Programme

O.1 -- Oral, ANSWCCMS-2023

Date: Friday, 10 November 2023

Time: 09:00 - 09:30

Properties of the eigenstates of graphene billiards: A comparison with relativistic and non-relativistic quantum billiards

Barbara Dietz

Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, Korea

We report on tight-binding model based studies of graphene billiards. These are obtained by cutting a hexagonal-lattice sheet to their shape and imposing on the wave-function components at the outer lattice sites along the boundary the Dirichlet condition. One objective was the study of aspects of Quantum Chaos in graphene billiards whose shape coincides with that of a billiard with chaotic classical dynamics [1,2] and in addition has a discrete rotational symmetry [5]. The eigenstates are separated into the associated symmetry classes. Generally, the spectra of graphene billiards can be divided into regions around the band edges, where they are governed by the nonrelativistic Schrödinger equation, and a region of low energy-excitations around zero energy that exhibit a linear dispersion relation and are governed by the relativistic Dirac equation for a spin-1/2 quasiparticle. We analyze the spectral properties in these regions and compare them to those for nonrelativistic and relativistic quantum billiards, respectively. Furthermore, we compute wave functions in configurational space and momentum distributions in quasi-momentum space and find for the latter around zero energy a selective excitation of valley states for the different symmetry classes. Finally, we present an experimental simulation with microwave photonic crystals [1-3,6] of such graphene billiards, or to be more precise, of discrete billiards formed by a combination of a honeycomb and a kagome lattice. [1] B. Dietz, T. Klaus, M. Miski-Oglu, and A. Richter Spectral properties of superconducting microwave photonic crystals modeling Dirac billiards Phys. Rev. B. 91, 035411 (2015) [2] B. Dietz, T. Klaus, M. Miski-Oglu, A. Richter, M. Wunderle, and C. Bouazza Spectral Properties of Dirac Billiards at the van Hove Singularities Phys. Rev. Lett. 116, 023901 (2016) [3] Wulayimu Maimaiti, Barbara Dietz, and Alexei Andreanov Microwave photonic crystals as an experimental realization of a combined honeycomb-kagome lattice Phys. Rev. B 102, 214301 (2020). [5] Weihua Zhang and Barbara Dietz Microwave photonic crystals, graphene, and honeycomb-kagome billiards with threefold symmetry: Comparison with nonrelativistic and relativistic quantum billiards Phys. Rev. B 104, 064310 (2021) [6] Weihua Zhang, Xiaodong Zhang, Jiongning Che, M. Miski-Oglu, and Barbara Dietz Properties of eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry Phys. Rev. B 107, 044308 (2023) , arXiv:2302.10094

Presenter: Barbara Dietz

Presentation file: