Related papers: Upper bound of a band complex
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…
In this note, we obtain an upper bound on the maximum number of distinct non-empty palindromes in starlike trees. This bound implies, in particular, that there are at most $4n$ distinct non-empty palindromes in a starlike tree with three…
Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are…
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…
The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed…
We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.
A subset of the Hamming cube over $n$-letter alphabet is said to be $d$-maximal if its diameter is $d$, and adding any point increases the diameter. Our main result shows that each $d$-maximal set is either of size at most $(n+o(n))^d$ or…
A two-dimensional electron gas in a static external magnetic field exhibits two distinct collective excitation modes. The lower frequency mode propagates along the periphery of the domain almost freely with an extended lifetime, which is…
An infinitary version of braid groups has been considered as a direct limit of n-braid groups. However, we can imagine more complicated braids with infinitely many strings. We invetisgate basic properties especially when the number of…
By studying connectedness at infinity of systolic groups we distinguish them from some other classes of groups, in particular from the fundamental groups of manifolds covered by euclidean space of dimension at least three. We also study…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of…
In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries.…
The properties of electrons in magnetically ordered crystals are of interest both from the viewpoint of realizing novel topological phases, such as magnetic Weyl semimetals, and from the applications perspective of creating energy-efficient…
One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
We construct a simple model for electrons in a three-dimensional crystal where a combination of short-range hopping and spin-orbit coupling results in nearly flat bands characterized by a non-trivial Z2 topological index. The flat band is…
We prove an upper bound for the number of cyclic transitive subgroups in a finite permutation group and clarify the structure of the groups for which this bound becomes sharp. We also give an application in the theory of number fields.