The local nature of incompressibility of quantum Hall effect

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.

Manifestation of many-body interactions in the integer quantum Hall effect regime

“…Furthermore, a very recent investigation of the local nature of compressibility in the bulk of a IQH sample strongly challenges existing single-particle theories. 13 A major step towards modelling electron-electron interactions in the QH is due to Chklovskii, Shklovskii and Glazman (CSG) who considered screening via the electrostatics of the edge channel region. 14 The key feature of their model is the different screening capabilities of partly and fully filled LLs that appear in alternating order towards the edge depletion zone of the electronic system.…”

Exchange-mediated dynamic screening in the integer quantum Hall effect regime

“…Their results fit even more closely to a system of non-interacting single carriers. On the other hand, a recent investigation of the local nature of compressibility in the bulk of a IQHE sample strongly challenges existing single-particle theories [14]. Such results raise the question whether many-particle effects are indeed effectively absent in the IQHE regime, or, quite opposite, whether they are responsible for implying the physics of almost noninteracting single particles.…”

Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor

“…It was shown that the interplay between quantum mechanics and electrostatics leads to the emergence of compressible and incompressible stripes, a concept related, yet somehow different, to the original edge states. An important effort has been devoted to the experimental observation of these stripes [10][11][12][13][14][15][16][17][18][19][20]. CSG work, as well as a large fraction of the subsequent litterature [21][22][23][24][25][26][27][28][29][30] was based on the Thomas-Fermi approximation which is suitable at high magnetic field but inadequate at low field where the LB approach is expected to work well.…”