$\Delta T$-noise in Multiterminal Hybrid Systems

The study of charge current fluctuations (noise) can give useful insights into the properties of nanoscale systems. In this work, the peculiar properties of noise in multiterminal hybrid normal-superconducting systems are explored in the thermal out-of-equilibrium regime, i.e., when temperature biases are present ($\Delta T$-noise). Using the Landauer-Büttiker approach, we identify two contributions: background noise and excess noise, analyzing them when both electrical and thermal biases are applied. When temperature biases are present, and superconducting terminals are grounded, we find that the first contribution depends not only on the electrical conductance, as the Johnson-Nyquist at equilibrium, but also on a quantity strictly related to the heat conductance. This is our first main result. On the other hand, the second contribution shows, as expected, additional terms originating from the partitioning of currents into different transport channels, including the ones associated with Andreev reflection processes. However, noise induced by the temperature differences unveil also interference terms that cannot be present either in voltage bias or in the absence of any Andreev processes. Finally, we apply the results obtained to two different specific physical situations. The first is a generic three-terminal normal-superconductor-normal system, and the second is a device based on spin-resolved co-propagating chiral channels in the integer quantum Hall regime with a superconducting region. In these example setups, we investigate mainly the shot-noise regimes, when high-voltage or high-temperature biases are applied. We find remarkable differences between the two limits, which ultimately show the different nature of electrically and thermally induced charge current fluctuations.