S. Chen, et al., “Competing Fractional Quantum Hall and Electron Solid Phases in Graphene”, PHYSICAL REVIEW LETTERS, vol. 122, p. 026802, 2019.Abstract
We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N = 2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.
K. Yang, Goerbig, M. O., and Doucot, B., “Hamiltonian theory for quantum Hall systems in a tilted magnetic field: Composite-fermion geometry and robustness of activation gaps”, PHYSICAL REVIEW B, vol. 98, p. 205150, 2018.Abstract
We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the z direction, the parallel component of the magnetic field introduces anisotropy into the effective two-dimensional interactions. The effects of such anisotropy can be effectively captured by the recently proposed generalized pseudopotentials. We find that the off-diagonal components of the pseudopotentials lead to mixing of composite fermions Landau levels, which is a perturbation to the picture of p filled Landau levels in composite-fermion theory. By changing the internal geometry of the composite fermions, such a perturbation can be minimized and one can find the corresponding activation gaps for different tilting angles, and we calculate the associated optimal metric. Our results show that the activation gap is remarkably robust against the in-plane magnetic field in the lowest and first Landau levels.