$Δ_T$ Noise from Electron-Hole Asymmetry in Normal and Superconducting Quantum Point Contacts

TL;DR

This work develops a self-consistent framework to study $Δ_T$ noise in two-terminal mesoscopic hybrids where a quantum point contact breaks electron-hole symmetry. By applying the Landauer–Büttiker formalism to $NQN$ and $NQS$ junctions and incorporating Andreev reflection, it computes thermovoltage, charge noise, and $Δ_T$ noise under finite thermovoltage. The key findings show oscillatory $Δ_T$ noise as a function of the normalized Fermi energy, with Andreev-enhanced noise in the $NQS$ case and an upper bound on the $Δ_T$ noise ratio that decreases with temperature, highlighting the role of thermal excitations in modulating nonequilibrium fluctuations. The results offer a comprehensive, experimentally accessible perspective on non-equilibrium transport fluctuations in superconducting hybrids beyond symmetry-protected zero-thermovoltage regimes.

Abstract

This work examines $Δ_T$ noise in two-terminal hybrid nanostructures featuring a quantum point contact (QPC), realized either between two normal metals (NQN) or between a normal metal and a superconductor (NQS). The inclusion of a QPC breaks electron-hole (e-h) symmetry, leading to a finite thermovoltage. In contrast, earlier studies on hybrid junctions incorporating insulating barriers, as e-h symmetry is preserved, have vanishing thermovoltage, and consequently, $Δ_T$ noise is calculated at zero thermovoltage. In our setup, the broken e-h symmetry allows for a finite thermovoltage, at which we compute the corresponding $Δ_T$ noise. Unlike earlier studies restricted by e-h symmetry and vanishing thermovoltage, our work establishes a self-consistent framework in mesoscopic hybrid junctions, revealing how Andreev reflection fundamentally reshapes $Δ_T$ noise once e-h symmetry is broken. This broad access to charge fluctuation signatures provides a more comprehensive understanding of non-equilibrium transport in linear response. To our knowledge, this work provides the first self-consistent analysis of $Δ_T$ noise in superconducting hybrid junctions where e-h symmetry is broken, explicitly revealing how Andreev reflection modifies $Δ_T$ noise beyond the symmetry-protected zero-thermovoltage regime.

Figures (9)

• Figure 1: Schematic diagram of the NQN junction. The black dashed line in the middle represents the QPC constriction. We consider $V_1 = \Delta V$, $V_2 = 0$, $\Delta T_1 = - \Delta T_2 = \Delta T/2$.
• Figure 2: Schematic diagram of the NQS junction. The black dashed line in the middle represents the QPC constriction. We consider $V_1 = \Delta V$, $V_2 = 0$, $\Delta T_1 = - \Delta T_2 = \Delta T/2$.
• Figure 3: Charge conductance in (a) NQN ($G_{NQN}$) and (b) NQS ($G_{NQS}$) (in units of $\frac{2e^2}{h}$) vs. normalized Fermi energy ($\frac{E_F - V_0}{\hbar \omega_x}$) at different temperatures considered above. Parameters are taken are $\hbar \omega_y = 2.73 meV$, $\hbar \omega_x =0.5 \hbar \omega_y$, where $T_C = 18K$.
• Figure 4: Charge thermovoltage in (a) NQN ($V^{NQN}_{th}$) and (b) NQS ($V_{th}^{NQS}$) (in units of $\frac{k_B T}{e}$), Seeback coefficient in (c) NQN ($S_{NQN}$) and (d) NQS ($S_{NQS}$) (in units of $\frac{k_B}{e}$) vs. normalized Fermi energy $\frac{E_F - V_0}{\hbar \omega_x}$. The parameters taken are $n = 4$, $\hbar \omega_y = 2.73 meV$, $\hbar \omega_x =0.5 \hbar \omega_y$ and $\Delta T = 0.05 T$, where $T_C = 18K$.
• Figure 5: Charge $\Delta_T$ noise in (a) NQN ($\Delta^{NQN}_{T}$) and (b) NQS ($\Delta_{T}^{NQS}$) (in units of $\frac{4e^2}{h} k_B T$) vs. normalized Fermi energy $\frac{E_F - V_0}{\hbar \omega_x}$. The parameters taken are $n = 4$, $\hbar \omega_y = 2.73 meV$, $\hbar \omega_x =0.5 \hbar \omega_y$ and $\Delta T = 0.05 T$, where $T_C = 18K$.