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 ¼ 53 and 8 3 , closely related to the paradigmatic hole-conjugate ν ¼ 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.

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.

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.

The proposals for realizing exotic particles through coupling of quantum Hall effect to superconductivity involve spatially non-uniform magnetic fields. As a step toward that goal, we study, both theoretically and experimentally, a system of Dirac electrons exposed to an Abrikosov flux lattice. We theoretically find that the non-uniform magnetic field causes a carrier-density–dependent reduction of the Hall conductivity. Our studies show that this reduction originates from a rather subtle effect: a levitation of the Berry curvature within Landau levels broadened by the non-uniform magnetic field. Experimentally, we measure the magneto-transport in a monolayer graphene-hexagonal boron nitride-niobium diselenide (NbSe2) heterostructure, and find a density-dependent reduction of the Hall resistivity of graphene as the temperature is lowered from above the superconducting critical temperature of NbSe2, when the magnetic field is uniform, to below, where the magnetic field bunches into an Abrikosov flux lattice.

Magnetic field driven domain-wall motion in the creep regime is investigated with Kerr microscopy in out-of-plane magnetized as deposited and annealed Ta/Pt/CoFeB/Pt multilayers. In addition to the effect of thermal annealing on the quasi-static magnetic properties of Ta (3 nm)/Pt (3 nm)/CoFeB (tCoFeB nm)/Pt (2 nm) film stacks where tCoFeB = {0.72, 0.93}, the study focuses on the modified interfacial Dzyaloshinskii-Moriya interaction (iDMI) that governs the dynamics of chiral domain walls. The strength of the iDMI decreases with an increase in both tCoFeB at a fixed annealing temperature and annealing temperature for a fixed tCoFeB. While the former behaviour arises due to the interfacial nature of iDMI, the latter correlates with the annealing induced suppression of magnetization and enhancement of interface roughness that could be respectively ascribed to B-segregation and Co-Fe-Pt intermixing.