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The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
Quantum many particle systems in which the kinetic energy, strong correlations, and band topology are all important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these…
We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
The Quantum Hall Effects in all even dimensions are uniformly constructed. Contrary to some recent accounts in the literature, the existence of Quantum Hall Effects does not {\it crucially} depend on the existence of division algebras. For…
Quantum Hall system possesses topologically protected edge states which have enormous theoretical and practical implications in both fermionic and bosonic systems. Harnessing the quantum Hall effect in optical platforms with lower…
We perform an experimental test where we directly observe light-induced electron transitions with a macroscopic spatial discontinuity. The effect is related to the fundamental indivisibility of macroscopic orbit-like quantum states…
The correspondence principle bridges the quantum and classical worlds by establishing a direct link between their dynamics. This well-accepted tenant of quantum physics has been explored in quantum systems wherein the number of particles is…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…
Further experiments showed the incorrectness of proposed interpretation. We have studied an in-plane resonant photo-response of an integer quantum Hall system in which time-reversal and parity symmetries are broken. The response of…
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect…
The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but…
Evidence of both fractional and integer quantum hall effects (QHE) in three dimensional bulk replica opal (250nm diameter) structures of non-crystalline carbon are presented. In a remarkably soft quantum limit of ~ 40K temperature and about…
Quantum superposition is normally sustained in a microscopic regime governed by Heisenberg uncertainty principle applicable to a single particle. Quantum correlation between paired particles implies the violation of local realism governed…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram,…
The quantum excitations in glasses have long presented a set of puzzles for condensed matter physicists. A common view is that they are largely disordered analogs of elementary excitations in crystals, supplemented by two level systems…
The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of $e^2/h$. Here we show that the…