Tohru Okamoto

Hall electric field-dependent broadening of extended state bands in Landau levels and breakdown of the quantum Hall effect

Current dependence of activation energy has been measured in the diagonal resistance of two standard butterfly-type Hall bars and a butterfly-type Hall bar with a short and narrow channel in the central part made from GaAs/AlGaAs heterostructures. The activation energy EA in each sample decreases with increasing current and is expressed by EA=EA0−aelBFH where EA0=ℏωC/2 at the plateau center for i=2 and 4, a=38±8, lB is the radius of the ground Landau orbit and FH the Hall electric field. The result suggests that broadening of extended state bands in Landau levels due to the Hall electric field give rise to the magnetic field dependence of the critical Hall electric field, Fcr∝B3/2, obtained in various butterfly-type Hall bars.

Metal–insulator transition and spin degree of freedom in Silicon 2D electron systems

Abstract Magnetotransport in 2DESs formed in Si-MOSFETs and Si/SiGe quantum wells at low temperatures is reported. Metallic temperature dependence of resistivity is observed for the n-Si/SiGe sample even in a parallel magnetic field of 9 T, where the spins of electrons are expected to be polarized completely. Correlation between the spin polarization and minima in the diagonal resistivity observed by rotating the samples for various total strength of the magnetic field is also investigated.

Collapse of quantized Hall resistance and breakdown of dissipationless state in the integer quantum Hall effect: filling factor dependence

Abstract Magnetic field dependence of critical current for collapse of quantized Hall resistance I cr (collapse) and critical current for breakdown of dissipationless state I cr (breakdown) have been measured near the filling factor ν =4 of Landau levels in a GaAs/AlGaAs heterostructure Hall bar. The difference I cr (breakdown)− I cr (collapse) decreases against the increase and the decrease in ν from 4 and the critical behavior disappears outside of the region 3.85 ν

Magnetic field dependence of the device-width-dependent breakdown current in the quantum Hall effect

Abstract Magnetic field dependence of the device-width-dependent breakdown current in the quantum Hall effect is measured in magnetic fields up to 23 T at 0.5 K for GaAs/AlGaAs Hall bars having a total length of 2900 micrometer, a source- and drain-electrode width of 400 micrometer and different widths 10, 20 and 35 micrometer in its central 600 micrometer long part. Results are explained in terms of localization in Landau levels without edge-state transport.

Collapse of quantized Hall resistance at high Hall electric fields

Abstract Collapse of quantized Hall resistance (QHR) – steep deviation of Hall resistance from the quantized value – at high Hall electric fields has been observed in butterfly-type Hall bars made from GaAs/AlGaAs heterostructures. The collapse is not caused by breakdown of quantum Hall effect (QHE) – abrupt increase in dissipation in the QHE state. A phenomeno-logical model for the collapse of the QHR and the breakdown of the QHE is discussed.

Magnetism in a Wigner solid and Aharonov–Bohm effect

Abstract Thermal activation energy EA in an insulation phase of a two-dimensional electron system formed in an Si inversion layer has been studied. All the results which depend both on total strength Btot and normal component B⊥ of a magnetic field are quantitatively explained by a model based on exchange interactions in a Wigner solid (rs∼8). We attribute the observed peculiar B⊥-dependence of EA in which two minima appear at B⊥≈0.6Nsφ0 and B⊥≈1.1Nsφ0 for φ0=h/e to the Aharonov–Bohm effect on the three-electron ring exchange interaction of which exchange constant is in the same order as that from the multidimensional WKB calculation of Roger (Phys. Rev. B 30 (1984) 6432).

Transport Properties of the Half-Filled Landau Level in GaAs/AlGaAs Heterostructures: Temperature Dependence of Electrical Conductivity and Magnetoresistance of Composite Fermions

The fractional quantum Hall effect (FQHE) was discovered at the Landau level filling factor of ν=1/3 in two-dimensional electron systems of GaAs/AlGaAs heterostructures in 1982 by Tsui, Stormer and Gossard [1]. For FQHE at ν=1/(2m+1), where m is an integer, Laughlin proposed trial states describing highly correlated quantum liquids, which provide a good description of FQHE at these filling factors [2]. Later on, higher quality heterostructures have experimentally made it possible to observe FQHE at ν=n/2mn+1) for integer n. Jain proposed an elegant explanation for FQHE at the filling factor ν=n/(2mn+1) by introducing new quasi-particles, called composite fermions (CFs) [3]. A CF is a composite particle comprising an electron and an even number, 2m, of flux quanta o0=h/e. In this picture, the integer quantum Hall effect (IQHE) of the CFs with 2m flux quanta corresponds to FQHE at ν=n/(2mn+1) as follows. The inverse of the filling factor ν–1=2m+n –1 is given by the number of available flux quanta per electron. However, 2m flux quanta are already a part of the CFs. Therefore, in the CF picture, the number of available flux quanta, excluding the gauge flux which is a part of the CFs, is n –1 per CF. Thus the CF state at the filling factor n is equivalent, in a mean field sense, to the electron state at the filling factor ν=n/(2mn+1). Following a similar procedure, Halperin, Lee and Read [4] developed a theory for the state at exactly half filling.

Collapse of the quantum Hall state by floating-up of extended-state bands with increasing disorder

We measured the diagonal and Hall conductivities across the transition between the integer quantum Hall effect state and the insulating state in a two-dimensional electron system formed in Si-MOSFETs. Sample dependence of the transition indicates that the insulating state is caused by Anderson localization due to disorder, not by a formation of an electron solid.