Electric-Field-Tunable Edge Transport in Bernal-Stacked Trilayer Graphene.

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 ∼0.2 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.

Electric-Field-Tunable Valley Zeeman Effect in Bilayer Graphene Heterostructures: Realization of the Spin-Orbit Valve Effect.

We report the discovery of electric-field-induced transition from a topologically trivial to a topologically nontrivial band structure in an atomically sharp heterostructure of bilayer graphene (BLG) and single-layer WSe_{2} per the theoretical predictions of Gmitra and Fabian [Phys. Rev. Lett. 119, 146401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.146401]. Through detailed studies of the quantum correction to the conductance in the BLG, we establish that the band-structure evolution arises from an interplay between proximity-induced strong spin-orbit interaction (SOI) and the layer polarizability in BLG. The low-energy carriers in the BLG experience an effective valley Zeeman SOI that is completely gate tunable to the extent that it can be switched on or off by applying a transverse displacement field or can be controllably transferred between the valence and the conduction band. We demonstrate that this results in the evolution from weak localization to weak antilocalization at a constant electronic density as the net displacement field is tuned from a positive to a negative value with a concomitant SOI-induced splitting of the low-energy bands of the BLG near the K(K^{'}) valley, which is a unique signature of the theoretically predicted spin-orbit valve effect. Our analysis shows that quantum correction to the Drude conductance in Dirac materials with strong induced SOI can only be explained satisfactorily by a theory that accounts for the SOI-induced spin splitting of the BLG low-energy bands. Our results demonstrate the potential for achieving highly tunable devices based on the valley Zeeman effect in dual-gated two-dimensional materials.

Vanishing Thermal Equilibration for Hole-Conjugate Fractional Quantum Hall States in Graphene.

Transport through edge channels is responsible for conduction in quantum Hall (QH) phases. Robust quantized values of charge and thermal conductances dictated by bulk topology appear when equilibration processes become dominant. We report on measurements of electrical and thermal conductances of integer and fractional QH phases, realized in hexagonal boron nitride encapsulated graphite-gated bilayer graphene devices for both electron and hole doped sides with different valley and orbital symmetries. Remarkably, for complex edges at filling factors ν=5/3 and 8/3, closely related to the paradigmatic hole-conjugate ν=2/3 phase, we find quantized thermal conductance whose values (3κ_{0}T and 4κ_{0}T, respectively where κ_{0}T is the thermal conductance quantum) are markedly inconsistent with the values dictated by topology (1κ_{0}T and 2κ_{0}T, respectively). The measured thermal conductance values remain insensitive to different symmetries, suggesting its universal nature. Our findings are supported by a theoretical analysis, which indicates that, whereas electrical equilibration at the edge is established over a finite length scale, the thermal equilibration length diverges for strong electrostatic interaction. Our results elucidate the subtle nature of crossover from coherent, mesoscopic to topology-dominated transport.

Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet.

Collective spin-wave excitations, magnons, are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. In a quantum Hall ferromagnets, detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if the excess electron and holes are equal, detecting an electrical signal is challenging. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is produced by equilibration between edge channels and propagating magnons. Our model also allows us to pinpoint the regime of ballistic magnon transport in our device.

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene.

The presence of "upstream" modes, moving against the direction of charge current flow in the fractional quantum Hall (FQH) phases, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here, we report noise measurements at the edges of FQH states realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at length, L = 4 µm and 10 µm away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for "hole-conjugate" FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remains independent of length, which matches our theoretical analysis demonstrating the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems.

Determination of topological edge quantum numbers of fractional quantum Hall phases by thermal conductance measurements.

To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream (Nd) and upstream (Nu) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance GQ, which is purely governed by edge quantum numbers Nd and Nu. Our experimental setup is realized with a hexagonal boron nitride (hBN) encapsulated graphite gated single layer graphene device. For temperatures up to 35 mK, our measured GQ at ν = 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime (Nd + Nu)κ0T, where κ0T is a quanta of GQ. With increasing temperature, GQ decreases and eventually takes the value of the equilibrated regime ∣Nd - Nu∣κ0T. By contrast, at ν = 1/3 and 2/5 (without CP modes), GQ remains robustly quantized at Ndκ0T independent of the temperature. Thus, measuring the quantized values of GQ in two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.

Observation of Time-Reversal Invariant Helical Edge-Modes in Bilayer Graphene/WSe2 Heterostructure.

Topological insulators, along with Chern insulators and quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the time-reversal invariant helical edge-modes in bilayer graphene/monolayer WSe2-based heterostructures-a phase generally considered as a precursor to the field of generic topological insulators. Our observation of this elusive phase depended crucially on our ability to create mesoscopic devices comprising both a moiré superlattice potential and strong spin-orbit coupling; this resulted in materials whose electronic band structure could be tuned from trivial to topological by an external displacement field. We find that the topological phase is characterized by a bulk bandgap and by helical edge-modes with electrical conductance quantized exactly to 2e2/h in zero external magnetic field. We put the helical edge-modes on firm ground through supporting experiments, including the verification of predictions of the Landauer-Büttiker model for quantum transport in multiterminal mesoscopic devices. Our nonlocal transport properties measurements show that the helical edge-modes are dissipationless and equilibrate at the contact probes. We achieved the tunability of the different topological phases with electric and magnetic fields, which allowed us to achieve topological phase transitions between trivial and multiple, distinct topological phases. We also present results of a theoretical study of a realistic model which, in addition to replicating our experimental results, explains the origin of the topological insulating bulk and helical edge-modes. Our experimental and theoretical results establish a viable route to realizing the time-reversal invariant Z2 topological phase of matter.

Universal quantized thermal conductance in graphene.

The universal quantization of thermal conductance provides information on a state's topological order. Recent measurements revealed that the observed value of thermal conductance of the 5 2 state is inconsistent with either Pfaffian or anti-Pfaffian model, motivating several theoretical articles. Analysis has been made complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dopant layer from the GaAs quantum well and the resulting soft confining potential. Here, we measured thermal conductance in graphene with atomically sharp confining potential by using sensitive noise thermometry on hexagonal boron-nitride encapsulated graphene devices, gated by either SiO2/Si or graphite back gate. We find the quantization of thermal conductance within 5% accuracy for ν = 1 ; 4 3 ; 2 and 6 plateaus, emphasizing the universality of flow of information. These graphene quantum Hall thermal transport measurements will allow new insight into exotic systems like even-denominator quantum Hall fractions in graphene.