Quantized heat flow probing thermal equilibration and edge structures of quantum Hall phases in graphene

Abstract

In condensed matter physics, usually, phases are described using Landau’s approach, which characterizes the phases in terms of underlying symmetries that are spontaneously broken. Over the past few decades, a different classification paradigm has been used based on the topological order. In a topological phase, certain quantized physical quantities whose values are insensitive to the detail of the system are characterized by topological invariants (TI). The first experimentally realized topological phase in condensed matter systems is the quantum Hall (QH) phase. Since the topological order of a QH phase is a bulk property, the best way to determine the topological order of these phases will involve experiments that can directly probe the bulk. But unfortunately, such an experimental probe was found to be tough to realize. However, thanks to the remarkable validity of the bulk-edge correspondence, which allows us to determine the topological order of these phases by measuring the TI quantity, like electrical and thermal conductance, which are sensitive to the edge modes structures. The quantization of the electrical and thermal Hall conductance in QH states was established long back. Although electrical Hall conductance has been widely used to understand the topological order of a QH state, it turns out to be insufficient in the hierarchical fractional quantum Hall (FQH) states, where the edge structure is complicated, and transport may occur via both the downstream (Nd) and upstream (Nu) modes. The electrical Hall conductance only reveals the downstream charged chiral edge modes and remains insensitive to the total number of the edge modes, their chirality, and character. By contrast, the quantized thermal Hall conductance is not only sensitive to the downstream charged modes, but it can also detect the other upstream modes, including the chargeless neutral modes and the celebrated Majorana modes, which are not detectable in electrical Hall conductance measurement. In the major part of this thesis, we utilize the Jhonson-Nyquist noise thermometry to measure the quantized thermal conductance to probe the topological edge structure of the various QH states in single layer and bilayer of graphene. We first measure the thermal conductance of integer and particle-like FQH states. The measured value matches very well with the theoretically predicted values, establishing the universality of the quantization of thermal conductance in graphene. Next, we measure the thermal conductance of the hole-like states (5/3 and 8/3, which are closely related to the paradigmatic hole-conjugate ν = 2/3 phase) for both electron and hole-doped sides with different valley and orbital symmetries realized in bilayer graphene. The measured quantized thermal conductance values are markedly consistent with the thermally non-equilibrated values instead of the thermally equilibrated ones. The non-equilibrated values indicate the divergence of the thermal equilibration length as supported by the theoretical calculations. Next, we target to achieve the crossover from a thermally non-equilibrated heat transport to fully-equilibrated heat transport. This crossover is pivotal to resolving the dichotomy between different models of edge structure or, in general, to determine the topological edge quantum numbers of FQH states hosting counter-propagating downstream and upstream edge modes. To achieve this crossover, we perform the temperature dependence measurement of the quantized thermal conductance of the FQH states emerging in the lowest Landau level of the single-layer graphene. For particle-like states, we didn't observe any temperature dependence suggesting only the downstream edge modes. Surprisingly, for the hole-like states, we observe a crossover between the two asymptotic limits of the thermal equilibration. Achieving such crossover opens a new route to finding the exact ground state of more complex even denominator FQH states. In the last parts of the thesis, we study two different problems which are not related to the thermal conductance measurement. In one of the works, we utilize the nonlocal resistance measurement to probe the presence of the dispersive edge modes in bernal stacked trilayer (ABA) graphene. The scaling exponent relating the nonlocal and local resistance was found to be unity over a wide range of the temperature and displacement field, suggesting the edge-mediated nonlocal charge transport. In another work, we investigate the electrical and magnetotransport properties in bilayer graphene encapsulated between two hexagonal boron nitride (hBN) crystals, where the top and bottom hBN are rotationally aligned with the bilayer graphene with a twist angle θt ∼ 0◦ and θb < 1◦, respectively. This results in the formation of two moir´e superlattices, with the appearance of satellite resistivity peaks together with the resistivity peak at zero carrier density. Furthermore, we measure the temperature (T) dependence of the resistivity (ρ). The resistivity shows a linear increment with temperature within the range 10 to 50 K for the density regime bounded by two satellites peaks with a large slope dρ/dT ∼ 8.5 Ω/K. The large slope of dρ/dT is attributed to the enhanced electron-phonon coupling arising due to the suppression of Fermi velocity in the reconstructed minibands.