Related papers: Invariants of disordered semimetals via the spectr…
Specific types of spatial defects or potentials can turn monolayer graphene into a topological material. These topological defects are classified by a spatial dimension $D$ and they are systematically obtained from the Hamiltonian by means…
We study the level-statistics of a disordered system undergoing the Anderson type metal-insulator transition. The disordered Hamiltonian is a sparse random matrix in the site representation and the statistics is obtained by taking an…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
Raman spectroscopy is a valuable characterization tool for two-dimensional materials. Starting from model Hamiltonians for Chern insulators and magnetized monolayers of transition metal dichalcogenides, we theoretically predict two…
We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and…
We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
We study low-frequency linearly-polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride), and topological (Dirac- and Weyl-semimetals), properties. In Dirac-like linearly-dispersing bands, the laser…
The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the…
We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a $4 \times 4$ matrix and six types of…
The surfaces of three dimensional topological insulators (3D TIs) are generally described as Dirac metals, with a single Dirac cone. It was previously believed that a gapped surface implied breaking of either time reversal $\mathcal T$ or…
We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet…
We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by…
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…
The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top…
An odd Fredholm module for a given invertible operator on a Hilbert space is specified by an unbounded so-called Dirac operator with compact resolvent and bounded commutator with the given invertible. Associated to this is an index pairing…
Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of…
We show that a class of weak three-dimensional topological insulators feature one-dimensional Dirac electrons on their surfaces. Their hallmark is a line-like energy dispersion along certain directions of the surface Brillouin zone. These…