Giant thermal modulation via a semiconductor-superconductor photonic field-effect heat transistor

Abstract

We present a groundbreaking demonstration of thermal modulation in a field-effect-controllable semiconductor-superconductor hybrid structure, wherein the heating mechanism is exclusively radiative. The architecture comprises two reservoirs separated by $\sim 1$ mm and interconnected via a completely non-galvanic electrical circuit, enabling the transfer of black-body radiation from the hot to the cold reservoir. Our device utilizes a superconducting Josephson field-effect transistor to achieve magnetic-field-free gate-tunable regulation of heat currents within the circuit. While prior studies have indicated the potential for electrostatic modulation of thermal transport properties, our framework demonstrates a temperature modulation of up to $\sim 45$ mK, exceeding prior findings by more than an order of magnitude. Furthermore, it proves a thermal transimpedance of $\sim 20$ mK/V at a bath temperature of $30$ mK. The development of such systems holds substantial promise for advancing heat management and routing in quantum chips and radiation sensors, as it enables precise nonlocal control of heat flow towards a designated structure, even when the heat source is distant and non-galvanically coupled.

Figures (8)

• Figure 1: Schematic representation of the experiment.a, Heat balance scheme of the system: $\dot{Q}_{inj}$ represents the injected power into the hot resistor, $\dot{Q}_{e-ph}$ denotes the reservoir electron-phonon heat exchanges towards the thermal bath, $\dot{Q}_\gamma$ indicates the photonic heat current, and $\dot{Q}_{ext}$ refers to other parasitic heat currents losses in the cold resistor. b, Lumped element model of the circuit. The hot/cold parts of the circuit (red and blue boxes) are represented with resistive reservoirs $R_{hot}$/$R_{cold}$ and effective Johnson-Nyquist AC voltage sources $u_{hot}$/$u_{cold}$. The circuit comprises the decoupling capacitors $C_{1,2}$ (grey box) and the JoFET, which is controllable by the gate voltage $V_g$ (green box). The JoFET is schematized as a frequency- and voltage-dependent impedance $Z(\omega,V_g)$. c-d, Functioning principle of the experiment. The two reservoirs are interconnected by a circuit whose total complex impedance can be adjusted via an external gate voltage $V_g$. When the JoFET mediates supercurrent (c), the impedance is purely inductive, allowing for maximum photonic heat transfer through the system (green semaphore). Conversely, when the JoFET is in the resistive state (d), it creates a strong impedance mismatch between the two reservoirs, thereby increasing the back-reflection of the radiative heat flow (red semaphore).
• Figure 2: Structure and wiring of the gate-tunable photonic heat transfer experiment.a, Schematic circuit including SEM photographs (the white scale bars in those photos are $5$$\mu$m) of the devices integrated on the InAsOI platform, wiring, and supply/measurement setup. Red- and blue-shaded SEM images show the hot and cold resistors, respectively, equipped with JJ thermometers. The green-shaded SEM image shows the gate-tunable photonic heat modulator, achieved by using two JoFETs connected in parallel and driven simultaneously. The ring-like configuration realizes a superconducting interferometer (SQUID). The hot and cold resistors are non-galvanically connected via the two capacitors. Red and blue wiring and schematics refer to the supply/measurement setups of the hot and cold reservoirs, respectively. b, 3D representation of the hot and cold resistors equipped with the Josephson thermometer. The two Al fingers in the middle define the SSmS JJ used to measure the electronic temperature. At the same time, the lateral Al leads connect the InAs mesa to the rest of the circuit and also provide the heating current. c, 3D representation of a single JoFET. The superconducting source and drain leads on the side define the SSmS junction, with the InAs mesa patterned on the electrical insulating substrate. The gate finger in the middle is non-galvanically connected to the InAs channel via the HfO$_2$ insulating layer. It is used to tune the electron density of the InAs channel, thereby affecting the photonic heat transfer.
• Figure 3: Electrical characterization of the Josephson field effect transistor.a, Gate-dependent $V-I$ characteristics of the JoFET. b, JoFET gate-dependent switching current. c, JoFET linear Josephson inductance plotted in logarithmic scale. d, JoFET normal-state resistance. Orange and green shaded boxes identify the dissipationless and resistive JoFET regimes, respectively. e, Numerical calculation of the gate-dependent photonic heat current from the hot to the cold reservoir. The orange and green curves refer to the JoFET in the inductive (orange solid line) and resistive (green solid line) regimes. The black-dashed curve represents a conventional non-superconducting FET acting as a gate-tunable resistor with value (d); the gray curve represents the case with no photon heat modulator. f-g, Experimental determination of the electron-phonon interaction parameters. (f) reports the e-ph coupling constant ($\Sigma$) while (g) depicts the power law constant ($n$) as a function of $T_{bath}$. The yellow shaded region indicates the validity range of our analysis.
• Figure 4: Gate-tunable photonic heat transport modulation.a, Experimental gate-dependent $T_{cold}$ for different $T_{hot}$ (reported in the legend) at $T_{bath}=30$ mK. Each point represents the mean of six switching current measurements taken on the thermometer at the cold reservoir; error bars are smaller than the point size. b-d, Gate-dependent $T_{cold}$ experimental and theoretical data comparison for different $T_{hot}$ at $T_{bath}=30$ mK. Solid lines include the additional loss term $\dot{Q}_{ext}$ while the dashed line does not.
• Figure 5: Influence of the bath temperature on the gate-tunable photonic heat transport modulationa, Experimental gate-dependent $T_{cold}$ for different $T_{bath}$ (reported in the legend) at $T_{hot}=350$ mK. Each point represents the mean of six switching current measurements taken on the thermometer at the cold reservoir; error bars are smaller than the point size. b, Numerical simulation of $\eta_T=(T_{cold}-T_{bath})/(T_{bath})$. The horizontal gray dashed line corresponds to $\eta_T^*=0.1$, where the relative difference between $T_{cold}$ and $T_{bath}$ is negligible. The vertical gray dashed line indicates $T_{bath}^*=170$ mK associated with $\eta_T^*=0.1$. The blue-shaded region represents the bath temperature range in which the cold reservoir operates properly. c-d, Temperature difference $\delta T_{cold}$ of the cold reservoir between the JoFET operating in the superconducting state ($V_g>-2V$) and the resistive state ($V_g<-4V$). Black points in panel c report data versus $T_{bath}$ while green points in panel d report data versus $T_{hot}$. e-f, Gate-dependent thermal transimpedance $\beta = \partial T_{cold}/\partial V_g$ for two different selected $T_{hot}$ at $T_{bath}=30$ mK. The magenta curve refers to experimental data, while the black dashed curve indicates theoretical results obtained with the model.