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Double-layer quantum Hall systems at total filling factor $\nu_T=1$ can exhibit a commensurate-incommensurate phase transition driven by a magnetic field $B_{\parallel}$ oriented parallel to the layers. Within the commensurate phase, the…
We investigate the spin-1/2 twisted three-leg antiferromagnetic quantum spin tube in the presence of the easy-plane anisotropy, using the numerical diagonalization of finite-size clusters. And we observe cases of the existence and the…
Direct transitions, driven by disorder, from several integral quantum Hall states to an insulator have been observed in experiment. This finding is enigmatic in light of a theoretical phase diagram, based on rather general considerations,…
We consider electron systems in quantum dots and imaging of the confined charge density by the Coulomb blockade microscopy (CBM) with the scanning probe technique. We apply an exact diagonalization method to study the reaction of the…
We study tunneling through an edge state formed around an antidot in the fractional quantum Hall regime using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. We identify a new regime where the Aharonov-Bohm…
We study an anisotropic cubic Dirac semi-metal subjected to a constant magnetic field. In the case of an isotropic dispersion in the $x$-$y$ plane, with parameters $v_{x}=v_{y}$, it is possible to find exact Landau levels, indexed by the…
Thermodynamic and electric properties of anisotropic compressible Hall states at higher Landau levels are studied using a mean field theory on the von Neumann lattice basis. It is shown that resistances agree with the recent experiments of…
The magnetization curve of the $(S,s)=(1,1/2)$ ferrimagnetic alternating spin chain with the single-ion anisotropy $D$ is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a…
As a high mobility two-dimensional semiconductor with strong structural and electronic anisotropy, atomically thin black phosphorus (BP) provides a new playground for investigating the quantum Hall (QH) effect, including outstanding…
Using variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy--state diagram of small quantum dots is studied in the magnetic field range where the density of magnetic flux quanta just exceeds the…
We consider quantum spin Hall effect in an anisotropic strip of stripes and address both integer and fractional filling factors. The first model is based on a gradient of spin-orbit interaction in the direction perpendicular to the stripes.…
In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/\phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $\phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the…
We develop a long wavelength approximation in order to describe the low-energy states of carbon nanotubes in a transverse magnetic field. We show that, in the limit where the square of the magnetic length $l = \sqrt{\hbar c /e B}$ is much…
We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias…
We use the dynamical structure factors of the quantum Hall states at $\nu=1/3$ and $\nu=1/2$ in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the…
A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it has been challenging to probe the zeroth Landau level due to large electron-hole puddles…
We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy…
We demonstrate experimentally that the transitions between adjacent integer quantum Hall (QH) states are equivalent to a QH-to-insulator transition occurring in the top Landau level, in the presence of an inert background of the other…
In this work, we argue that an anisotropic interaction potential may stabilize anisotropic liquid phases of electrons even in a strong magnetic field regime where normally one expects to see only isotropic quantum Hall or isotropic Fermi…
The zeroth Landau level (0LL) in graphene has emerged as a flat-band platform in which distinct many-body phases can be explored with unprecedented control by simply tuning the strength and/or direction of magnetic fields1-22. A rich set of…