 Award ID(s):
 1904497
 NSFPAR ID:
 10339016
 Date Published:
 Journal Name:
 Communications Physics
 Volume:
 4
 Issue:
 1
 ISSN:
 23993650
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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We report complex magnetotransport patterns of the ν = 1 integer quantum Hall state in a GaAs/AlGaAs sample from the newest generation with a record high electron mobility. The reentrant integer quantum Hall effect in the flanks of the ν = 1 plateau indicates the formation of the integer quantum Hall Wigner solid, a collective insulator. Moreover, at a fixed filling factor, the longitudinal resistance versus temperature in the region of the integer quantum Hall Wigner solid exhibits a sharp peak. Such sharp peaks in the longitudinal resistance versus temperature so far were only detected for bubble phases forming in high Landau levels but were absent in the region of the Anderson insulator. We suggest that in samples of sufficiently low disorder, sharp peaks in the longitudinal resistance versus temperature traces are universal transport signatures of all isotropic electron solids that form in the flanks of integer quantum Hall plateaus. We discuss possible origins of these sharp resistance peaks and we draw a stability diagram for the insulating phases in the νT phase space.more » « less

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of twodimensional systems have shown evidence for Wigner crystals2,3,4,5,6,7,8,9,10,11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use highresolution scanning tunnelling microscopy measurements to directly image a magneticfieldinduced electron WC in Bernalstacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zeropoint motion of electrons in the WC lattice.more » « less

The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in manybody condensed matter physics. Among the numerous FQHSs, those observed at evendenominator Landau level filling factors are of particular interest as they may host quasiparticles obeying nonAbelian statistics and be of potential use in topological quantum computing. The evendenominator FQHSs, however, are scarce and have been observed predominantly in lowdisorder twodimensional (2D) systems when an excited electron Landau level is half filled. An example is the wellstudied FQHS at filling factor
$\mathit{\nu}\mathbf{=}$ 5/2 which is believed to be a BardeenCooperSchrieffertype, paired state of fluxparticle composite fermions (CFs). Here, we report the observation of evendenominator FQHSs at$\mathit{\nu}\mathbf{=}$ 3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahighquality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as evendenominator FQHSs of CFs, emerging from pairing of higherorder CFs when a CF Landau level, rather than an electron or a hole Landau level, is halffilled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for evendenominator FQHSs, and suggest the realization of FQHSs with nonAbelian anyons. 
This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the ν = 2/5 phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream and may support either charge or chargeneutral excitations. From topological considerations, particlelike QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counterpropagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particlelike phases at ν = 1, 1/3, and 2/5 as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorderinduced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases and could explain the absence of anyonic interference in electronic MachZehnder setups.

We investigate the homogeneous chiral edge theory of the filling ν = 4 / 3 fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge 2 e 3 chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each conserved charge and momentum sector, indicating the existence of hidden conserved quantities and the possibility that the generic edge theory of the ν = 4 / 3 fractional quantum Hall state is integrable. We further show that a global symmetry preserving irrelevant nonlinear kinetic term will lead to the transition of LSS from Poisson to WignerDyson at high energies. This further supports the possibility that the model without irrelevant terms is integrable.more » « less