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Register a new userHeat transport through quantum Hall edge states: Tunneling versus capacitive coupling to reservoirs
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We study the heat transport along an edge state of a two-dimensional electron gas in the quantum Hall regime, in contact to two reservoirs at different temperatures. We consider two exactly solvable models for the edge state coupled to the reservoirs. The first one corresponds to filling $ u=1$ and tunneling coupling to the reservoirs. The second one corresponds to integer or fractional filling of the sequence $ u=1/m$ (with $m$ odd), and capacitive coupling to the reservoirs. In both cases we solve the problem by means of non-equilibrium Green function formalism. We show that heat propagates chirally along the edge in the two setups. We identify two temperature regimes, defined by $Delta$, the mean level spacing of the edge. At low temperatures, $T< Delta$, finite size effects play an important role in heat transport, for both types of contacts. The nature of the contacts manifest themselves in different power laws for the thermal conductance as a function of the temperature. For capacitive couplings a highly non-universal behavior takes place, through a prefactor that depends on the length of the edge as well as on the coupling strengths and the filling fraction. For larger temperatures, $T>Delta$, finite-size effects become irrelevant, but the heat transport strongly depends on the strength of the edge-reservoir interactions, in both cases. The thermal conductance for tunneling coupling grows linearly with $T$, whereas for the capacitive case it saturates to a value that depends on the coupling strengths and the filling factors of the edge and the contacts.
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Motivated by recent experiments we consider transport across an interacting magnetic impurity coupled to the Majorana zero mode (MZM) observed at the boundary of a topological superconductor (SC). In the presence of a finite tunneling amplitude we observe hybridization of the MZM with the quantum dot, which is manifested by a half-integer zero-bias conductance $G_0=e^2/2h$ measured on the metallic contacts. The low-energy feature in the conductance drops abruptly by crossing the transition line from the topological to the non-topological superconducting regime. Differently from the in-gap Yu-Shiba-Rosinov-like bound states, which are strongly affected by the on-site impurity Coulomb repulsion, we show that the MZM signature in the conductance is robust and persists even at large values of the interaction. Interestingly, the topological regime is characterized by a vanishing Fano factor, $F=0$, induced by the MZM. Combined measurements of the conductance and the shot noise in the experimental set-up presented in the manuscript allow to detect the topological properties of the superconducting wire and to distinguish the low-energy contribution of a MZM from other possible sources of zero-bias anomaly. Despite being interacting the model is exactly solvable, which allows to have an exact characterization of the charge transport properties of the junction.
Current statistics of an antidot in the fractional quantum Hall regime is studied for Laughlins series. The chiral Luttinger liquid picture of edge states with a renormalized interaction exponent $g$ is adopted. Several peculiar features are found in the sequential tunneling regime. On one side, current displays negative differential conductance and double-peak structures when $g<1$. On the other side, universal sub-poissonian transport regimes are identified through an analysis of higher current moments. A comparison between Fano factor and skewness is proposed in order to clearly distinguish the charge of the carriers, regardless of possible non-universal interaction renormalizations. Super-poissonian statistics is obtained in the shot limit for $g<1$, and plasmonic effects due to the finite-size antidot are tracked.
Specific heat has had an important role in the study of superfluidity and superconductivity, and could provide important information about the fractional quantum Hall effect as well. However, traditional measurements of the specific heat of a two-dimensional electron gas are difficult due to the large background contribution of the phonon bath, even at very low temperatures. Here, we report measurements of the specific heat per electron in the second Landau level by measuring the thermalization time between the electrons and phonons. We observe activated behaviour of the specific heat of the 5/2 and 7/3 fractional quantum Hall states, and extract the entropy by integrating over temperature. Our results are in excellent agreement with previous measurements of the entropy via longitudinal thermopower. Extending the technique to lower temperatures could lead to detection of the non-Abelian entropy predicted for bulk quasiparticles at 5/2 filling
We investigate minimal excitation states for heat transport into a fractional quantum Hall system driven out of equilibrium by means of time-periodic voltage pulses. A quantum point contact allows for tunneling of fractional quasi-particles between opposite edge states, thus acting as a beam splitter in the framework of the electron quantum optics. Excitations are then studied through heat and mixed noise generated by the random partitioning at the barrier. It is shown that levitons, the single-particle excitations of a filled Fermi sea recently observed in experiments, represent the cleanest states for heat transport, since excess heat and mixed shot noise both vanish only when Lorentzian voltage pulses carrying integer electric charge are applied to the conductor. This happens in the integer quantum Hall regime and for Laughlin fractional states as well, with no influence of fractional physics on the conditions for clean energy pulses. In addition, we demonstrate the robustness of such excitations to the overlap of Lorentzian wavepackets. Even though mixed and heat noise have nonlinear dependence on the voltage bias, and despite the non-integer power-law behavior arising from the fractional quantum Hall physics, an arbitrary superposition of levitons always generates minimal excitation states.
We consider the trial wavefunctions for the Fractional Quantum Hall Effect (FQHE) that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized screening (i.e. short-range correlations only) inside the quantum Hall droplet, and using the language of boundary conformal field theory (boundary CFT). These inner products take universal values in this limit: they are equal to the corresponding inner products in the bulk 2d chiral CFT which underlies the trial wavefunction. This is a bulk/edge correspondence; it shows the equality between equal-time correlators along the edge and the correlators of the bulk CFT up to a Wick rotation. This approach is then used to analyze the entanglement spectrum (ES) of the ground state obtained with a bipartition AcupB in real-space. Starting from our universal result for inner products in the thermodynamic limit, we tackle corrections to scaling using standard field-theoretic and renormalization group arguments. We prove that generalized screening implies that the entanglement Hamiltonian H_E = - log {rho}_A is isospectral to an operator that is local along the cut between A and B. We also show that a similar analysis can be carried out for particle partition. We discuss the close analogy between the formalism of trial wavefunctions given by conformal blocks and Tensor Product States, for which results analogous to ours have appeared recently. Finally, the edge theory and entanglement spectrum of px + ipy paired superfluids are treated in a similar fashion in the appendix.
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