Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts

Abstract

We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Due to the Berry curvature states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum number with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calculations. arXiv:1809.01920v1 [cond-mat.mes-hall]

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts

“…As a result, additional plateaus are observed with a sequence G = 6, 8, 10, 12, 14...e 2 /h around B ⊥ = 0.5 T, as discussed in Ref. [11]. Upon further increasing the magnetic field, the newly split energy levels merge with neighboring levels to form 4-fold degenerate energy levels again, at B ⊥ = 1 T. The sequence of quantized conductance plateaus becomes G = 6, 10, 14, 18...e 2 /h.…”

“…Diamond-like feature are numbered with the corresponding conductance values. The height of the large diamonds at G = 6, 10, 14, 18, 22 and 26 e 2 /h has a range from 2 ∼ 5 meV which corresponds to the energy level difference of the valley splitting [6,11,17]. At B ⊥ = 0.5 T, see Fig.…”

“…1(a) (orange/purple curve taken at SG/BG combination indicated by the respective dot) show the conductance of the QPC after subtracting a series resistance which originates from the Ohmic contacts. The contact resistance and the bilayer graphene bulk resistance show a value between 900 and 920 Ω, independent of the channel gate voltage [11]. For the following data presented in this manuscript, the QPC conductance is the measured two-terminal conductance with a suitable series resistance subtracted.…”

“…In general we observe conductance quantization at values n × 4e 2 /h, see Fig 1(b). The number 4 accounts for spin and valley degeneracies [7,11]. For small back-gate voltage or displacement field, i.e.…”

“…Next, we discuss how the four-fold degenerate states split in a magnetic field. Zeeman splitting of spin states [6,11,13] occurs for any magnetic field orientation. Valley splitting, on the other hand, is an orbital effect [6], and will therefore only occur for magnetic fields perpendicular to the sample plane.…”