Program

P.15 -- Poster, NCTP-42

Date: Tuesday, 1 August 2017

Time: 16h00 - 17h30

Energy spectra of single-layer graphene quantum rings

Dinh Thi Dieu Linh (1), Nguyen Hai Chau (2) and Nguyen Van Lien (3)

(1) Institute of Physics, VAST, 10 Dao Tan, Ba Dinh Distr., 118011 Hanoi, Vietnam; (2) Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany; (3) Institute for Bio-Medical Physics, 109A Pasteur, 1st Distr., 710115 Hochiminh City, Vietnam

Quantum rings have been originally studied in the physics of metal/semiconductor nanostructures. The ring geometry results in a specific energy spectrum and allows to observe the most basic quantum phenomena such as the Aharonov-Bohm (AB) effect and the related persistent current (i.e. the equilibrium current driven by the magnetic field threading the ring). Graphene, a single layer of carbon atoms in a honeycomb lattice, shows unique electronic properties such as the Dirac-like low-energy spectrum or a very high carrier mobility, providing an effective possibility to probe the quantum phenomena. Indeed, the AB-conductance oscillations have already been observed in different graphene quantum rings (GQRs). Actually, an impressive progress in fabricating GQRs should also lead to equally notable results on the observation of the ring energy spectra and associated dynamical properties. Theoretically, the energy spectra were mainly studied for closed GQRs in the single particle approximation, using either the tight-binding method or the continuum models, where charge carriers are effectively described as massless Dirac fermions. It was shown that the energy spectra strongly depend on the ring geometry and the edge structure. An extensively studied class of GQRs is the circular GQRs (CGQRs) that are created by an axially symmetric confinement potential such as the electrostatic potentials induced by an appropriate gate or a charged scanning tunnelling microscope (STM) tip. Generally, due to the Klein tunnelling, the gate/tip induced electrostatic potentials can confine carriers in just the quasi-bound states (QBSs) with a finite trapping time. Recently, Ref.[1] (J.Phys.:Condens.Matter 2016, 28, 275302; arXiv:1705. 01035) suggested the effective approaches to calculate the QBS-energy spectrum of any structure created by an axially symmetric potential in a continuous graphene sheet. On the one side, the QBS-spectrum can be extracted from the local density of states (LDOS). Each resonance emerged in the LDOS expresses a QBS with the definite resonance position (level) and resonance width. On the other side, one can directly determine the QBS-spectrum by solving the Dirac equation with an outgoing wave boundary condition. Generally, the energy spectrum is then complex: the real part and the imaginary part of a complex energy give, respectively, the resonance level and the resonance width of a QBS. And, in turn, the resonance width of a QBS measures the inverse of its trapping time. These approaches have been successfully applied to calculate the QBS-spectra of different circular graphene quantum dots. This report is aimed at presenting the new results on the QBS-energy spectra of CGQRs that have been calculated using the approaches [1]. Calculations are carried out for the two types of CGQRs created by either a rectangular radial confinement potential or a smooth one. The QBS-spectra are in detail examined in dependence on the ring radius, the ring width, the confinement potential magnitude as well as the mass gap. Obtained results are discussed in comparison to those derived from other CGQR-models and to available experiments.

Presenter: Đinh Thị Diệu Linh