相关论文: Evolution from Landau Quantization to Discrete Sca…

The raise of the symmetry breaking mechanism by Landau[1] is a landmark in the studies of phase transitions. The Kosterlitz-Thouless phase transition[2-3] and the fractional quantum Hall effect[4], however, are believed to be induced by…

We have investigated the fractional quantum Hall states for the Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of the electrons in the graphene significantly…

When two or more energy bands become degenerate at a singular point in the momentum space, such singularity, or ``Dirac points", gives rise to intriguing quantum phenomena as well as unusual material properties. Systems at the Dirac points…

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…

It is revealed that in a relativistically degenerate dense highly-magnetized electron-ion plasma the effective quantum-potential due to the total quantum-force acting on fermions may cancel-out causing a quantum transverse collapse in the…

Two-dimensional Dirac semimetals with a single massless Dirac cone exhibit the parity anomaly. Usually, such a kind of anomalous topological semimetallic phase in real materials is unstable where any amount of disorder can drive it into a…

We have studied the quantum oscillations in the conductivity of metallic, p-type Bi$_2$Se$_{2.1}$Te$_{0.9}$. The dependence of the oscillations on the angle of the magnetic field with the surface as well as the Berry phase determined from…

The realization of synthetic gauge fields for charge neutral ultracold atoms and the simulation of quantum Hall physics has witnessed remarkable experimental progress. Here, we establish key signatures of fractional quantum Hall systems in…

Among the most interesting predictions in two-dimensional materials with a Dirac cone is the existence of the zeroth Landau level (LL), equally filled by electrons and holes with opposite chirality. The gapless edge states with helical spin…

The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of two-dimensional massless Dirac fermions. At finite magnetic fields, the parity anomaly reveals itself as a non-zero…

BiSbTeSe$_2$ is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low temperature surface transport in this material is heralded by…

We explore topological transitions in the type of propagation of surface electromagnetic modes in massive anisotropic tilted Dirac systems. The presence of tilting and mass gives rise to an indirect band gap that strongly modifies the joint…

Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking…

The recent experimental observations of the quantum Hall effect in 3D topological semimetals have attracted great attention, but there are still debates on its origin. We systematically study the dependence of the quantum Hall effect in…

Quantum sensing of meV-scale scattering and absorption of impinging particles with electrons in solid state detectors is a challenging technological advancement with the potential to enable breakthroughs in quantum information applications…

In this brief review, we survey the problem of electrostatic confinement of massless Dirac particles, via a number of exactly solvable one- and two-body models. By considering bound states at zero energy, we present a route to obtain truly…

Two-dimensional systems in magnetic fields host rich physics, most notably the quantum Hall effect arising from Landau level quantization. In a broad class of two-dimensional models, flat bands with topologically nontrivial band…

We use a recently developed kinetic model derived from the Dirac equation, in order to study electromagnetic wave propagation in superstrong magnetic fields, such as in magnetars, where relativistic Landau quantization is prominent. The…

The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. Topological insulators…

Discrete fermionic and bosonic models for hyperbolic lattices have attracted significant attention across a range of fields since the experimental realization of hyperbolic lattices in metamaterial platforms, sparking the development of…