Related papers: Higher (Odd) Dimensional Quantum Hall Effect and E…
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to novel…
Monolayer (ML) semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure -- just like graphene -- facilitates gate-tunability, while the sizable…
A topological theory of d-wave superconductors is derived in this thesis. Ginzburg-Landau theory describes superconductivity by defining a complex order parameter and applying Landau's theory for phase transitions. However, there is no…
The effect of an Aharonov-Bohm (AB) pseudo magnetic field on a two dimensional electron gas in graphene is investigated. We consider it modeled as in the usual AB effect but since such pseudo field is supposed to be induced by elastic…
We report here a systematic study of the energy gaps at the odd-integer quantum Hall states $\nu=3$ and 5 under tilted magnetic (B) fields in a high quality Si two-dimensional electron system. Out of the coincidence region, the valley…
The quantum Hall regime in a smooth random potential is considered when two disorder-broadened Zeeman levels overlap strongly. Spin-orbit coupling is found to cause a drastic change in the percolation network which leads to a strong…
Quantum oscillations offer a powerful probe for the geometry and topology of the Fermi surface in metals. Onsager's semiclassical quantization relation governs these periodic oscillations in 1/B, leading to a linear Landau fan diagram.…
We theoretically study the Hall effect on interacting $M$-leg ladder systems, comparing different measures and properties of the zero temperature Hall response in the limit of weak magnetic fields. Focusing on $SU(M)$ symmetric interacting…
One-dimensional (1D) quasicrystals exhibit physical phenomena associated with the 2D integer quantum Hall effect. Here, we transcend dimensions and show that a previously inaccessible phase of matter --- the 4D integer quantum Hall effect…
An inaccuracy of composite fermion model is identified for Landau level fillings out of 1/p, p odd. The corrected version of hierarchy for fractional quantum Hall effect is proposed by mapping onto integer effect within the cyclotron braid…
Quantum Hall (QH) states are predicted to display an intriguing non-dissipative stress response to a shear deformation rate, a phenomenon variously known as asymmetric or Hall viscosity, or Lorentz shear response. Just as the QH effect…
We derive an effective two-dimensional Hamiltonian to describe the low energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase $2\pi$. Its…
Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question…
We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a…
Recent experiments on the twisted semiconductor bilayer system $t$MoTe$_2$ have observed integer and fractional quantum anomalous Hall effects, which occur in topological moir\'e bands at zero magnetic field. Here, we present a global phase…
Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field form degenerate energy bands, the Landau levels. We discuss the unitary correspondence between states in higher Landau levels and those in the lowest Landau level,…
We describe the lowest Landau level of a quantum electron star in AdS4. In the presence of a suitably strong magnetic field, the dynamics of fermions in the bulk is effectively reduced from four to two dimensions. These two-dimensional…
We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies (1/3, 2/5, 3/7 ...; 1/5, 2/9, 3/13, ..., etc.) found experimentally. The construction…
We numerically study a 5/2 fractional quantum Hall system with even number of electrons using the exact diagonalization where both the strong Landau level (LL) mixing and a finite width of the quantum well have been considered and adapted…
We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the…