$Δ_T$ Noise in Mesoscopic Hybrid Junctions: Influence of Barrier Strength and Thermal Bias

TL;DR

The paper examines $Δ_T$ noise, the shot-noise-like component arising from a finite temperature difference under zero current, in mesoscopic NIN and NIS junctions with insulating barriers. Using Landauer–Büttiker theory for NIN and BTK formalism for NIS, it derives analytic results for $Δ_T$ noise in NIN and provides numerical results for NIS across barrier strengths, showing a strong enhancement of $Δ_T$ noise in NIS due to Andreev reflection and a nonmonotonic dependence on barrier strength. It decomposes total quantum noise into thermal and shot components, clarifying that $Δ_T$ noise is a small, quadratic contribution in $ΔT$ and highlighting that previous work conflated total noise with $Δ_T$ noise. The findings quantify how barrier strength and Andreev processes control $Δ_T$ noise, offering a route to probe thermal-quantum transport in hybrid mesoscopic devices via noise measurements.

Abstract

Quantum noise is a fundamental probe of quantum transport phenomena, offering insights into current correlations and wave-particle duality. A particularly intriguing form of such noise, $Δ_T$ noise, emerges under a finite temperature difference in the absence of charge current at zero voltage bias. In this work, we investigate $Δ_T$ noise in mesoscopic hybrid junctions incorporating insulating barriers, where the average charge current remains zero at zero bias. Using quantum shot noise measurements, we demonstrate that $Δ_T$ noise in metal-insulator-superconductor (NIS) junctions is approximately $16$ times greater than in metal-insulator-metal (NIN) counterparts. Our analysis further reveals that $Δ_T$ noise exhibits a non-monotonic dependence on barrier strength, rising to a peak before declining, while increasing monotonically with the applied temperature bias. These findings underscore the rich interplay between thermal gradients and barrier properties in determining quantum noise characteristics in hybrid mesoscopic systems.

Figures (6)

• Figure 1: Schematic diagram of metal (N) - insulator (I) - metal (N) or metal-insulator-superconductor (NIS) junction. Both the left normal metal and right normal metal (or, superconductor) are grounded. $\mathcal{T}_{NIN}$ ($\mathcal{T}_{NIS}$) is the net transmission probability across the NIN (NIS) junction. $T_1 = \Bar{T} + \frac{\Delta T}{2}$ and $T_2 = \Bar{T} - \frac{\Delta T}{2}$ are the temperatures of the left and right normal metal (or, superconductor) respectively, where $\Bar{T}$ is the average temperature and $\Delta T$ is the temperature bias applied across the junction. For superconductor, the critical temperature $T_c > T_2$.
• Figure 2: $\Delta_T^{NIN}$ noise (Quantum noise $Q^{NIN}_{11}$ in units of $\frac{2e^2}{h} k_B \bar{T}$ in inset) in units of $\frac{2e^2}{h} 10^{-2} k_B \bar{T}$ (a) vs. $Z$, with $\Delta T=0.25K$ (blue), $\Delta T=0.50K$ (red) and (b) vs. $\Delta T$ with $Z \to 0$ (blue), $Z=1.0$ (red), $Z=5.0$ (orange) and at zero bias voltage ($V_1=V_2=0$) and $\Bar{T} = 3.0K$. We consider the superconducting gap $\Delta_0 = 1.76 k_B T_c$, where $T_c = 18K$.
• Figure 3: $\Delta_T^{NIS}$ noise (Quantum noise $Q^{NIS}_{11}$ in units of $\frac{2e^2}{h} k_B \bar{T}$ in inset) in units of $\frac{2e^2}{h} 10^{-2} k_B \Bar{T}$ (a) vs. $Z$, with $\Delta T=0.25K$ (blue), $\Delta T=0.50K$ (red) and (b) vs. $\Delta T$ with $Z \to 0$ (blue), $Z=1.0$ (red), $Z=5.0$ (orange) and at zero bias voltage ($V_1=V_2=0$) and $\Bar{T} = 3.0K$. We consider the superconducting gap $\Delta_0 = 1.76 k_B T_c$, where $T_c = 18K$.
• Figure 4: (a) $\bar{\Delta}_T^{NIN}$, (b) $\bar{\Delta}_T^{NIS}$ in units of $10^{-2} k_B \Bar{T}$ vs. $Z$ with $\Delta T=0.25K$ (blue), $\Delta T=0.50K$ (red) and vs. $\Delta T$ (in insets) with $Z \to 0$ (blue), $Z=1.0$ (red), $Z=5.0$ (orange) and at zero bias voltage ($V_1=V_2=0$) and $\bar{T} = 3.0K$. We consider the superconducting gap $\Delta_0 = 1.76 k_B T_c$, where $T_c = 18K$.
• Figure 5: (a) $\frac{\Delta_T^{NIS}}{\Delta_T^{NIN}}$, (b) $\frac{\bar{\Delta}_T^{NIS}}{\bar{\Delta}_T^{NIN}}$ vs. $Z$ with $\Delta T=0.25K$ (blue), $\Delta T=0.50K$ (red) and vs. $\Delta T$ (in insets) with $Z \to 0$ (blue), $Z=1.0$ (red), $Z=5.0$ (orange) and at zero bias voltage ($V_1=V_2=0$) and $\bar{T} = 3.0K$. We consider the superconducting gap $\Delta_0 = 1.76 k_B T_c$, where $T_c = 18K$.