相关论文: High contrast elliptic operators in honeycomb stru…

We decipher the microscopic mechanism of the formation of tilt in the two-dimensional Dirac cone of $8Pmmn$ borphene. In our ab-initio calculations, we identify relevant low-energy degrees of freedom on the $8Pmmn$ lattice and find that…

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice. We investigate the topological properties of a silicene superstructure generated by an external periodic potential. The superstructure is a quantum…

The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished, physically most…

We show that a simplified version of the Dirac interaction operator given by $\hat H_\mathrm{I} \propto \int d\mathbf{k}d\mathbf{p}(\hat a(\mathbf{k}) + \hat a^\dagger(-\mathbf{k})) \hat b^\dagger(\mathbf{p} + \mathbf{k}) \hat…

Twisted bilayer graphene (TBG) hosts nearly flat bands with narrow bandwidths of a few meV at certain {\em magic} twist angles. Here we show that in twisted gapped Dirac material bilayers, or massive twisted bilayer graphenes (MTBG),…

Using density functional theory calculations including an on-site Coulomb term, we explore electronic and possibly topologically nontrivial phases in $3d$ transition metal oxide honeycomb layers confined in the corundum structure…

We consider the unperturbed operator $H_0: = (-i \nabla - {\bf A})^2 + W$, self-adjoint in $L^2({\mathbb R}^2)$. Here ${\bf A}$ is a magnetic potential which generates a constant magnetic field $b>0$, and the edge potential $W = \bar{W}$ is…

It is shown that the symmetry enforced Dirac points exist at some time reversal symmetric momenta in antiferroemgnetic compound GdB$_4$. These Dirac points may be controlled by the external magnetic field or by the deformation of the…

A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a…

An analytic description of high harmonic generation (HHG) in solids induced by intense low-frequency pulses is presented within an adiabatic approach, which treats laser-matter interactions nonperturbatively. We derive the analytical…

The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a…

We propose that the noncentrosymmetric LiGaGe-type hexagonal $ABC$ crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. The symmetry-protected Dirac points arise due to a band…

We investigate the effect of an in-plane AC electric field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points…

We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Dirichlet boundary condition in non-Lipschitz domains $\widetilde{\Omega} \subset \mathbb C$. The suggested method is…

Hexagonal Boron Nitride substrates have been shown to dramatically improve the electric properties of graphene. Recently, it has been observed that when the two honeycomb crystals are close to perfect alignment, strong lattice distortions…

We theoretically reexamine nearly uniform electron models with weak crystalline potentials. In particular, we theorize the modulation of the plane-wave branches at linear regions where multiple Bragg planes intersect. Any such linear…

In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim…

The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain…

We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking…

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…