Related papers: Flat Midgap Topological Surface and Hypersurface B…
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood systems in complex surfaces, and use these to study various notions of convexity and concavity. Every tame, topologically embedded 2-complex…
A three-dimensional strong-topological-insulator or -semimetal hosts topological surface states which are often said to be gapless so long as time-reversal symmetry is preserved. This narrative can be mistaken when surface state…
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the height. When the weight has at most quadratic…
We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.
Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the…
We report on microscopic tight-binding modeling of surface states in Bi$_2$Se$_3$ three-dimensional topological insulator, based on a sp$^3$ Slater-Koster Hamiltonian, with parameters calculated from density functional theory. The effect of…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
Inspired by the discovery of superconductivity in moir\'e materials with isolated narrow bandwidth electronic bands, here we analyze critically the question of what is the maximum attainable $T_c$ in interacting flat-band systems. We focus…
In this Letter, we introduce a paradigm to realize magneto-mechanical metastructures inspired by multi-layer 2D materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts.…
We study the effects of the Coulomb interactions between electrons on the Hofstadter butterfly, which characterizes the subband structure of the Landau levels of a two-dimensional electron gas in a perpendicular homogeneous magnetic field…
We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the…
Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that…
In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission properties. Specifically, the reflection and…
We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a…
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based…
This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff…
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well…
Recent interest in point and line node semimetals has led to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range…