Spatial confinement, magnetic localization, and their interactions on massless Dirac fermions

Abstract

It is of keen interest to researchers understanding different approaches to confine massless Dirac fermions in graphene, which is also a central problem in making electronic devices based on graphene. Here, we studied spatial confinement, magnetic localization and their interactions on massless Dirac fermions in an angled graphene wedge formed by two linear graphene p-n boundaries with an angle ~ 34°. Using scanning tunneling microscopy, we visualized quasibound states temporarily confined in the studied graphene wedge. Large perpendicular magnetic fields condensed the massless Dirac fermions in the graphene wedge into Landau levels (LLs). The spatial confinement of the wedge affects the Landau quantization, which enables us to experimentally measure the spatial extent of the wave functions of the LLs. The magnetic fields induce a sudden and large increase in energy of the quasibound states because of a  Berry phase jump of the massless Dirac fermions in graphene. Such a behavior is the hallmark of the "Klein tunneling" in graphene. Our experiment demonstrated that the angled wedge is a unique system with the critical magnetic fields for the  Berry phase jump depending on distance from summit of the wedge.

Relativistic Artificial Molecules Realized by Two Coupled Graphene Quantum Dots

“…Very recently, it was demonstrated explicitly that the magnetic fields will lead to a sudden jump in phase by  of the quasiparticles as the sign of the incident angle is changed by a critical magnetic field. Such an effect results in a larger separation of the ±m sublevels than the separation in our experiment because we cannot reach the critical magnetic field (about tens Tesla in our system) [37][38][39][40]. In our experiment, the magnetic field induced split of ±m increases linearly with magnetic field.…”

“…The fourfold degeneracy of the first quasibound state also proves the formation of the artificial molecule because that the molecular states increase the number of electrons contained in the first quasibound state. A perpendicular magnetic field bends the trajectory of electrons and break the time reversal symmetry in graphene QDs, which consequently lifts the degeneracy of the ±m sublevels in the quasibound states [36][37][38][39][40][41]. Very recently, it was demonstrated explicitly that the magnetic fields will lead to a sudden jump in phase by  of the quasiparticles as the sign of the incident angle is changed by a critical magnetic field.…”

Spectroscopic Evidence for a Spin- and Valley-Polarized Metallic State in a Nonmagic-Angle Twisted Bilayer Graphene

“…Figures 1d and 1e show representative STS spectra recorded in two different regions of the 1.49º TBG and the doping in the two regions differs about 30 meV. The slight difference of the doping may arise from variations of the distance between Cu substrate and graphene owning to intercalation of S atoms that segregated from the Cu substrate, as demonstrated very recently 51,52 . The spectra shown in Figs.…”

Recent progresses of quantum confinement in graphene quantum dots

“…When a small critical magnetic field B c reached, the orbit with angular momentum antiparallel to the magnetic field is bended into a "skipping" orbit with loops [Fig. 3(b)] [12,59]. During this transition, the trajectory in momentum-space is changed to enclosing the Dirac point at critical magnetic field, and the value of Berry phase discontinuously jumps from 0 towards π.…”

“…And the splitting energy between σ * +1/2 (σ +1/2 ) and σ * −1/2 (σ −1/2 ) increases linearly with increasing magnetic field. This kind of large splitting of bonding states and antibonding states in magnetic fields are attributed to the lifting of angular momentum ±m of the quasi-bound states, because that external magnetic field bends the trajectory of charge carriers and breaks the time inversion symmetry of the Klein GQDs [12,31,40,42,43,59].…”