Graphene: Junctions and STM Spectra

Abstract

The presence of low-energy Dirac-like quasiparticles is one of the central features responsible for plethora of recent theoretical and experimental studies on graphene. In this review, we focus on the effect of the Dirac nature of these quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness d and arbitrary gate voltages V0 applied across the barrier region. The second aspect involves study of the presence of localized magnetic impurities in graphene in which we discuss the unconventional nature of Kondo physics in graphene and the tunablity of Kondo effect with a gate voltage. We also chart out the nature of scanning tunneling conductance spectra for both doped and undoped graphene in the presence of impurities and discuss the effect of Dirac nature of graphene quasiparticles on such spectra. In particular, we provide a detailed analysis of the phenomenon that that the position of the impurity in the graphene matrix plays a crucial role in determining the nature of the STM specta.

The Kondo effect of an adatom in graphene and its scanning tunneling spectroscopy

“…When the chemical potential µ is tuned to meet the Dirac points, the curve at the zero bias does not show any Kondo peak, which is a consequence of the zero density of states at the Dirac points. This is consistent with that reported in the literature [18,[29][30][31][32]. In this case, a critical coupling between the adatom and the conduction electron is required.…”

“…When the Fermi energy is near the Dirac points, the Kondo effect is absent since a critical coupling strength must be satisfied for developing the Kondo effect [10,18,[29][30][31][32], as also obtained by using the numerical renormalization group calculations in the gapless Kondo and/or Anderson models [33][34][35]. Once the Fermi energy is tuned to be away from the Dirac points, whether it is below or above the Dirac points, the Kondo resonance is found to exist in a wide parameter regime ranging from the Kondo regime to the mixed valence regime, and even to the empty orbital regime 5 .…”

Electron cooling with graphene-insulator-superconductor tunnel junctions and applications to fast bolometry

“…Here, we introduce the main equations and discuss the electron tunneling through a GIS junction. The tunneling rate is proportional to the Density of States (DoS) of graphene and superconductor [68]. The graphene DoS ν G reads [69]…”

“…The electric and thermal currents depend on n through the tunnel resistance R t . The latter is proportional to the DoS of both the graphene and the superconductor and to the modulus square of the tunneling amplitude [68,77]. Since ρ G0 ∝ √ n, the GIS tunnel resistance depends on the carrier density as…”