Related papers: Duality and Non-linear Response for Quantum Hall S…
Breaking of inversion symmetry leads to nonlinear and nonreciprocal electron transport, in which the voltage response does not invert with the reversal of the current direction. Many systems have incorporated inversion symmetry breaking…
We study the plateaux of the integer quantum Hall resistance in a bilayer electron system in tilted magnetic fields. In a narrow range of tilt angles and at certain magnetic fields, the plateau level deviates appreciably from the quantized…
We review recent investigations of the femtosecond non-linear optical response of the two-dimensional electron gas (2DEG) in a strong magnetic field. We probe the Quantum Hall (QH) regime for filling factors $\nu \sim 1$. Our focus is on…
Two-dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many- particle ground…
We construct an explicit duality between the interacting quantum Hall system in the lowest Landau level and a non-interacting Landau problem. This is done by absorbing the interaction into the gauge field in the form of an effective…
We dig out a deeper mathematical structure of the quantum Hall system from a perspective of the Langlands program. An algebraic expression of the Hamiltonian with the quantum group is a cornerstone. The Langlands duality of the quantum…
When the chemical potential of an electron system has a discontinuity at a density $n^{*}$, the system is said to be incompressible and a finite energy is required to create mobile charges in the bulk of the system. The quantum Hall effect…
We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other…
Plasmons are fundamental excitations of metals which can be described in terms of electron dynamics, or in terms of the electromagnetic fields associated with them. In this work we develop a quantum description of plasmons in a double layer…
Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states:…
Quantum optical fields offer numerous control knobs which are not available with classical light and may be used for monitoring the properties of matter by novel types of spectroscopy. It has been recently argued that such quantum…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
Linear response methods applied to electron systems often display a level of accuracy which is notable when viewed in terms of the strengths of perturbing interactions. Neglect of higher response terms is in fact justifiable in many cases…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
We consider the influence of an external periodic potential on the fractional quantum Hall effect of two-dimensional interacting electron systems. For many electrons on a torus, we find that the splitting of incompressible ground state…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
We have studied the fractional and integer quantum Hall (QH) effects in a high-mobility double-layer two-dimensional electron system. We have compared the "stability" of the QH state in balanced and unbalanced double quantum wells. The…
We theoretically study the Hall response of a lattice system following a quench where the topology of a filled band is suddenly changed. In the limit where the physics is dominated by a single Dirac cone, we find that the change in the Hall…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which…