Tuning a circular p–n junction in graphene from quantum confinement to optical guiding

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

“…Quantitative analyses show that for all the EWGMs identified the Q-factors seem always to be ≤ 10 2 , very small compared to those in ordinary optical WGM-microresonators (of 10 5 − 10 8 [1,3]), while the corresponding mode radii may tunably be in nanometerscale. Our theoretical results are in a good agreement with existent experimental data [12,14,15], putting a question to the application potential of the EWGM identified.…”

“…And, moreover, the scanning tunnelling microscope (STM)-tip induced circular graphene np-junctions that are extensively exploited to study different properties of Dirac fermions confined by an axially symmetric electrostatic potential barrier [9][10][11] should act as electronic WGM-resonators in producing circular electronic modes analogous to the optical WGMs. Indeed, recently, electronic Whispering-Gallery Modes (EWGMs) have been reported in several STM-experiments [12][13][14]. Owing to the dual-gate structure, the back-gate and top-gate, STM-based EWGMresonators are fully tunable in the meaning that both the resonator size and the np-interface potential may be independently varied by changing suitably the back-gate voltage, the top-gate potential and the tip-to-graphene distance [14].…”

“…Indeed, recently, electronic Whispering-Gallery Modes (EWGMs) have been reported in several STM-experiments [12][13][14]. Owing to the dual-gate structure, the back-gate and top-gate, STM-based EWGMresonators are fully tunable in the meaning that both the resonator size and the np-interface potential may be independently varied by changing suitably the back-gate voltage, the top-gate potential and the tip-to-graphene distance [14]. EWGMs in these resonators can be detected by measuring the tunnelling differential conductance that feature the local density of states (LDOSs) spectrum in dependence on the tip-sample bias, back-gate voltage, and spatial position (from the centre of the tip).…”

“…[12] this potential is simply assumed to have the parabolic form, while in the tight-binding model used in Ref. [14] it is the Thomas-Fermi approximated potential. Both the studies have unambiguously confirmed an emergence of EWGMspectra in STM-tip induced circular graphene resonators.…”

Zero‐Energy Vortices in Dirac Materials

“… to probe the transmission of Dirac electrons through a sharp circular potential well defined by substrate engineering. Later experimental work on confinement in circular pn junctions created by the tip‐induced charge, has seen signatures of both atomic collapse states and whispering‐gallery modes . Notably, the theoretical model for the tip potential was based on an infinite harmonic well which is known to not have bound states, and the truly bound states at zero‐energy were overlooked.…”