Imaging the Superconducting Proximity Effect in S-S'-S Transition Edge Sensors

Abstract

Proximity effects at superconducting interfaces, between different superconductors (S-S') or between superconductors and normal metals (S-N), are fundamental to the performance of superconducting electronics, yet only few experiments have directly probed the spatial structure of proximity effects within a device. This is particularly relevant for transition edge sensors (TESs), where the interplay of direct and inverse proximity effects governs detector sensitivity. Here, we use scanning superconducting interference device (SQUID) susceptometry to directly image the local diamagnetic response in functional S-S'-S TES structures. We resolve long range proximity coupling extending over tens of micrometers, revealing that the local transition temperature is dramatically tuned by neighboring regions, being either enhanced by superconducting (S) leads or suppressed by normal metal (N) contacts. Our observations are quantitatively supported by Ginzburg Landau modeling of the device geometry and calculations of the temperature dependent diamagnetism based on self-consistent Usadel equations. By providing spatially resolved measurements of the interplay of proximity effects in TES devices, this work establishes a framework for understanding and controlling superconducting states in heterogeneous superconducting structures.

Figures (4)

• Figure 1: (a) Schematic of the SQUID pickup loop with concentric field coil above the TES. An AC current through the field coil generates a local magnetic field, which is screened by currents in the superconductor. This alters the magnetic flux in the pick-up loop, detected as a change in mutual inductance between the two coils $\delta M$. (b) Optical image of the AlMn TES with Nb leads. AlMn extends to the entire purple colored plane. (c) Horizontal line cuts taken at the center of the device (dashed black line in (b)) of the local DR of the TES as a function of temperature. The aqua colored curve highlights the temperature at which the AlMn between the Nb leads shows an appreciable DR due to the proximity effect, while the bare AlMn far from the leads shows none. (d) DR of TES as a function of temperature for different locations with respect to leads. Points correspond to measured values at fixed positions obtained by taking line cuts through the data in (c) as indicated by the colored vertical lines. Solid lines correspond to a model of the DR obtained from solving a 1D Usadel model of the device. (e) Temperature dependence of superconducting gap obtained from 1D Usadel model of device structure used to calculate the expected DR (solid lines) in (d).
• Figure 2: (a) Optical image of the 50µm TES device structure. Mo leads ($T_{c_L}\sim$0.9K) contact the MoAu bilayer with $T_{c_0} =$ 92.8mK. The Au layer overhangs the device forming normal metal banks along the edge of the device. (b) Measured $T_{c_\chi}$ map extracted from a more extensive image series that includes (e-h) by finding the highest temperature at which the local DR surpasses a threshold level above the noise floor. (c) Simulated local $T_{c_{GL}}$ map obtained by solving the GL equations and finding the highest temperature at which the order parameter surpasses a threshold value. Colors of the temperature contours are the same as in (b). (d) Temperature dependent transport of device in a voltage biased circuit with a 180µΩ shunt resistor, plotting ratio of voltage across TES $V_{\mathrm{TES}}$ to total bias current $I_b=$100µA. (e-h) Imaging of the local diamagnetic response of the TES at select temperatures spanning the superconducting transition of the device.
• Figure 3: Temperature dependent DR, $\delta M(T)$, for the bare MoAu bilayer and three square TES devices with different dimensions. Data points show the measured $\delta M(T)$ at the center of each TES, rescaled by its value measured at $T=50mK$. Proximity effects become more pronounced with decreasing device size, as reflected in the shift in $T_{c_{\chi}}$ and the rounding of the transition. Lines in (a) correspond to the DR calculated from a model of the gap at the center of the device as shown in (b) obtained by solving the 2D Usadel equations. Solid lines in (a) assume a common thickness and $\lambda_0$ for all devices, while the dashed line in (a) assumes a smaller effective thickness for the 16µm device.
• Figure 4: (a) Optical image of the 100µm meander TES device structure. The Mo layer is patterned into the leads and meander, while the Au layer is deposited on top, forming a MoAu bilayer in the meander region and Au-only banks and fingers. (b) Measured $T_{c_\chi}$ map. (c) Simulated local $T_{c_{GL}}$ map obtained by solving the GL equations. Both maps are extracted using the same procedure as in Fig. \ref{['MoAu_50']}, and the same GL parameters are used as in Fig.\ref{['MoAu_50']}(c). Colors of the temperature contours are the same in (b) and (c). (d) Temperature dependent transport of device in a voltage biased circuit with a 180µΩ shunt resistor, plotting ratio of voltage across TES $V_{\mathrm{TES}}$ to total bias current $I_b=$100µA. (e-h) Images of the DR at select temperatures across the superconducting transition.