On the density of states of circular graphene quantum dots

Abstract

We suggest a simple approach to calculate the local density of states that effectively applies to any structure created by an axially symmetric potential on a continuous graphene sheet such as circular graphene quantum dots or rings. Calculations performed for the graphene quantum dot studied in a recent scanning tunneling microscopy measurement [Gutierrez et al. Nat. Phys. 12, 1069-1075(2016] show an excellent experimental-theoretical agreement.

Quantitative study of electronic whispering gallery modes in electrostatic-potential induced circular graphene junctions

“…Importantly, both the potentials in eqs.2 and 3 become constant in the two limits of small and large distances, r ≤ r i and r ≥ r f , that would somewhat facilitate the LDOS-computations [20]. In particular case of U g ≡ 0, these potentials U (r) of eqs( 2) and (3) seem to have the ordinary trapezoidal profiles.…”

“…Given U (r), we computed LDOSs for the studied resonator, using the approach suggested in Refs. [19,20](see Supplementary Materials). Shortly, the computing procedure is as following: (i) solving the Dirac equation of Hamiltonian (1) to calculate LDOSs with a given angular momentum j -the partial LDOSs (S4); (ii) taking the sum of partial LDOSs over all possible j provides LDOS ρ(E, r) (S3) that depends on the energy E and the distance r; and (iii) integrating ρ(E, r) over r provides the total density of states (TDOS) ρ T (E) (S9).…”

Zero‐Energy Vortices in Dirac Materials

“…The principle signature of bound or quasi‐bound states in Dirac materials is through the local density of states data obtained by STM measurements . As mentioned previously, the results of the atomic cluster experiments of ref.…”

Enhanced indirect exchange interactions in the presence of circular potentials in graphene

“…Around Dirac points electrons exhibit Klein tunneling which makes it difficult to control electrons using external fields in pristine graphene [2]. However, it has been theoretically shown that it may still be possible to create quasibound states (QBS) using external electric fields [3][4][5][6]. Magnetic fields combined with electric fields were also shown to produce confinement in pristine graphene [7][8][9][10].…”

“…( 2), the eigenstates of H K (K ) [Eq. ( 1)] of energy E , and the total angular momentum quantum number j = m ± 1/2 around K (K ) Dirac points, are given as follows [4][5][6]:…”