Related papers: Four-Dimensional Quantum Hall Effect with Ultracol…
Two-dimensional (2D) silicon carbide is an emergent direct band-gap semiconductor, recently synthesized, with potential applications in electronic devices and optoelectronics. Here, we study nuclear quantum effects in this 2D material by…
We propose an experimental scheme to probe the contribution of a single Dirac cone to the Hall conductivity as half-odd topological number sequence. In our scheme, the quantum anomalous Hall effect as in graphene is simulated with cold…
We review our recent theoretical works on the the quantum spin Hall effect. First we compare edge states in various 2D systems, and see whether they are robust or fragile against perturbations. Through the comparisons we see the robust…
Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion,…
Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
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…
The quantum Hall effect (QHE) with quantized Hall resistance of h/{\nu}e2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing…
We explore the critical properties of a topological transition in a two-dimensional, amorphous lattice with randomly distributed points. The model intrinsically breaks the time-reversal symmetry without an external magnetic field, akin to a…
The recent discoveries about topological insulators have been promoting theoretical and experimental research. In this dissertation, the basic concepts of topological insulators and the Quantum Hall Effect are reviewed focusing the…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
Studies of ultracold atoms in optical lattices link various disciplines, providing a playground where fundamental quantum many-body concepts, formulated in condensed-matter physics, can be tested in much better controllable atomic systems,…
When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are…
The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical…
We investigate an interplay between quantum geometrical effects and surface plasmons through surface plasmonic structures, based on an electron hydrodynamic theory. First we demonstrate that the quantum nonlinear Hall effect can be…
We present a theoretical framework to describe the integer quantum Hall effect (IQHE) in three-dimensional (3D) electron systems. This extends our previous single-electron approach, which was successfully applied to two-dimensional (2D)…
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as…
Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an…
Atomic vapors can be prepared and manipulated at very low densities and temperatures. When they are rotating, they can reach a quantum Hall regime in which there should be manifestations of the fractional quantum Hall effect. We discuss the…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics…