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The nature of the fractional quantum Hall effect at $\nu=1/2$ observed in wide quantum wells almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the…
A many-particle Hamiltonian is proposed in order to explain the fractional quantum Hall effect (FQHE) for fractional filling factors $\nu < 1$. The solutions of the corresponding Hartree-Fock equations make it possible to discuss the FQHE…
The Integer Quantum Hall Effect (IQHE) is a distinctive phase of two-dimensional electronic systems subjected to a perpendicular magnetic field. Thus far, the IQHE has been observed in semiconductor heterostructures and in mono- and…
The warping effect on the fractional quantum Hall (FQH) states in topological insulators is studied theoretically. Based on the perturbed wavefunctions, which include contributions from the warping term, analytical expressions for Haldane's…
In certain backgrounds string theory exhibits quantum Hall-like behavior. These backgrounds provide an explicit realization of the effective non-commutative gauge theory description of the fractional quantum Hall effect (FQHE), and of the…
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…
Quantized anomalous Hall effects (QAHEs) occur in remarkable electronic states which possess not only quantized Hall signals but in some cases regions of dissipationless electron transport. The initial demonstrations of a QAHE in a…
We report complex magnetotransport patterns of the $\nu=1$ integer quantum Hall state in a GaAs/AlGaAs sample from the newest generation with a record high electron mobility. The reentrant integer quantum Hall effect in the flanks of the…
We analyse various microscopic properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic FQHE to be robust.…
We study finite temperature ($T$) properties of the continuum quantum field theory of systems with a ferromagnetic ground state. A scaling theory of the $T=0$ system is discussed carefully, and its consequences for crossovers between…
We studied the unusual Quantum Hall Effect (QHE) near the charge neutrality point (CNP) in high-mobility graphene sample for magnetic fields up to 18 T. We observe breakdown of the delocalized QHE transport and strong increase in…
We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges…
The fractional quantum Hall (FQH) effect is reported in a high mobility CdTe quantum well at mK temperatures. Fully-developed FQH states are observed at filling factor 4/3 and 5/3 and are found to be both spin-polarized ground state for…
HgTe quantum wells with a thickness of ${\sim}$7 nm may have a graphene-like band structure and have been recently proposed to be potential candidates for quantum Hall effect (QHE) resistance standards under the condition of operation in…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero…
We have measured the temperature (0.1 <= T <= 15 K) and magnetic field (0 <= B <= 12 T) dependences of longitudinal and Hall resistivities for the p-Ge_0.93Si_0.07/Ge multilayers with different Ge layer widths 10 <= d_w <= 38 nm and hole…
We present a supersymmetric description of the quantum Hall effect (QHE) in graphene. The noninteracting system is supersymmetric separately at the so-called K and K' points of the Brillouin zone corners. Its essential consequence is that…
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…
We examine the application of $c=1$ conformal field theory to the description of the fractional quantum Hall effect (FQHE). It is found that the Gaussian model together with an appropriate boundary condition for the order parameter…