Size scaling of the exchange interaction in the quantum Hall effect regime
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In: Physical Review B, Vol. 102.2020, No. 23, 235305, 30.12.2020.
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TY - JOUR
T1 - Size scaling of the exchange interaction in the quantum Hall effect regime
AU - Werner, Daniel
AU - Oswald, Josef
N1 - Publisher Copyright: © 2020 authors. Published by the American Physical Society.
PY - 2020/12/30
Y1 - 2020/12/30
N2 - We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall effect (IQHE) regime in terms of many-body physics at higher Landau levels (LLs). We investigate the dependence of many-particle interactions on the lateral size of the electron system. We use the exchange enhancement of the g-factor for spin-polarized Landau levels as an indicator for the strength of the exchange interaction. The driving force for the g-factor enhancement is a Hund's rule behavior for the occupation of spin-split Landau levels that lowers the many-particle ground state energy by arranging as many spins in parallel as possible. By increasing the total number of electrons and total number of available states per LL, it can therefore be expected that the exchange-enhanced spin gap should increase as well. In contrast to the dependence on the magnetic field, an increase of the total number of states by simply increasing the system size at constant magnetic field shows a clear saturation behavior above a lateral system size of 1000 nm. The importance of this result is underlined by an extended introduction, which demonstrates the permanent dominance of many-body interactions in all transport regimes of the IQHE. A modeling of IQHE systems therefore has to include many-body interactions, and our results open a pathway towards many-body modeling of quantum Hall systems of macroscopic size.
AB - We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall effect (IQHE) regime in terms of many-body physics at higher Landau levels (LLs). We investigate the dependence of many-particle interactions on the lateral size of the electron system. We use the exchange enhancement of the g-factor for spin-polarized Landau levels as an indicator for the strength of the exchange interaction. The driving force for the g-factor enhancement is a Hund's rule behavior for the occupation of spin-split Landau levels that lowers the many-particle ground state energy by arranging as many spins in parallel as possible. By increasing the total number of electrons and total number of available states per LL, it can therefore be expected that the exchange-enhanced spin gap should increase as well. In contrast to the dependence on the magnetic field, an increase of the total number of states by simply increasing the system size at constant magnetic field shows a clear saturation behavior above a lateral system size of 1000 nm. The importance of this result is underlined by an extended introduction, which demonstrates the permanent dominance of many-body interactions in all transport regimes of the IQHE. A modeling of IQHE systems therefore has to include many-body interactions, and our results open a pathway towards many-body modeling of quantum Hall systems of macroscopic size.
KW - 2-Dimensional electron liquid
KW - charge-density-wave
KW - bubble
KW - stripe
UR - http://www.scopus.com/inward/record.url?scp=85099144638&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.102.235305
DO - 10.1103/PhysRevB.102.235305
M3 - Article
AN - SCOPUS:85099144638
VL - 102.2020
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 23
M1 - 235305
ER -