Coulomb interaction in quasibound states of graphene quantum dots

Coexistence of electron whispering-gallery modes and atomic collapse states in graphene/WSe2 heterostructure quantum dots

“…S7 for the spatial distribution of the quasibound states).According to our analysis, the resonance peaks located at the edge of GQDs arise from the quasibound states via the WGMs confinement. The energy levels these quasibound states at the edge can be estimated as (here is the effective radius of the GQD), as observed in our experiment (see Fig.S4d) and reported in previous studies(10,12,13). Whereas the energy levels of the quasibound states at the center of the GQD follow an exponential function , where , is the energy of Dirac point [m denotes the orbital states ( )].…”

“…Obviously, the WSe2 QD generates a circular p-n junction, i.e., a GQD, on graphene. The almost equally spaced peaks in the spectrum are the quasibound states confined in the GQD via the WGMs (9)(10)(11)(12)(13)(14)(15). Such a result is further confirmed by carrying out STS mapping at different resonance energies (Fig.…”

“…Because of the "small" velocity of the Dirac fermions, a Coulomb impurity in graphene with a charge Z ≥ 1 can result in the formation of atomic collapse states (ACSs) around it (16,17). In previous experiments, pronounced resonances of the two types of the quasibound states were clearly observed (9)(10)(11)(12)(13)(14)(15)(16)(17)(18). Due to their distinct underlying origins, the two quasibound states are expected to be observed in the two different systems.…”

“…For example, the massless Dirac fermions nature of the charge carriers in graphene enables us to demonstrate several oddball predictions by quantum electrodynamics (QED), among which the Klein tunneling (5) and atomic collapse (6)(7)(8) are the two most famous effects that have attracted much attention. Very recently, it was demonstrated that the two effects lead to the formation of two types of quasibound states in graphene (9)(10)(11)(12)(13)(14)(15)(16)(17)(18). The Klein tunneling, i.e., the anisotropic transmission of the massless Dirac fermions across the potential barrier, in graphene leads to the formation of quasibound states in circular p-n junctions, i.e., graphene quantum dots (GQDs), via whispering-gallery modes (WGMs) (9)(10)(11)(12)(13)(14)(15).…”

“…Very recently, it was demonstrated that the two effects lead to the formation of two types of quasibound states in graphene (9)(10)(11)(12)(13)(14)(15)(16)(17)(18). The Klein tunneling, i.e., the anisotropic transmission of the massless Dirac fermions across the potential barrier, in graphene leads to the formation of quasibound states in circular p-n junctions, i.e., graphene quantum dots (GQDs), via whispering-gallery modes (WGMs) (9)(10)(11)(12)(13)(14)(15). Because of the "small" velocity of the Dirac fermions, a Coulomb impurity in graphene with a charge Z ≥ 1 can result in the formation of atomic collapse states (ACSs) around it (16,17).…”