相关论文: On Brillouin Zones

We construct a Wannier basis for twisted bilayer graphene that is projected only from the Bloch functions of the twisted bilayer flat bands. The $C_3$ and $C_{2} \mathcal{T}$ symmetries act locally on the Wannier functions while the Wannier…

We study the topological gap labeling of general 3D quasicrystals and we find that every gap in the spectrum is characterized by a set of the third Chern numbers. We show that a quasi-periodic structure has multiple Brillouin zones defined…

Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work…

A dynamical theory of hypersurface deformations is presented. It is shown that a (n+1)-dimensional space-time can be always foliated by pure deformations, governed by a non zero Hamiltonian. Quantum deformations states are defined by…

The b-boundary is a mathematical tool used to attach a topological boundary to incomplete Lorentzian manifolds using a Riemaniann metric called the Schmidt metric on the frame bundle. In this paper, we give the general form of the Schmidt…

A tight-binding model for $e_g$ orbitals on a simple cubic lattice with finite thickness is investigated. The hopping integrals for nearest-neighboring sites are considered. We examine the electronic band structures for systems with (001),…

We introduce a new class of moir\'e systems and materials based on monolayers with triangular lattices and low-energy states at the M points of the Brillouin zone. These M-point moir\'e materials are fundamentally distinct from those…

A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In…

We show that for a stratum of projectivized abelian differentials with sufficiently many simple zeroes, the inclusion into the appropriate moduli space of pointed curves induces an injection at the level of orbifold fundamental group,…

Zone diagram is a variation on the classical concept of a Voronoi diagram. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a…

A mechanical diamond, a classical mechanics of a spring-mass model arrayed on a diamond lattice, is discussed topologically. Its frequency dispersion possesses an intrinsic nodal structure in the three-dimensional Brillouin zone (BZ)…

We extend the construction of Garsia-Rodemich spaces in different directions. We show that the new space \textbf{B,} introduced by Bourgain-Brezis-Mironescu \cite{bbm}, can be described via a suitable scaling of the Garsia-Rodemich norms.…

We prove a simple identity relating the length spectrum of a Riemann surface to that of the same surface with an arbitrary number of additional cusps. Our proof uses the Brownian loop measure introduced by Lawler and Werner. In particular,…

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…

The classical Liouville theorem states that a bounded harmonic function on all of $\RR^n$ must be constant. In the early 1970s, S.T. Yau vastly generalized this, showing that it holds for manifolds with nonnegative Ricci curvature.…

Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group.…

Quantum geometry strongly impacts physical properties in flat-band systems. We consider its role in bosonic condensation and superfluidity on flat bands, and show that the superfluid weight has an important contribution proportional to the…

Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type…

Using transition-metal dichalcogenides as an example, we show that the quantum interference arising in two- and three-photon absorption processes can lead to controllable, highly localized carrier distributions in the Brillouin zone. We…

We generalize the classical Blaschke Rolling Theorem to convex domains in Riemannian manifolds of bounded sectional curvature and arbitrary dimension. Our results are sharp and, in this sharp form, are new even in the model spaces of…