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

Abstract

Quantum Hall effects PACS 73.43.Nq -Quantum phase transitions PACS 73.23.-b -Electronic transport in mesoscopic systemsAbstract -We study many-body interaction effects in the spatially-resolved filling factor (ν) distribution for higher Landau levels (LLs) via self-consistent Hartree-Fock simulations in the integer quantum Hall (IQH) regime. Our results indicate a strong, interaction-induced tendency to avoid the simultaneous existence of partially filled spin-up and spin-down LLs. Rather, we find that such partially filled LLs consist of coexisting regions of full and empty LLs. At the boundaries between the regions of full and empty LLs, we observe edge stripes of nearly constant ν close to half filling. This suggests that the exchange interaction induces a behavior similar to a 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 static Thomas-Fermi screening [1]. Our results are consistent with a local, lateral ν dependence of the exchange-enhanced spin splitting. Hence, on quantum-coherent length scales as probed here, the electron system of the IQH effect behaves similar to a non-interacting single particle system -not because of the absence, but rather due to the dominance of many-body effects.

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

“…2 of Ref. 17) we observe strong resistance fluctuations in both, as also expected for QH structures of mesoscopic size. 36 In Fig.…”

“…In Ref. 17, we have shown that the B-dependences of the longitudinal resistance, R xx , and the Hall resistance, R xy , exhibit the expected R xx peaks in the transition regime between QH plateaus and Hall plateaus at zero R xx . In the transition regime between plateaus (cp.…”

“…Reinterpreting our Hartree-Fock results using the language of enhanced g-factors allows us to recover the aforementioned phenomenology. 17 Here, we compare the Hartree-Fock results to Hartree and non-interacting calculations and also present higher temperature effects.…”

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

“…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.…”