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 -