Related papers: Duality and Non-linear Response for Quantum Hall S…
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers…
Quantum linear response theory considers only the response of a closed quantum system to a perturbation up to first order in the perturbation. This theory breaks down when the system subjects to environments and the response up to second…
We discuss the possible origin of the duality observed in the quantum Hall current-voltage characteristics. We clarify the difference between "particle-vortex" (complex modular) duality, which acts on the full transport tensor, and…
An existence theory is established for a coupled non-linear elliptic system, known as "vortex equations", describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the…
In the quantum Hall regime, electronic correlations in double-layer two-dimensional electron systems are strong because the kinetic energy is quenched by Landau quantization. In this article we point out that these correlations are…
In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing…
We develop a theory that describes the response of non-reciprocal devices employing 2-dimensional materials in the quantum Hall regime capacitively coupled to external electrodes. As the conduction in these devices is understood to be…
Wave-particle duality, intertwining two inherently contradictory properties of quantum systems, remains one of the most conceptually profound aspects of quantum mechanics. By using the concept of energy capacity, the ability of a quantum…
A recent experiment by Shahar et al, on the phase transitions between quantum Hall states and the insulator, found that the current-voltage characteristics in the two phases are related by symmetry. It was suggested in this work that this…
The traditional quantum control theory focuses on linear quantum system. Here we show the effect of nonlinearity on quantum control of a two-level system, we find that the nonlinearity can change the controllability of quantum system.…
We study nonlinear response of a quantum Hall system in semiconductor-heterostructures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity…
The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(\nu e^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck…
The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where…
In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for rotating fermion…
At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of…
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…
Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can…
We study two-dimensional systems with Galilean invariance gapped under magnetic fields. When such quantum Hall systems are coupled with external sources for charge, energy, and momentum currents, they exhibit invariance under the Milne…
We establish the existence of an exact non-perturbative self-duality in a variety of quantum impurity problems, including the Luttinger liquid or quantum wire with impurity. The former is realized in the fractional quantum Hall effect,…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…