RESUMEN
This Letter presents a nonlocal study on the electric-field-tunable edge transport in h-BN-encapsulated dual-gated Bernal-stacked (ABA) trilayer graphene across various displacement fields (D) and temperatures (T). Our measurements revealed that the nonlocal resistance (R_{NL}) surpassed the expected classical Ohmic contribution by a factor of at least 2 orders of magnitude. Through scaling analysis, we found that the nonlocal resistance scales linearly with the local resistance (R_{L}) only when the D exceeds a critical value of â¼0.2 V/nm. Additionally, we observed that the scaling exponent remains constant at unity for temperatures below the bulk-band gap energy threshold (T<25 K). Further, the value of R_{NL} decreases in a linear fashion as the channel length (L) increases. These experimental findings provide evidence for edge-mediated charge transport in ABA trilayer graphene under the influence of a finite displacement field. Furthermore, our theoretical calculations support these results by demonstrating the emergence of dispersive edge modes within the bulk-band gap energy range when a sufficient displacement field is applied.
RESUMEN
Motivated by the spin-momentum locking of electrons at the boundaries of certain topological insulators, we study a one-dimensional system of spin-orbit coupled massless Dirac electrons withs-wave superconducting pairing. As a result of the spin-orbit coupling, our model has only two kinds of linearly dispersing modes, and we take these to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that thes-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. We find that the continuum model also has zero energy end modes. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of twos-wave superconductors with different phases of the pairing, with aδ-function potential barrier lying at the junction of the two superconductors. Remarkably, we find that the system has asingleAndreev bound state (ABS) which is localized at the junction. When the pairing phase difference crosses a multiple of 2π, an ABS touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constantV0and a term which oscillates with a frequencyω. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequencyωJ= 2eV0/âis a rational fraction ofω. We discuss experiments which can realize such junctions.