Active electron cooling of graphene

TL;DR

This work tackles cryogenic heat management in nanoscale graphene devices by introducing a non-local graphene thermal transistor powered by superconducting SINIS tunnel junctions. The authors demonstrate active cooling of graphene electrons, achieving a maximum graphene temperature reduction of $\delta T_G=(15.5\pm0.5)\,\text{mK}$ at $T_b\approx 448\,\text{mK}$ and a notable drain cooling of $T_b- T_{D,\min}\approx3\,\text{mK}$, supported by a comprehensive thermal model that reproduces the observed data. The study provides detailed device design, fabrication, and parameter measurements (including tunnel resistances, energy gaps, and Dynes broadening), along with a model-based extraction of $T_G$ from drain thermometry. These results establish non-local superconducting cooling as a viable route to reduce quasiparticle poisoning and noise in graphene-based quantum devices, with potential applications in graphene-based cold electron bolometers and other hybrid superconducting technologies.

Abstract

In the emergent field of quantum technology, the ability to manage heat at the nanoscale and in cryogenic conditions is crucial for enhancing device performance in terms of noise, coherence, and sensitivity. Here, we demonstrate the active cooling and refrigeration of the electron gas in a graphene thermal transistor, by taking advantage of nanoscale superconductive tunnel contacts able to pump or extract heat directly from the electrons in the device. Our prototypes achieved a top cooling of electrons in graphene of about 15 mK at a bath temperature of about 450 mK, demonstrating the viability of the proposed device architecture. Our experimental findings are backed by a detailed thermal model that accurately replicated the observed device behavior. Alternative cooling schemes and perspectives are discussed in light of the reported results. Finally, our graphene thermal transistor could find application in superconducting hybrid quantum technologies.

Figures (8)

• Figure 1: Schematics and basic characterization of the graphene electron cooler.a Schematic representation of the device. The electronic temperature ($T_S$) of the metallic Al$_{0.98}$Mn$_{0.02}$ source electrode ($S$, red) is decreased/increased with respect to the substrate phonon temperature ($T_b$) by voltage biasing ($V_{cool}$) a couple of superconducting Al tunnel coolers ($c_1$ and $c_3$, yellow). The temperature ($T_D$) of the Al$_{0.98}$Mn$_{0.02}$ drain electrode ($D$, orange) is measured by current biasing ($I_{th}$) a couple of superconducting tunnel thermometers ($t_1$ and $t_3$, yellow) while recording the voltage drop ($V_{th}$). The measured modulation of $T_D$ is due to the change of the graphene electronic temperature ($T_G$). b Current ($I_{cool}$) versus voltage ($V_{cool}$) characteristics of the cooling tunnel junctions ($c_1$ and $c_3$) for selected values of the bath temperature ($T_b$). c Calibration of the thermometers ($t_1$ and $t_3$) in the form of the voltage ($V_{th}$) versus $T_b$ characteristics at constant current bias $I_{th}=300\,{\rm pA}$.
• Figure 2: Temperature modulation of the drain electrode.a Electronic temperature of the drain electrode ($T_D$) as a function of the voltage bias of the source coolers ($V_{cool}$) recorded at selected values of bath temperature ($T_b$). b$T_D$ versus $V_{cool}$ characteristics recorded at $T_b=448\,{\rm mK}$. The system shows cooling, that is $T_D<T_b$ for specific values of $V_{cool}$. $T_{D,min}$ represents the minimum recorded value of $T_D$. c$T_D$ versus $V_{cool}$ characteristics recorded at $T_b=307\,{\rm mK}$. The system shows refrigeration: the coolers are able to decrease the drain temperature from a maximum value ($T_{D,max}$), but $T_D>T_b$ always applies.
• Figure 3: Thermal modeling of the device, data analysis, and graphene temperature estimation.a Thermal model accounting for the predominant thermal exchange processes in our structure. The heat interactions between the different elements are indicated by the springs. The sign of the thermal currents depends on the operation regime: refrigeration/cooling or heating. b Experimental modulations of $T_D$ (circles) by $V_{cool}$ along with the theoretical model (lines) obtained at $T_b=448\,{\rm mK}$ (red), $T_b=375\,{\rm mK}$ (yellow) and $T_b=307\,{\rm mK}$ (green). c Electronic temperature of drain ($T_D$, orange), graphene ($T_G$, grey) and source ($T_S$, red) extracted by fitting the experimental data at $T_b=448\,{\rm mK}$. The maximum difference between the experimental value and the model of $T_D$ is 0.4 mK, which corresponds to an error of $\pm1.6$ mK on $T_G$ and of $\pm4.8$ mK on $T_S$.
• Figure 4: Electron refrigeration of graphene.a Electronic temperature of graphene ($T_G$) versus the cooler voltage bias ($V_{cool}$) extracted for selected values of phonon temperature ($T_b$). The maximum error in the estimate of $T_G$ is $\pm2$ mK. b Voltage-to-temperature transfer function ($\mathcal{T}=\text{d}T_G/\text{d}V_{cool}$) versus cooler voltage bias ($V_{cool}$) extracted for selected values of phonon temperature ($T_b$). The maximum error in the estimate of $\mathcal{T}$ is $\pm16\,{\rm K/ V}$. c Electronic refrigeration of graphene ($\delta T_G=T_{G,min}-T_{G,max}$) versus phonon temperature ($T_b$) extracted for different data sets. The inset schematically depicts the definition of $T_{G,min}$ and $T_{G,max}$. The dotted line is a guide to the eye. d Normalized graphene electronic refrigeration ($\delta T_G/T_b$) versus $T_b$ extracted for different data sets. The dotted line is a guide to the eye.
• Figure 5: Raman spectroscopy. Typical Raman spectrum of the graphene channel of our thermal transistor (blue) along with the Lorentian fit (red) of the $G$ and $2D$ peaks. The position of the two Raman modes is $\sim1582.7$ cm$^{-1}$ and $\sim2676.5$ cm$^{-1}$ for the $G$ and $2D$ peak, respectively. By constructing the related correlation plot Lee2012-rg, we extracted a small strain ($\sim0.1\%$) and a charge concentration $n_G\simeq3\times10^{12}\,{\rm cm^{-2}}$ for the graphene channel.