A Zero-Bias Superconducting Voltage Amplifier Based on the Bipolar Thermoelectric Effect

Abstract

We introduce a zero-bias superconducting voltage amplifier that harvests energy from a thermal gradient by exploiting negative differential resistance (NDR) in an asymmetric tunnel junction. The device is based on an asymmetric superconductor-insulator-superconductor (SIS) junction with an energy-gap ratio of $Δ_1/Δ_2 = 0.5$, connected in series with a load resistor. Owing to the superconducting bipolar thermoelectric effect, the current-voltage characteristic of the junction exhibits a region of NDR, in which the net current flows opposite to the applied voltage. This mechanism enables voltage amplification in the absence of any external electrical bias, relying solely on the temperature difference between the electrodes ($T_H \simeq 1$ K, $T_B \simeq 20$ mK). Numerical simulations predict a voltage gain of 20 dB, a 1 dB compression point at an input amplitude of 2 $μ$V, and a total harmonic distortion below $-50$ dB. The input-referred noise is approximately 1 nV/$\sqrt{Hz}$, with an associated thermal load on the order of nanowatts. The frequency response is broadband from near DC, with a $-3$ dB cutoff around 180 MHz, set by the RC time constant of the junction. Using Al-, Al-Cu-, and AlO$_x$-based technologies, the amplifier is compatible with conventional superconducting circuit fabrication processes. These findings demonstrate that thermoelectric superconducting junctions can deliver bias-free voltage amplification from near DC up to about 200 MHz, making them promising candidates for transition-edge sensor readout, quantum circuit instrumentation, and low-frequency cryogenic signal processing.

Figures (4)

• Figure 1: Device concept and operating principle. (a) Device schematic. The amplifier comprises an asymmetric superconductor–insulator–superconductor (SIS) tunnel junction ($\text{Al}/\text{AlO}_x/\text{Al-Cu}$) connected in series with a load resistor $R_L$. The superconducting energy gaps of the two electrodes are $\Delta_2(T=0) = 0.20$ meV and $\Delta_1(T=0) = 0.10$ meV, respectively. A thermal gradient ($T_H \simeq 1$ K, $T_B = 20$ mK) provides the driving energy, such that the device operates as a bias-free voltage divider. (b) Energy-band diagram illustrating the superconducting bipolar thermoelectric effect. The combination of gap asymmetry ($\Delta_1/\Delta_2 = 0.5$) and thermal gradient ($T_H \gg T_B$) ensures the condition $\Delta_2(T_H) > \Delta_1(T_B)$. Thermal broadening of the quasiparticle distribution in the hot electrode leads to an effective alignment of quasiparticle energies with the gap-edge density-of-states (DOS) singularities in the cold electrode. This specific energy alignment induces a net charge current flowing opposite to the applied voltage for $|V| \lesssim \Delta_2(T_H) - \Delta_1(T_B)$, thereby yielding a negative absolute resistance ($IV < 0$) and a negative differential resistance $r_d = (\text{d}I/\text{d}V)^{-1} < 0$ at zero applied bias. (c) Voltage amplification mechanism. The current–voltage ($I$–$V$) characteristic of the junction (blue curve) intersects the load line determined by $R_L$ (red line) at a zero-bias operating point. A small AC input signal $V_{in}$ modulates this operating point, giving rise to an amplified output voltage $V_{out}$. The corresponding voltage gain is given by $G_V = |r_d|/(|r_d| - R_L)$, with $G_V > 1$ for $R_L < |r_d|$. The amplification process is fully powered by the thermal gradient; no external DC power is required.
• Figure 2: Current–voltage characteristics and differential conductance as functions of temperature. (a) Current–voltage ($I$–$V$) characteristics as a function of the bath temperature $T_B$ at fixed hot-electrode temperature $T_H = 1$ K. For $T_B < 0.3$ K, the $I$–$V$ curves display a region of negative differential conductance extending over the bias interval $|V_T| \lesssim \Delta_2(T_H) - \Delta_1(T_B)$. This region vanishes for $T_B \gtrsim 0.3$ K, in correspondence with the suppression of the bipolar thermoelectric effect. (b) $I$–$V$ characteristics as a function of the hot-electrode temperature $T_H$ at fixed $T_B = 20$ mK. The occurrence of negative differential conductance is highly sensitive to $T_H$: for $T_H \gtrsim 1.1$ K, the superconducting gap $\Delta_2(T_H)$ is substantially suppressed, whereas for $T_H \lesssim 0.9$ K, thermal broadening is insufficient to significantly populate quasiparticle states above the gap edge. Optimal device performance is achieved at $T_H \simeq 1$ K with $T_B = 20$ mK. (c) Zero-bias conductance map $G(0)$ as a function of $T_H$ and $T_B$. The blue region ($G(0) < 0$) indicates the amplification regime associated with negative differential conductance, whereas the red region corresponds to the positive-conductance regime, in which the thermoelectric response is effectively quenched.
• Figure 3: Figures of merit: gain, saturation, and linearity. (a) Voltage gain $G_V$ (blue) and 1 dB compression point $V_{-1\text{dB}}$ (red) as functions of load resistance $R_L$ at $T_B = 20$ mK and $T_H = 1$ K. The gain is given by $G_V = |r_d|/(|r_d| - R_L)$, where $r_d = (dI/dV)^{-1} \simeq -2000~\Omega$. As $R_L$ approaches $|r_d|$, the gain diverges, whereas the 1 dB compression point tends to zero. The vertical dashed line indicates the chosen operating point $R_L = 1800~\Omega$, which yields $G_V \simeq 20$ dB and $V_{-1\text{dB}} \simeq 2~\mu$V. (b) Linearity metric $L_{\text{THD}}$ as a function of input amplitude $V_{\text{in}}$ for $R_L = 1800~\Omega$ at several bath temperatures. The quantity $L_{\text{THD}}$ is defined as $-20\log_{10}\!\bigl(\sqrt{\sum_{i=2}^{\infty} A_i^2/A_1}\bigr)$, where $A_i$ denote the output harmonic amplitudes. Linearity deteriorates with increasing drive amplitude. In contrast, increasing bath temperature improves linearity due to the reduction of gain, which suppresses nonlinear distortion. The non-monotonic features originate from a cancellation of the third-order harmonic contribution to the total harmonic distortion (see Appendix \ref{['sec:appendix1']}).
• Figure 4: Frequency response: gain and input-referred voltage noise. (a) Voltage gain $G_V$ as a function of frequency $f$ for various bath temperatures $T_B$ at fixed $T_H = 1$ K and $R_L = 1800~\Omega$. The response is broadband, starting near DC, with a $-3$ dB cutoff at around $180$ MHz, set by the junction RC time constant. Increasing $T_B$ suppresses the thermoelectric response, leading to an increase in $|r_d|$ and a corresponding reduction in gain. (b) Input-referred voltage noise spectral density $\sqrt{S_V^{\mathrm{in}}}$ as a function of frequency for different load resistor temperatures. For an on-chip resistor at $T_B = 20$ mK, the noise is predominantly determined by shot noise originating from the hot electrode, resulting in $\sqrt{S_V^{\mathrm{in}}} = 0.86$ nV/$\sqrt{\text{Hz}}$. As the load resistor temperature is increased, its Johnson noise contribution eventually becomes the dominant component of the total noise floor. The noise spectrum is essentially frequency-independent from near-DC up to the amplifier bandwidth, beyond which it rolls off.