Thermal conductance and nonequilibrium superconductivity in a diffusive NSN wire probed by shot noise

Heat-Mode Excitation in a Proximity Superconductor

“…While in the NS device the slope expectedly doubles [15,33], see the dotted lines in Figure 2c with the effective charge e * ≈ 2e denoted by "2e", in the NSN device, it increases much more weakly and corresponds to e * ≈ 1.6e assuming the same F. Unlike in SNS junctions [42], a fractional value of e * here is not related to a quasiparticle charge in the superconductor, but reflects an unusual boundary condition for the heat flux underneath the S-terminal, see Ref. [31] and Supplemental Materials for the details. While the doubled e * is a direct consequence of the full reflection of heat flux at the S-terminal [32], its intermediate value means that the missing heat flux in the NSN device is transmitted towards the nearby floating N-terminal.…”

“…Throughout the experiment, the S-terminal is grounded, terminal N1 is biased and terminal N2 is floating (or vice versa). Note that grounding of the S-terminal protects the Al from non-equilibrium superconductivity effects [25,31]. The S-terminal serves as a nearly perfect sink for the charge current.…”

“…We proceed with a quantitative description of the Andreev heat guiding by solving the diffusion equation for the electronic energy distribution (EED), inspired by a quasiclassical approach [31,32]. In the proximitized region, the boundary conditions take into account ARs for the sub-gap transport and residual normal reflections above the gap.…”

“…Thermal conductance G th and interface resistance r are the only two parameters that, together with known G 1 , G 2 , determine the solution for the EED and the noise temperature T N of the floating NS junction [44]. For convenience, we choose electrical units for the thermal conductance [31] G th = e 2 ν * D * /L S , where ν * is the effective one-dimensional density of states, D * is the diffusion coefficient in the NW region covered by the superconductor and L S is the length of the S-terminal. With this choice, in case of energy-independent G th , one can express the heat flux caused by a small thermal bias δT applied across the proximity region as Q = G th L 0 TδT, where L 0 = π 2 k 2 B /3e 2 is the Lorenz number.…”

Anderson localization at the boundary of a two-dimensional topological superconductor

“…As we study a superconducting class without a spinrotational symmetry, experimental verification of our results requires thermal transport measurements. That could be a challenging task, however, recent developments indicate that such measurements are possible at a mesoscopic scale [39,40]. To perform disorder-averaging experimentally, one can use a common trick of varying magnetic field or chemical potential in a range that preserves topological state in the system but effectively perturbs the disorder potential.…”