相关论文: Band representation, band connectivity and irreduc…
A quadratic band crossing (QBC) is a crossing of two bands with quadratic dispersion, which has been intensively investigated due to its appearance in Bernal-stacked bilayer graphene. Here, we study an extension of QBCs, the triply…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
A general symmetry-controlled mechanism is proposed for realizing dual flat-bands of bound state in the continuum (BIC) and its radiative counterpart in photonic crystal slabs. By breaking the vertical mirror symmetry of slab,…
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…
Understanding how to optimize electronic band structures for thermoelectrics is a topic of long-standing interest in the community. Prior models have been limited to simplified bands and/or scattering models. In this study, we apply more…
We investigate optimal band structures in band-converged systems to achieve high zT using numerical calculations based on a virtual spectral conductivity model. We consider a two parabolic band system, in which multiple band parameters can…
For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…
Let L be a Schroedinger operator with periodic magnetic and electric potentials, a Maxwell operator in a periodic medium, or an arbitrary self-adjoint elliptic linear partial differential operator in R^n with coefficients periodic with…
Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological…
Motivated by recent experiments demonstrating the creation of atomically sharp interfaces between hexagonal sapphire and cubic SrTiO$_3$ with finite twist, we here develop and study a general electronic band theory for this novel class of…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the…
Twisted bilayer graphene (TBG) can host the moir\'{e} energy flat bands with two-fold degeneracy serving as a fruitful playground for strong correlations and topological phases. However, the number of degeneracy is not limited to two.…
Topology plays an important role in non-hermitian systems. How to characterize a non-hermitian topological system under open-boundary conditions(OBCs) is a challenging problem. A one-dimensional(1D) topological invariant defined on a…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
It is proved that for general, not necessarily periodic quasi one dimensional systems, the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial…
It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states…
We develop an approach to design, engineer, and measure band structures in a synthetic crystal composed of electric circuit elements. Starting from the nodal analysis of a circuit lattice in terms of currents and voltages, our Laplacian…
We show that topological frequency band structures emerge in two-dimensional electromagnetic lattices of metamaterial components without the application of an external magnetic field. The topological nature of the band structure manifests…
A band is a semigroup in which each element is idempotent. In recent years, there has been a lot of activity on the representation theory of the subclass of left regular bands due to connections to Markov chains associated to hyperplane…