Hsiao, Wei-Han | Search NASA

DOE OSTI2020

Landau quantization of multilayer graphene on a Haldane sphere

Here, we consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary nonrelativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current toolkits of the numerical studies on fractional quantum Hall effects in systems of graphite multilayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Self-dual ν = 1 bosonic quantum Hall state in mixed-dimensional QED

Here, we consider a (2 + 1)-dimensional Wilson-Fisher boson coupled to a (3 + 1)-dimensional U(1) gauge field. This theory possesses a strong-weak duality in terms of the coupling constant e and is self-dual at a particular value of $\mathcal{e}$. We derive exact relations between transport coefficients for a $\mathcal{ν}$ = 1 quantum Hall state at the self-dual point. Using boson-fermion duality, we map the $\mathcal{ν}$ = 1 bosonic quantum Hall state to a Fermi sea of the dual fermion and observe that the exact relationships between transport coefficients at the bosonic self-dual point are reproduced by a simple random-phase approximation (RPA), coupled with a Drude formula, in the fermionic theory. We explain this success of the RPA by pointing out a cancellation of a parity-breaking term in the fermion theory which occurs only at the self-dual point, resulting in the fermion self-dual theory explored previously. In addition, we argue that the equivalence of the self-dual structure can be understood in terms of electromagnetic duality or modular invariance, and these features are not inherited by the nonrelativistic cousins of the present model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗