Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field

Abstract

We analytically derived the effective two-body interaction for a finite thickness quantum Hall system with a harmonic perpendicular confinement and an in-plane magnetic field. The anisotropic effective interaction in the lowest Landau level (LLL) and first Landau level (1LL) are expanded in the basis of the generalized pseudopotentials (PPs), and we analyze how the coefficients of some prominent isotropic and anisotropic PPs depend on the thickness of the sample and the strength of the in-plane magnetic field. We also investigate the stability of the topological quantum Hall states, especially the Laughlin state and its emergent guiding center metric, which we can now compute analytically. An interesting reorientation of the anisotropy direction of the Laughlin state in the 1LL is revealed, and we also discuss various possible experimental ramifications for this quantum Hall system with broken rotational symmetry.

arXiv comment14 pages, 10 figures, comments very welcome

References in corpus (36)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Observation of the Fractional Quantum Hall Effect in Graphene
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Rapidly Rotating Atomic Gases
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Geometrical Description of the Fractional Quantum Hall Effect
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Evidence for a fractional quantum Hall state with anisotropic longitudinal transport
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect
• Landau Level Mixing in the Perturbative Limit
• Generalized Quantum Hall Projection Hamiltonians
• Microscopic theory of the quantum Hall hierarchy
• Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field
• Theory of unconventional quantum Hall effect in strained graphene
• Composite Fermions with Tunable Fermi Contour Anisotropy
• Fractional quantum Hall effect in a tilted magnetic field
• Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
• Density Induced Interchange of Anisotropy Axes at Half-Filled High Landau Levels
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Geometric construction of Quantum Hall clustering Hamiltonians
• Quantum Hall effects in fast rotating Fermi gases with anisotropic dipolar interaction
• Reorientation of quantum Hall stripes within a partially filled Landau level
• Enhancement of the $\nu =5/2$ Fractional Quantum Hall State in a Small In-Plane Magnetic Field
• Anisotropy Driven Transition from Moore-Read State to Quantum Hall Stripes
• Composite fermions in bands with N-fold rotational symmetry

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• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Viscoelastic response of quantum Hall fluids in a tilted field
• Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking
• Geometry of flux attachment in anisotropic fractional quantum Hall states
• Resolving Hall and dissipative viscosity ambiguities via boundary effects
• Phase transition and intrinsic metric of the dipolar fermions in quantum Hall regime
• Interaction-dependent anisotropy of fractional quantum Hall states
• Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: robustness of activation gaps
• The behavior of the fractional quantum Hall states in the LLL and 1LL with in-plane magnetic field and Landau level mixing: a numerical investigation
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Collective excitations of quantum Hall states under tilted magnetic field
• Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Anisotropy of the hydrostatic stress for Hall droplets with in-plane magnetic field