Related papers: Thomas Precession, Berry potential and the Meron
A general and beautiful picture for the realization of topological insulators is that the mass term of the Dirac model has a nodal surface wrapping one Dirac point. We show that this geometric picture based on Dirac points can be…
We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows…
The planar phase of superfluid $^3$He has Dirac points in momentum space and the analog of Dirac monopole in the real space. Here we discuss the combined effect of Dirac point and Dirac monopole. It is shown that in the presence of the…
Two different aspects of parabolic iteration in the complex upper half-plane are considered here. First, from a noncommutative probability perspective, a Berry-Esseen type estimate for the convergence speed of the monotone central limit…
Nonlinear Hall effect arises in materials without inversion symmetry, and the intrinsic contribution is typically from Berry curvature dipole of non-universal Fermi pockets. Here we propose that nonlinear Hall effect can reach quantization…
In this paper we prove a conjecture of Hershel Farkas that if a 4-dimensional principally polarized abelian variety has a vanishing theta-null, and the hessian of the theta function at the corresponding point of order two is degenerate, the…
We investigate a spatially flat Friedmann-Lema\^itre-Robertson-Walker cosmology in which a decaying vacuum term causes matter production at late times. Assuming a decay proportional to the Hubble rate, the ratio of the background energy…
We show that a general $n$-dimensional polarized abelian variety $(A,L)$ of a given polarization type and satisfying $ h^0(A, L) \geq \dfrac{8^n}{2} \cdot \dfrac{n^n}{n !}$ is projectively normal. In the process, we also obtain a sharp…
We show that the position-momentum duality offers a transparent interpretation of the band geometry at the topological band crossings. Under this duality, the band geometry with Berry connection is dual to the free-electron motion under…
A matrix Berry phase can be generated and detected by {\it all electric means} in II-VI or III-V n-type semiconductor quantum dots by changing the shape of the confinement potential. This follows from general symmetry considerations in the…
We introduce both an exactly solvable model and a coupled-layer construction for an exotic, three-dimensional phase of matter with immobile topological excitations that carry a protected internal degeneracy. Unitary transformations on this…
Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective…
The response of electrons under linearly polarized light in Dirac materials as borophene or graphene is analyzed in a continuous wave regime for an arbitrary intense field. Using a rotation and a time-dependent phase transformation, the…
A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the the missing…
Generalized Dirac monopoles in momentum space are constructed in even d+1 dimensions from the Weyl Hamiltonian in terms of Green's functions. In 3+1 spacetime dimensions, the (unit) charge of the monopole is equal to both the winding number…
Based on the analogy with non-minimal SU(2) symmetric Wu-Yang monopole with regular metric, the solution describing a non-minimal U(1) symmetric Dirac monopole is obtained. In order to take into account the curvature coupling of…
The band geometric properties of quantum materials play an elemental role in the linear and nonlinear transport of electrons. In this paper, we propose that the interplay of the Berry curvature, the orbital magnetic moment and the Lorentz…
Noncentrosymmetric metals are anticipated to exhibit a $dc$ photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing…
We consider Dirac quasi-particles, as realized with cold atoms loaded in a honeycomb lattice or in a $\pi$-flux square lattice, in the presence of a weak correlated disorder such that the disorder fluctuations do not couple the two Dirac…
We point out that unitary representations of the Virasoro algebra contain Berry phases obtained by acting on a primary state with conformal transformations that trace a closed path on a Virasoro coadjoint orbit. These phases can be computed…