A New Quantum Effect in the Transverse Magnetoresistance of Two-Dimensional Conductors with a Narrow Constriction in the Conducting Channel

Observation and an explanation of breakdown of the quantum Hall effect

“…But we propose that the nearly dissipationless conduction channel is very narrow in our samples as the critical current is approached, and that the conduction channel becomes entirely pinched-off and dissipative above the critical current. Our samples therefore may have effective geometries similar to those of Bliek et al [ 5 ] near breakdown. We assume the global current-carrying equipotentials of the percolation model [ 6 ], as strongly suggested by experiments which measured the potential distribution across quantum Hall devices [ 7 ].…”

“…The current density J x =I x /L y =E y /( h /4 q 2 ) varies between 240–600 A/m. This is an astonishingly large number compared with that found in [ 5 ], but the current has a better opportunity of finding a dissipationless path in wide high-quality samples. Also, qV H ≈ 200 ℏω c .…”

“…We make an initial attempt to interpret our observations by using a modified version of the QUILLS model of Eaves and Sheard [ 4 ] because that is a model which seems to provide a satisfactory explanation. Eaves and Sheard used their model to interpret the experimental data of Bliek et al [ 5 ] who made breakdown measurements on GaAs/AlGaAs samples in which Hall potential probe sets were placed on either side of a 1 μ m wide constriction. Their V x vs B curves show features similar to our data, and their Hall voltages were also quantized.…”

Spectroscopic study of quantized breakdown voltage states of the quantum Hall effect

“…Field Figure 1 shows two sweeps of Vx (4,6) versus the magnetic field B for the i =2 (12,906.4 fl) quantized Hall resistance plateau at a temperature of 0.33 K and a current I of + 220 jxA, where positive current corresponds to electrons entering the source and exiting the drain. This current is approaching the 227 [lA critical current value above which, in this magnetic field region, Vx is non-zero for these particular potential probes.…”

Evidence that voltage rather than resistance is quantized in breakdown of the quantum Hall effect

“…It could be, however, that it is the longitudinal resistance R x that is quantized, rather than V x , since R x = V x / I x . Indeed, Bliek et al [ 10 ] assumed a quantized R x in a phenomenological model to explain breakdown structures in their curves of V x versus B for samples with narrow constrictions. Also, although not quantized, Sachrajda et al [ 11 ] assumed magnetic field and current dependent resistive channels along the sample to explain their breakdown data.…”