Related papers: Geometric and General Relativistic Techniques for …
We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field…
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal…
Starting with the modified Dirac equations for free massive particles with the $\gamma_5$-extension of the physical mass $m\rightarrow m_1 + \gamma_5 m_2$, we consider equations of relativistic quantum mechanics in the presence of an…
Topological physics has broadened its scope from the study of topological insulating phases to include nodal phases containing band structure singularities. The geometry of the corresponding quantum states is described by the quantum metric…
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly.…
We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we…
The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically…
In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
We employ the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms which are subjected to a geometric gauge field created by coupling two…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far…
In this thesis we build a phenomenological, strongly coupled quantum field theory in $2+1$-dimensions through AdS/CFT holography, by building a $3+1$-dimensional, negatively curved gravity theory with a $SU(2)$ gauge field, and a scalar…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
We observe geometric resonance features of composite fermions on the flanks of the even denominator {\nu} = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and…
In this paper, we analyse the quantum coherence behaviors of a single qubit in the relativistic regime beyond the single-mode approximation. Firstly, we investigate the freezing condition of quantum coherence in fermionic system. We also…
In this paper, we investigate the emergence of non-Hermitian phase transitions on a quantum wormhole surface. We consider a single fermion whose dynamics are governed by the Dirac equation confined to move on a quantum wormhole surface. The…
Using first principles calculations, we have demonstrated the creation of multiple quantum states, in the experimentally accessible metal organic framework BHT-Ni. Specifically, quantum spin Hall and quantum anomalous Hall states are…
The quantum geometry, comprising Berry curvature and quantum metric, plays a fundamental role in governing electron transport phenomena in solids. Recent studies show that the quantum metric dipole drives scattering-free nonlinear Hall…
The interplay between quantum geometry and magnetic order offers a novel strategy for designing next-generation nanodevices. Here, we demonstrate that interlayer magnetic coupling in two-dimensional (2D) CoPSe3 bilayers enables precise…