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Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an…
We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a…
Quantum spin-Hall edges are envisaged as next-generation transistors, yet they exhibit dissipationless transport only over short distances. Here we show that in a diffusive sample, where charge puddles with odd spin cause back-scattering, a…
A quantum anomalous Hall (QAH) insulator breaks reciprocity by combining magnetic polarization and spin-orbit coupling to generate a unidirectional transmission of signals in the absence of an external magnetic field. Such behavior makes…
The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single particle picture,…
An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…
Quantum wire networks (``quantum crossbars'', QCB) represent a 2D grid formed by superimposed crossing arrays of parallel conducting quantum wires, molecular chains or metallic single-wall carbon nanotubes. QCB coupled only by capacitive…
We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331…
Fractional quantum Hall (FQH) systems are strongly interacting electron systems with topological order. These systems are characterized by novel ground states, fractionally charged and neutral excitations. The neutral excitations are…
In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and…
Coupled quantum Hall edge channels show intriguing non-trivial modes, for example, charge and neutral modes at Landau level filling factors 2 and 2/3. We propose an appropriate and effective model with Coulomb interaction and…
Microwave absorption spectra of a single square of two-dimensional electrons (2DES) have been investigated using an optical detection technique. Fundamental dipole and harmonic quadrupole plasmon modes have been identified and compared to…
We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This…
We study theoretically the two interacting one-dimensional helical modes at the edges of the quantum spin Hall systems. A new type of inter-edge correlated liquid (IECL) without the spin gap is found. This liquid shows the diverging density…
We propose a quantum stripe (smectic) coupled-Luttinger-liquid model for the anisotropic states which occur in two-dimensional electron systems with high-index partial Landau level filling, $\nu^{*} = \nu - \lbrack\nu\rbrack$. Perturbative…
We investigate the entanglement entropy in the Integer Quantum Hall effect in the presence of an edge, performing an exact calculation directly from the microscopic two-dimensional wavefunction. The edge contribution is shown to coincide…
We study tunneling between two nearby cleaved edge quantum wires in a perpendicular magnetic field. Due to Coulomb forces between electrons, the wires form a strongly-interacting pair of Luttinger liquids. We calculate the low-temperature…
A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based…
We develop a unified theoretical description of the induced interaction and quantum noise in a system of two spins (qubits) coupled via a quasi-one-dimensional electron gas in the Luttinger liquid regime. Our results allow evaluation of the…