The stabilizer group of honeycomb lattices and its application to deformed monolayers

Abstract

Abstract. Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing graphene or boron nitride. New crystalline arrays with conical (Dirac) points are obtained; in particular, a model for dichalcogenide monolayers is proposed and analyzed. In our studies we encounter unitary and non-unitary transformations. We show that the latter give rise to P T -symmetric Hamiltonians, in compliance with known results in the context of boosted Dirac equations. The results of the unitary part are applied to the description of invariant bandgaps and dispersion relations in materials such as MoS 2 . A careful construction based on atomic orbitals is proposed and the resulting dispersion relation is compared with previous results obtained through DFT.

Exact Green's functions for localized irreversible potentials

“…3. However, it is necessary to work in the quasi-parabolic energy regime that is below the Dirac point [36] ( D ), obtaining the upper graph, a parabola with regions where the Maxwellian potential acts. It is worth mentioning that the region of the potential for p < −P R is not bounded above as in the graph below.…”

Dynamical symmetry in a minimal dimeric complex

“…Microwave resonators [25], bent waveguides with corners [26] and, in general, arrays of potential wells such as molecular structures, motivate the introduction of tight-binding Hamiltonians. We focus on planar arrays with C 3 symmetry for simplicity, although an isospectral study with dimers in three dimensions can be found in [27].…”

Wigner function in the polariton phase space

“…The Wigner function is the tool of choice when it comes to the quantum dynamical description of oscillatory systems in phase space that has been mostly employed with continuous variables such as position and momentum, or time and frequency. Interestingly, conjugate variables can be found also in lattices [4][5][6], where it is advantageous to employ operator methods in order to elucidate dynamical features of tight-binding models [7,8]. Moreover, peculiar connections [9,10] between a discrete position operator and the number of quanta of relativistic oscillators motivate further the definition of Wigner functions in lattices made of excitations.…”