electro-optic imaging of potential distributions in the quantum Hall regime , 1995 .

[61]  S. Luryi,et al.  Quantum percolation and quantization of Hall resistance in two-dimensional electron gas , 1982 .

[62]  K. Klitzing,et al.  BREAKDOWN OF THE QUANTUM HALL EFFECT IN PERIODIC AND APERIODIC ANTIDOT ARRAYS , 1997 .

[63]  R. Gerhardts.  Path-integral approach to the two-dimensional magneto-conductivity problem , 1975 .

[64]  S. Kawaji,et al.  High precision measurements of the hall effect for silicon mos inversion layers in strong magnetic fields , 1982 .

[65]  von Klitzing K,et al.  Quantum Hall effect in the absence of edge currents. , 1992, Physical review. B, Condensed matter.

[66]  R. Mani,et al.  Inhomogeneous broadening and the breakdown of the quantum Hall effect in GaAs/AlGaAs , 1989 .

[67]  J. S. Blakemore.  Semiconducting and other major properties of gallium arsenide , 1982 .

[68]  M. Buchanan,et al.  Narrow channel breakdown in GaAs/AlGaAs Heterostructures , 1988 .

[69]  F. Sheard,et al.  Size-dependent quantised breakdown of the dissipationless quantum Hall effect in narrow channels , 1986 .

[70]  G. Dorda,et al.  New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance , 1980 .

[71]  L. J. Challis,et al.  Power dissipation in the quantum Hall regime , 1990 .

[72]  S. Kawaji,et al.  Collapse of Quantized Hall Resistance and Breakdown of IQHE in GaAs/AlGaAs Heterostructures , 1998 .

[73]  Shtrikman,et al.  Crossover between different regimes of current distribution in the quantum Hall effect. , 1995, Physical review. B, Condensed matter.

[74]  Quantum Transport in Semiconductor Nanostructures , 2004, cond-mat/0412664.

[75]  T. Klapwijk,et al.  CURRENT CONTACTS AND CURRENT DISTRIBUTION IN THE QUANTUM HALL-EFFECT , 1990 .

[76]  Gudmundsson,et al.  Statistical model for inhomogeneities in a two-dimensional electron gas implying a background density of states between Landau levels. , 1986, Physical review. B, Condensed matter.

[77]  S. Hiyamizu,et al.  Breakdown of the quantum Hall effect due to electron heating , 1985 .

[78]  J. Niemeyer,et al.  A New Quantum Effect in the Transverse Magnetoresistance of Two-Dimensional Conductors with a Narrow Constriction in the Conducting Channel , 1987 .