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

Abstract

We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall (IQH) regime in terms of many-body physics at higher Landau levels (LL). The results exhibit a strong tendency to avoid the simultaneous existence of partly filled spin-up and spin-down LLs. Partly filled LLs appear as a mixture of coexisting regions of full and empty LLs. We obtain edge stripes with approximately constant filling factor ν close to half-odd filling at the boundaries between the regions of full and empty LLs, which we explain in terms of the g-factor enhancement as a function of a locally varying ν across the compressible stripes.The many-particle interactions follow a behaviour as it would result from applying Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to screening based on a Thomas-Fermi approximation. For addressing carrier transport, we use a non-equilibrium network model (NNM) that handles the lateral distribution of the experimentally injected non-equilibrium chemical potentials µ. PACS numbers: 73.43.-f, 73.43.Nq, 73.23.-b arXiv:1707.01364v1 [cond-mat.mes-hall] 5 Jul 2017 which allows seamless integration to the self-consistent Hartree-Fock approach of section II A (here ν denotes SUPPORTING INFORMATION

Revision of the edge channel picture for the integer quantum Hall effect

“…Therefore the potential fluctuations are preserved like assumed by the early models neglecting e-e interaction and using them to explain the creation of a channel network like proposed by Chalker and Coddington 21 and frequently used also by others 22,23 . However, as explained earlier 16,17 , in our case the channels consist of the cluster boundaries visible as green colored stripes in Fig. 2b.…”

“…In this paper, we focus on the theoretical foundations of the scaling theory and the CSG theory, that have been successfully justified many times [7][8][9][10][11][12][13][14] although they seem to rest on conflicting theoretical foundations 15 . In recent papers we argue that both pictures can only coexist on the basis of many body interactions [15][16][17][18] . Werner et al have shown that many body interactions are almost completely captured within a system of size 1000 × 1000nm 15 .…”

“…We use a Hartree-Fock approach as explained in previous work [16][17][18][19] , where we have shown that the keymechanism dictating the electron system is a Hund's rule behaviour for the occupation of the spin-split LLs. The resulting g-factor enhancement appears as an almost local quantity depending on the local filling factor.…”

“…This strongly modifies the screening behaviour and can even result in an effective overall attractive potential. It creates bubbles and stripes in ultra clean samples 18 , or it results in the formation of clusters of full and empty spin-split LLs that are triggered by disorder and the edge potential 16,17 . The boundaries of those clusters finally create narrow channels that align along the edge or the random potential fluctuations.…”

“…We also addressed non-equilibrium transport using the non-equilibrium network model (NNM) as introduced earlier 26 and explained repeatedly 16,27 . Fig.…”