Thermal conductance and noise of Majorana modes along interfaced ν=5/2\nu=5/2 fractional quantum Hall states

We study transport along interfaced edge segments of fractional quantum Hall states hosting non-Abelian Majorana modes. With an incoherent model approach, we compute, for edge segments based on Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian topological orders, thermal conductances, voltage biased noise, and delta-$T$ noise. We determine how the thermal equilibration of edge modes impacts these observables and identify the temperature scalings of transitions between regimes of differently quantized thermal conductances. In combination with recent experimental data, we use our results to estimate thermal and charge equilibration lengths in real devices. We also propose an experimental setup which permits measuring several transport observables for interfaced fractional quantum Hall edges in a single device. It can, e.g., be used to rule out edge reconstruction effects. In this context, we further point out some subtleties in two-terminal thermal conductance measurements and how to remedy them. Our findings are consistent with recent experimental results pointing towards a particle-hole-Pfaffian topological order at filling $\nu=5/2$ in GaAs/AlGaAs, and provide further means to pin-point the edge structure at this filling and possibly also other exotic fractional quantum Hall states.Comment: 17+10 pages; 12+2 figures; Updated Sec. VII and Fig. 12. References adde

Transport signatures of fractional quantum Hall binding transitions

Certain fractional quantum Hall edges have been predicted to undergo quantum phase transitions which reduce the number of edge channels and at the same time bind electrons together. However, detailed studies of experimental signatures of such a “binding transition” remain lacking. Here, we propose quantum transport signatures with focus on the edge at filling ν=9/5. We demonstrate theoretically that in the regime of nonequilibrated edge transport, the bound and unbound edge phases have distinct conductance and noise characteristics. We also show that for a quantum point contact in the strong back-scattering (SBS) regime, the bound phase produces a minimum Fano factor F$_{SBS}$=3 corresponding to three-electron tunneling, whereas single-electron tunneling is strongly suppressed at low energies. Together with recent experimental developments, our results will be useful for detecting binding transitions in the fractional quantum Hall regime

Transport signatures of fractional quantum Hall binding transitions

Certain fractional quantum Hall edges have been predicted to undergo quantum phase transitions which reduce the number of edge channels and at the same time bind electrons together. However, detailed studies of experimental signatures of such a ``binding transition\u27\u27 remain lacking. Here, we propose quantum transport signatures with focus on the edge at filling ν=9/5. We demonstrate theoretically that in the regime of non-equilibrated edge transport, the bound and unbound edge phases have distinct conductance and noise characteristics. We also show that for a quantum point contact in the strong back-scattering regime, the bound phase produces a minimum Fano-factor F$_{SBS}$=3 corresponding to three-electron tunneling, whereas single electron tunneling is strongly suppressed at low energies. Together with recent experimental developments, our results will be useful for detecting binding transitions in the fractional quantum Hall regime

Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies

Nonequilibrium situations where selected currents are suppressed are of interest in fields like thermoelectrics and spintronics, raising the question of how the related noises behave. We study such zero-current charge, spin, and heat noises in a two-terminal mesoscopic conductor. In the presence of voltage, spin and temperature biases, the nonequilibrium (shot) noises of charge, spin, and heat can be arbitrarily large, even if their average currents vanish. However, as soon as a temperature bias is present, additional equilibrium (thermal-like) noise necessarily occurs. We show that this equilibrium noise sets an upper bound on the zero-current charge and spin shot noises, even if additional voltage or spin biases are present. We demonstrate that these bounds can be overcome for heat transport by breaking the spin and electron-hole symmetries, respectively. By contrast, we show that the bound on the charge noise for strictly two-terminal conductors even extends into the finite-frequency regime.Comment: 17 pages, 5 figure

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. Such understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state