Abstract
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories.
Highlights
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated
The mutual relation between the integer quantized Hall effect[1] (IQHE) and topology is intensively investigated during the last decades theoretically[2,3,4,5]
Salient features of the integer quantized Hall effect1 (IQHE) are the precise Hall conductance measured as integer multiples of the conductance quanta e2/h (e is the elementary charge and h is the Planck constant) accompanied by zero longitudinal resistance at certain magnetic field intervals
Summary
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. To probe whether the bulk remains incompressible one can impose an external AC current excitation between the inner contacts and measure the potential difference as a function of magnetic field B. In contrast to the above single-particle description of the IQHE, it has been proposed that the direct Coulomb interaction modifies the electronic distribution and the bulk becomes compressible within the plateau, that is, the bulk behaves like a metal with a high TDOS at EF (refs 9–11) In this situation, the incompressible states (commonly called strips) reside at the edges of the sample, due to a similar level bending of the Landau levels. Complementary information and discussion are given in Supplementary Notes 1–8
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