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Register a new userUnveiling quantum Hall transport by Efros-Shklovskii to Mott variable range hopping transition with Graphene
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The quantum localization in the quantum Hall regime is revisited using Graphene monolayers with accurate measurements of the longitudinal resistivity as a function of temperature and current. We experimentally show for the first time a cross-over from Efros-Shklovskii Variable Range Hopping (VRH) conduction regime with Coulomb interactions to a Mott VRH regime without interaction. This occurs at Hall plateau transitions for localization lengths larger than the interaction screening length set by the nearby gate. Measurements of the scaling exponents of the conductance peak widths with both temperature and current give the first validation of the Polyakov-Shklovskii scenario that VRH alone is sufficient to describe conductance in the Quantum Hall regime and that the usual assumption of a metallic conduction regime on conductance peaks is unnecessary.
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The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we present how the appearance of different edge channels in a field-effect device is influenced by the inhomogeneous capacitance profile existing near the sample edges, a condition of particular relevance for graphene. We apply this practical idea to experiments on high quality graphene, demonstrating the potential of quantum Hall transport as a spatially resolved probe of density profiles near the edge of this two-dimensional electron gas.
Anomalous Hall effect (AHE) is important for understanding the topological properties of electronic states, and provides insight into the spin-polarized carriers of magnetic materials. AHE has been extensively studied in metallic, but not variable-range-hopping (VRH), regime. Here we report the experiments of both anomalous and ordinary Hall effect (OHE) in Mott and Efros VRH regimes. We found unusual scaling law of the AHE coefficient $Rah=aRxx^b$ with b>2, contrasting the OHE coefficient $Roh=cRxx^d$ with d<1. More strikingly, the sign of AHE coefficient changes with temperature with specific electron densities.
We study a quantum dot coupled to two semiconducting reservoirs, when the dot level and the electrochemical potential are both close to a band edge in the reservoirs. This is modelled with an exactly solvable Hamiltonian without interactions (the Fano-Anderson model). The model is known to show an abrupt transition as the dot-reservoir coupling is increased into the strong-coupling regime for a broad class of band structures. This transition involves an infinite-lifetime bound state appearing in the band gap. We find a signature of this transition in the continuum states of the model, visible as a discontinuous behaviour of the dots transmission function. This can result in the steady-state DC electric and thermoelectric responses having a very strong dependence on coupling close to critical coupling. We give examples where the conductances and the thermoelectric power factor exhibit huge peaks at critical coupling, while the thermoelectric figure of merit ZT grows as the coupling approaches critical coupling, with a small dip at critical coupling. The critical coupling is thus a sweet spot for such thermoelectric devices, as the power output is maximal at this point without a significant change of efficiency.
We propose and analyse a scheme for performing a long-range entangling gate for qubits encoded in electron spins trapped in semiconductor quantum dots. Our coupling makes use of an electrostatic interaction between the state-dependent charge configurations of a singlet-triplet qubit and the edge modes of a quantum Hall droplet. We show that distant singlet-triplet qubits can be selectively coupled, with gate times that can be much shorter than qubit dephasing times and faster than decoherence due to coupling to the edge modes. Based on parameters from recent experiments, we argue that fidelities above 99% could in principle be achieved for a two-qubit entangling gate taking as little as 20 ns.
We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the A-power of the jump length and depend on the energy marks via a Boltzmann--like factor. The case A=1 corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with arbitrary start point, converges to a Brownian motion whose diffusion matrix is positive definite, and independent of the environment. Finally, we extend the above result to other point processes including diluted lattices.
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