Quantum Hall Valley Nematics

Abstract

Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantum Hall physics links charge conduction to topological defects. We discuss how these combine to yield a rich phase structure, and their implications for transport and spectroscopy measurements. In parallel, we discuss relevant experimental systems. We close with an outlook on future directions.

28 pages, 5 figures. Invited review article; comments welcome

References in corpus (23)

• Intra-Landau level Cyclotron Resonance in Bilayer Graphene
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Low-temperature, in situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator
• Observation of Quantum Hall Valley Skyrmions
• Angle dependence of the orbital magnetoresistance in bismuth
• Nematic Valley Ordering in Quantum Hall Systems
• Valley polarization and susceptibility of composite fermions around nu=3/2
• Theory of Nematic Fractional Quantum Hall State
• Integer quantum Hall effect on a six valley hydrogen-passivated silicon (111) surface
• Transference of Transport Anisotropy to Composite Fermions
• Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer graphene
• Dependence of spin susceptibility of a two-dimensional electron system on the valley degree of freedom
• Thermodynamic evidence for valley-dependent density of states in bulk bismuth
• Density dependence of valley polarization energy for composite fermions
• Imaging anyons with scanning tunneling microscopy
• Interacting multi-channel topological boundary modes in a quantum Hall valley system
• Multivalley two-dimensional electron system in an AlAs quantum well with mobility exceeding $2\times 10^6$ cm${}^2$V${}^{-1}$s${}^{-1}$
• Composite Fermions with a Warped Fermi Contour
• Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference
• Temperature-dependent transport in a sixfold degenerate two-dimensional electron system on a H-Si(111) surface
• Anisotropic composite fermions and fractional quantum Hall effect
• Spontaneous symmetry breaking of magnetostriction in metals with multi-valley band structure

Cited by in corpus (14)

• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Microscopic Model for Fractional Quantum Hall Nematics
• Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν = 1 Landau Level Crossing
• Boundary conductance in macroscopic bismuth crystals
• Spin Reversal of a Quantum Hall Ferromagnet at a Landau Level Crossing
• Gully quantum Hall ferromagnetism in biased trilayer graphene
• Interaction between interface and massive states in multivalley topological heterostructures
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Topology- and symmetry-protected domain wall conduction in quantum Hall nematics
• Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
• Local Probes for Quantum Hall Ferroelectrics and Nematics
• Variational wavefunctions for fractional topological insulators
• Spontaneous Breaking of the SU(3) Flavor Symmetry in a Quantum Hall Valley Nematic
• Renormalization group analysis of weakly interacting van der Waals Fermi system