Related papers: Fractional Quantum Hall Effect in Topological Flat…
Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor $\nu=2+4/9$, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown…
Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic…
We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they may well capture the topological behavior…
Exact diagonalization of a two-dimensional electron gas in a strong magnetic field in the disk geometry shows that there exists a filling factor range in the second Landau level where the states significantly differ from those in the lowest…
When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particl es called `composite…
Narrow band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy fermion systems, and topological phases such as fractional quantum Hall…
For various two dimensional lattices such as honeycomb, kagome, and square-octagon, gauge conventions (string gauge) realizing minimum magnetic fluxes that are consistent with the lattice periodicity are explicitly given. Then many-body…
We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that…
The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far…
We study a 1D lattice Hamiltonian, relevant for a wide range of interesting physical systems like, e.g., the quantum-Hall system, cold atoms or molecules in optical lattices, and TCNQ salts. Through a tuning of the interaction parameters…
The quantum anomalous Hall (QAH) effect is a topologically nontrivial phase, characterized by a non-zero Chern number defined in the bulk and chiral edge states in the boundary. Using first-principles calculations, we demonstrate the…
While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual…
We observe geometric resonance features of composite fermions on the flanks of the even denominator {\nu} = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and…
The fractional quantum Hall effect (FQHE) is studied in the semiclassical limit in the framework of the Hofstadter model with a short-range interaction between fermions. In the mean-field approximation, the repulsion between fermions leads…
Topological transports of fermions are governed by the Chern numbers of the energy bands lying below the Fermi energy. For bosons, e.g. phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest…
We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar…
Recent experiments on bilayer graphene twisted near the magic angle have observed spontaneous integer quantum Hall states in the presence of an aligned hexagonal boron nitride (hBN) substrate. These states arise from valley ferromagnetism,…
Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for…
The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of high Chern number QAH effect in…
We consider fractional quantum Hall states in systems where two flat Chern number $C=\pm 1$ bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor $\nu=1$ this setting…