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Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms ($W$-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on…
Physics of two-dimensional electron gases under perpendicular magnetic field often displays three distinct stages when increasing the field amplitude: a low field regime with classical magnetotransport, followed at intermediate field by a…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the…
The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a…
We present magnetotransport measurements of a strongly hybridized inverted InAs/GaSb double quantum well. We find that the spin-orbit interaction leads to an appreciable spin-splitting of hole-like states, which form distinct Landau levels…
Landau levels in certain models are known to protrude into the zero-field energy gap. These are known as anomalous Landau levels (ALLs). We study whether ALLs can lead to Fermi-surface like quantum oscillation in the absence of a zero-field…
We investigate the interplay of disorder and interaction in two-dimensional electron systems in a strong magnetic field, focusing on the transition between Wigner crystals and fractional quantum Hall liquids. We first study classical Wigner…
We investigate the quantum Hall problem in the lowest Landau level in two dimensions, in the presence of an arbitrary number of $\delta$-function potentials arranged in different geometric configurations. When the number of delta functions…
We investigate theoretically the fractional quantum Hall effect at half-filling in the lowest Landau level observed in asymmetric wide quantum wells. The asymmetry can be achieved by a potential bias applied between the two sides of the…
Controlling topological phases is a central goal in quantum materials and related fields, enabling applications such as robust transport and programmable edge states. Here we uncover a mechanism in which local on-site impurities act as…
"Topological ordered" phases such as gapped quantum spin-liquids and fractional quantum Hall states possess ground state degeneracy on a torus. We show that the topological nature of this degeneracy has interesting consequences for the…
Fully taking into account of the honeycomb lattice structure, fractional quantum Hall states of graphene are considered by a pseudopotential projected into the n = 0 Landau band. By using a chirality as an internal degree of freedom, the…
The quest for universal signatures of topological phases is fundamentally important since these properties are robust to variations in system-specific details. Here we present general results for the response of quantum Hall states to…
We investigate the topological insulating states of the $p$-band systems in optical lattices induced by the onsite orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises…
The fractional quantum Hall state at Landau level (LL) filling factor 5/2 is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be…
We observe fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $\nu=1/2$ in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50 nm and having bilayer-like charge distributions.…
Dynamical Hall conductivity {\sigma}_H({\omega}) of a 2D electron gas with impurities in the perpendicular magnetic field is analyzed. Plateau-like behavior at low frequencies as well as at high frequencies provided the complete filling of…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
The geometric response of quantum Hall liquids is an important aspect to understand their topological characteristics in addition to the electromagnetic response. According to the Wen-Zee theory, the topological spin is coupled to the…