Tunable interactions and phase transitions in Dirac materials in a magnetic field

Abstract

A partially filled Landau level (LL) hosts a variety of correlated states of matter with unique properties. The ability to control these phases requires tuning the effective electron interactions within a LL, which has been difficult to achieve in GaAs-based structures. Here we consider a class of Dirac materials in which the chiral band structure, along with the mass term, gives rise to a wide tunability of the effective interactions by the magnetic field. This tunability is such that different phases can occur in a single LL, and phase transitions between them can be driven in situ. The incompressible, Abelian and non-Abelian, liquids are stabilized in interaction regimes different from GaAs. Our study points to a realistic method of controlling the correlated phases and studying the phase transitions between them in materials such as graphene, bilayer graphene, and topological insulators.

4 pages, 3 figures; supersedes earlier version

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• Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level
• Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
• Tunable Fractional Quantum Hall Phases in Bilayer Graphene
• Even denominator fractional quantum Hall state in bilayer graphene
• Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene
• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Fractional Quantum Hall Phase Transitions and Four-flux Composite Fermions in Graphene
• Odd- and even-denominator fractional quantum Hall states in monolayer WSe${}_2$
• Spin-helical transport in normal and superconducting topological insulators
• Fractional and integer quantum Hall effects in the zeroth Landau level in graphene
• Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• New Dirac points and multiple Landau level crossings in biased trilayer graphene
• Competing Fractional Quantum Hall and Electron Solid Phases in Graphene
• Fractional quantum Hall effect in a tilted magnetic field
• Landau level splittings, phase transitions, and non-uniform charge distribution in trilayer graphene
• Importance of interband transitions for the fractional quantum Hall effect in bilayer graphene
• Interaction-induced insulating state in thick multilayer graphene
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States
• Composite fermion pairing induced by Landau level mixing
• Universality of Quantum Phase Transitions in the Integer and Fractional Quantum Hall Regimes
• Evidence for a topological "exciton Fermi sea" in bilayer graphene
• Tunability of the Fractional Quantum Hall States in Buckled Dirac Materials
• Bootstrapping the Quantum Hall problem
• Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions
• Multiple crossing of Landau levels of two-dimensional fermions in double HgTe quantum wells
• Competing Laughlin state and Wigner crystal in bilayer graphene
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Numerical studies of the fractional quantum Hall effect in systems with tunable interactions
• Quantum Hall ferroelectric helix in bilayer graphene
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid