Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects

摘要

The fractional quantum Hall effect (FQHE) in the second orbital Landau levelat filling factor 5/2 remains enigmatic and motivates our work. We consider theeffect of the quasi-2D nature of the experimental FQH system on a number of FQHstates (fillings 1/3, 1/5, 1/2) in the lowest, second, and third Landau levels(LLL, SLL, TLL,) by calculating the overlap, as a function of quasi-2D layerthickness, between the exact ground state of a model Hamiltonian and theconsensus variational wavefunctions (Laughlin wavefunction for 1/3 and 1/5 andthe Moore-Read Pfaffian wavefunction for 1/2). Using large overlap as astability, or FQHE robustness, criterion we find the FQHE does not occur in theTLL (for any thickness), is the most robust for zero thickness in the LLL for1/3 and 1/5 and for 11/5 in the SLL, and is most robust at finite-thickness(4-5 magnetic lengths) in the SLL for the mysterious 5/2 state and the 7/3state. No FQHE is found at 1/2 in the LLL for any thickness. We examine theorbital effects of an in-plane (parallel) magnetic field finding itsapplication effectively reduces the thickness and could destroy the FQHE at 5/2and 7/3, while enhancing it at 11/5 as well as for LLL FQHE states. Thein-plane field effects could thus be qualitatively different in the LLL and theSLL by virtue of magneto-orbital coupling through the finite thickness effect.In the torus geometry, we show the appearance of the threefold topologicaldegeneracy expected for the Pfaffian state which is enhanced by thicknesscorroborating our findings from overlap calculations. Our results haveramifications for wavefunction engineering--the possibility of creating anoptimal experimental system where the 5/2 FQHE state is more likely describedby the Pfaffian state with applications to topological quantum computing.