Publisher：Physical Review B  

Recent experiments on pentalayer rhombohedral graphene moiré superlattices have observed the quantum anomalous Hall effect at a moiré filling factor of ν=1 and various fractional values. These phenomena are attributed to a flat Chern band induced by electron-electron interactions. In this study, we demonstrate that at ν=2, many-body effects can lead to the emergence of quantum spin Hall and quantum valley Hall states, in addition to the quantum anomalous Hall state, even in the absence of spin-orbit coupling or valley-dependent potentials. These three topological states can be selectively induced by the application and manipulation of a magnetic field. Furthermore, we show that at ν=3 and 4, the ground state can be a combination of topologically trivial and nontrivial states, unlike the cases of ν=1 and 2. This contrasts with the conventional quantum Hall effect in graphene where the ground state at filling factor ν is given as the particle-hole counterpart at 4-ν.

DOI： 10.1103/PhysRevB.110.245135

Web of Science

Scopus

Publisher：Physical Review B  

Quantum-Hall-superconductor hybrids have been predicted to exhibit various types of topological order, providing possible platforms for intrinsically fault-tolerant quantum computing. In this paper, we investigate disorder effects on the Rashba-coupled quantum-Hall system combined with the type-II superconductor. By diagonalizing the Bogoliubov-de Gennes Hamiltonian projected into a Rashba-coupled Landau level, we demonstrate the emergence of a topological superconducting phase resulting from disorders and proximity-induced pairing. Distinctive gapless modes appear in the real-space entanglement spectrum, which is consistent with topological superconductivity. Historically, the spherical geometry has been commonly used for identifying topologically ordered states, especially quantum-Hall physics, due to its compact and contractible nature. Motivated by this, we develop a formulation to construct this hybrid system on a sphere. Our numerical demonstrations are all performed on the spherical geometry.

DOI： 10.1103/PhysRevB.110.035147

Web of Science

Scopus

Language：English   Publishing type：Research paper (scientific journal)  

Publisher：Physical Review B  

Although a parent Hamiltonian for the Laughlin 1/3 wave function has been long known in terms of the Haldane pseudopotentials, no parent Hamiltonians are known for the lowest-Landau-level projected wave functions of the composite fermion theory at n/(2n+1) with n≥2. If one takes the two lowest Landau levels to be degenerate, the Trugman-Kivelson interaction produces the unprojected 2/5 wave function as the unique zero energy solution. If the lowest three Landau levels are assumed to be degenerate, the Trugman-Kivelson interaction produces a large number of zero energy states at ν=3/7. We propose that adding an appropriately constructed three-body interaction yields the unprojected 3/7 wave function as the unique zero energy solution and report extensive exact diagonalization studies that provide strong support to this proposal.

DOI： 10.1103/PhysRevB.108.085130

Web of Science

Scopus

Publisher：Physical Review B  

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction (V3Pf) between electrons confined to the lowest Landau level provides exact solutions for quasiholes, and thereby allows a proof of principle for the existence of quasiholes obeying non-Abelian braid statistics. We construct, in terms of two- and three-body Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for both quasiholes and quasiparticles, and provide evidence of non-Abelian statistics for the latter as well. The structure of the quasiparticle states of this model is in agreement with that predicted by the bipartite composite-fermion model of quasiparticles. We further demonstrate, for systems for which exact diagonalization is possible, adiabatic continuity for the ground state, the ordinary neutral excitation, and the topological exciton as we deform our model Hamiltonian continuously into the lowest Landau-level V3Pf Hamiltonian.

DOI： 10.1103/PhysRevB.107.115163

Scopus

Language：English   Presentation type：Oral presentation (general)  

Venue：Minneapolis   Country：United States  

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：東北大学   Country：Japan  

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan