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arXiv:1805.00805 · Chinese Physics B

Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing: A numerical investigation

Lin-Peng Yang, Qi Li, Zi-Xiang Hu

Published Aug 1, 2018• 6 citations
arXivHTMLPDF

Abstract

By exactly solving the effective two-body interaction for two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopotentials (PPs) without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall (FQH) states both in the lowest Landau level (LLL) and first Landau level (1LL). The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values. While the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.

DOI
10.1088/1674-1056/27/8/087306

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By exactly solving the effective two-body interaction for two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopotentials (PPs) without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall (FQH) states both in the lowest Landau level (LLL) and first Landau level (1LL). The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values. While the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.
We investigated the behavior of fractional quantum Hall (FQH) states in a two-dimensional electron system with layer thickness and an in-plane magnetic field. Our comparisons across various filling factors within the first Landau level revealed a crucial observation. A slight in-plane magnetic field specifically enhances the nematic order of the ν=7/3ν= 7/3ν=7/3 FQH state. For this particular filling, through calculating the energy gap, the Ising nematic order parameter, the pair-correlation function, and the static structure factor, we observed that as the in-plane magnetic field increases, the system first enters into an anisotropic FQH phase without closing the spectrum gap, then the FQH nematic (FQHN) phase after neutral gap closing. The system eventually enters a gapless one-dimensional charge density wave (CDW) phase for a large in-plane field. We thus provide a full phase diagram of the ν=7/3ν= 7/3ν=7/3 state in a tilted magnetic field, demonstrating the existence of the FQHN, which aligns with recent resonant inelastic light scattering (RILS) experimental observations.
The $\ensuremath{\nu}=5/2$ fractional quantum Hall effect is a system of intense experimental and theoretical interest as its ground state may host non-Abelian excitations, but the exact nature of the ground state is still undetermined. We present the results of an exact diagonalization study of an electron system in the disk configuration, including the effects of Landau level (LL) mixing and the finite thickness of the quantum well confining the electrons. The degeneracy between the two leading candidates for the ground state, the Pfaffian and anti-Pfaffian, is broken by interactions with a neutralizing background, in addition to the inclusion of two- and three-body interactions via LL mixing. As a result of the neutralizing background in the disk configuration, there is a phase transition from the anti-Pfaffian to the Pfaffian as LL mixing is turned on, in stark contrast to what is observed in spherical geometry. This behavior is in agreement with existing experiments, showing the appearance of the Pfaffian state at strong LL mixing before the system enters a compressible phase. The inclusion of LL mixing leads to an increased charge e/4e/4e/4 quasihole size. LL mixing interactions are also shown to overcome the effects of edge reconstruction. Due to finite thickness effects, these properties are enhanced dramatically. We also find that only the Pfaffian and anti-Pfaffian states continue to possess energy gaps at finite width, while gaps for compressible stripe states close, which is in agreement with available experimental data.
The discovery of the quantum Hall effect in 1980 opened to physics one of the simplest systems for studying many-body correlations. Numerical techniques and trial wavefunctions have proven useful for describing the novel collective behavior of the electrons, but have not fully explained all features of the fractional quantum Hall effect. For example, it is predicted that Landau level mixing should have a moderate effect on the system for all but the very strongest magnetic fields, but this effect has not been extensively studied. Among the tools most useful to modeling and describing the quantum Hall system is the Haldane pseudopotential, which is the energy of electron pairs as a function of their coupled total angular momentum. Because the pseudopotential uniquely determines the correlative behaviors in the quantum Hall system, the study of the pseudopotential is particularly important. In this dissertation I will first derive novel analytic expressions for the pair interactions and the pseudopotential using the techniques of angular momentum algebra. Then, I will use these results to numerically determine the effect of Landau level mixing on the pair pseudopotentials.
The fractional quantum Hall (FQH) nematic state is a conjectured state of matter in which FQH topological order coexists with spontaneously broken rotation symmetry. Recent experiments on GaAs quantum wells suggest this state, as well as the concomitant isotropic-nematic phase transition, may be realized in a two-dimensional electron gas at certain rational filling factors. Although effective field theories of the FQH nematic state have been constructed, there has been so far no explicit realization of this state as the ground state of a microscopic model of interacting electrons. The authors show via a variational approach and numerical exact diagonalization that tuning Haldane pseudopotentials in a model of interacting electrons in the lowest Landau level induces a quantum phase transition out of the isotropic Laughlin FQH liquid and into the FQH nematic state.
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with the combinatorial summation (CoS) algorithm, we obtain results with controlled accuracy for the microscopic model of interacting electrons in the lowest Landau level (LLL) in the thermodynamic limit. Starting from the macroscopically degenerate LLL at finite temperature, including interactions order by order, and applying a controlled resummation to the resulting series, we observe the emergence of the incompressible 1/3-filled state as the temperature is lowered. By analysing the long-time decay of the Green's function, we find spectral properties consistent with an energy gap at 1/3-filling, whereas at 1/2-filling our results are consistent with the pseudogapped behaviour previously observed experimentally and suggested theoretically. Our work provides the first demonstration that fractionalised phases of matter can be reliably described with Feynman's diagrammatic technique in terms of the fundamental electronic degrees of freedom, while also showing applicability of expansions in the bare Coulomb potential for precision calculations.
We compare ground-state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point via the finite-thickness effect and direct alterations to the the first two Haldane pseudopotentials. In the comparison we find that in the LLL, either the 331 state or the MR Pfaffian may be lower in energy depending on the deviations. In the SLL, however, the MR Pfaffian is consistently lower in energy except for large deviations. These results suggest that even under moderate deviations in the interaction potential (through various physical processes such as finite thickness, Landau-level mixing, etc.), the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half-filled SLL (i.e., $\ensuremath{\nu}=5/2$), consistent with recent experimental investigations.