Related papers: Laughlin states on higher genus Riemann surfaces
The observation of the fractional quantum Hall (FQH) effect in 2D electron gases ushered in investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary…
The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in…
The intriguing re-entrant integer quantized Hall states recently discovered in high Landau levels of high-mobility 2D electron systems are found to exhibit extremely non-linear transport. At small currents these states reflect insulating…
The ability to pump quantised amounts of charge is one of the hallmarks of topological materials. An archetypical example is Laughlin's gauge argument for transporting an integer number of electrons between the edges of a quantum Hall…
We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in…
We consider fractional quantum Hall states built on Laughlin's original N-body wave-functions, i.e., they are of the form holomorphic times gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear…
We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly,…
We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case…
Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite…
We evaluate the transport gaps in the most prominent fractional quantum Hall states in the $\mathbf{n}{=}0$ and $\mathbf{n}{=}1$ Landau Levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body…
By the method of intense terahertz laser spectroscopy, we provide strong evidence that if an integer quantum Hall (IQH) system has asymmetric confining potential and the external quantizing magnetic field has a nonzero in-plane component,…
Cyclotron braid subgroups are defined in order to identify the topological origin of Laughlin correlations in 2D Hall systems. Flux-tubes and vortices for composite fermion constructions are explained in terms of unavoidably multilooped…
The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron…
Here we present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $\nu=1/3$ fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring…
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct…
We study hard core bosons on a two leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength…
Landau level bending near the edge of graphene, described using 2d Dirac equation, provides a microscopic framework for understanding the quantum Hall Effect (QHE) in this material. We review properties of the QHE edge states in graphene,…
The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy…
The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the…
Transport properties of bilayer quantum Hall systems at $\nu=1/q$, where $q$ is an odd integer, are investigated. The edge theory is used for the investigation, since tunneling between the two layers is assumed to occur on the edge of the…