Strong nonlinear thermoelectricity generation and close-to-Carnot efficient heat engines in Superconductor-Insulator-2D electron gas junctions

Abstract

We find that a novel Superconductor-Insulator-2D electron gas tunnel junction (SISm) strongly and efficiently generates thermoelectricity via a nonlinear mechanism. We simulate across the parameter space of the junction, finding and discussing different regimes with features useful for thermoelectricity generation or for specific applications. The generated Seebeck potential can go up to $6.75Δ_0$ with a huge nonlinear Seebeck coefficient, and efficiency can get very close to Carnot efficiency $η=0.96η_C$, a record for a solid-state device model. Thermoelectric performance is far better than analogous junctions, with fewer fabrication challenges, as the device can be fabricated via standard methods.

Figures (5)

• Figure 1: SISm junction scheme and band alignment for a moderately degenerate 2DEG ($E_c-\mu_{\rm Sm}=-0.9\Delta_0$). If $T_{\rm S}>T_{\rm Sm}$, a quasielectron current $I_0$ forms, while quasiholes are blocked by the semiconductor gap. In open-circuit, $V$ builds up until $\mu_{\rm Sm}$ reaches $\sim \Delta(T_{\rm S})$, where a current of electrons at the peak energy starts flowing backwards, canceling $I_0$. More information in the main text.
• Figure 2: IV curves for different values of $E_c$ at $T_{\rm S}=0.7T_c$. Thermoelectricity is generated in all regimes for $0\lesssim V\lesssim\Delta/e$, and for $V>\Delta/e$ if $E_c\geq 0$. The inset shows that for $V>\Delta/e$, $I$ changes sign for $E_c=0.03\Delta_0$, but not for $E_c=0.5\Delta_0$.
• Figure 3: Parts of IV curves for different values of $E_c$ and $T_{\rm S}$ showing different behaviors. a)$E_c=-1.5\Delta_0$. For different values of $T_{\rm S}$, the system transitions from an Ohmic-like behavior at $T_{\rm S}=0.08T_c$ to generating thermoelectricity at $T_{\rm S}=0.46T_c$. At $T_{\rm S}=0.23T_c$, the system shows an intermediate behavior that leads to a bistable state described in the main text. b)$E_c=-0.8\Delta_0$. The system shows a strong dependence of $V_S$ on $T_{\rm S}$ for $0.15T_c\lesssim T_{\rm S}\lesssim0.22T_c$. c)$E_c=0.03\Delta_0$. For $T_{\rm S}\gtrsim0.18T_c$, $V_S>\Delta$, up to $\sim 6\Delta_0$ for $T_{\rm S}=0.95T_c$. More information in the main text.
• Figure 4: Figures of merit for nonlinear thermoelectricity. a) Seebeck potential $V_S$ dependence on $T_{\rm S},T_{\rm Sm}$ for $E_c=0.03\Delta_0$. For $T_{\rm Sm}=7.6\times10^{-3}T_c$ (the lowest), $V_S$ becomes larger than $\Delta_0$, with some values shown in Fig.\ref{['fig2']}c) as zeroes, with maximum $V_S\sim 6.75\Delta_0$ for $T_{\rm S}\rightarrow T_c$. Larger $T_{\rm Sm}$ reduce $V_S$, but $V_S>\Delta_0$ holds for relatively large $T_{\rm Sm}\sim0.1T_c$. b) Peltier current $I_0$ dependence on $T_{\rm S},T_{\rm Sm}$ for $E_c=-0.8\Delta_0$. The maximum is at $T_{\rm S}\sim T_c$, with a peak at $T_{\rm S}\sim 0.75T_c$, explained in the main text. The dependence on $T_{\rm Sm}$ is negligible. c) Generated power $W$ and efficiency $\eta$ for different values of $E_c,T_{\rm S}$ with $T_{\rm Sm}=7.6\times10^{-3}T_c$. We limit the analysis to $V$ values where the junction is a heat engine. For $T_{\rm S}=0.25T_c$, $W$ is multiplied by $10^3$ for readability. $\eta_C$ is the Carnot efficiency. For $E_c=-0.8\Delta_0$, setting $T_{\rm S}=0.9T_c$ shows $W_{\rm max}=0.1\,G_T(\Delta_0/e)^2$. $E_c=0.03\Delta_0$ shows an efficiency of $\eta=0.96\eta_C$ close to Carnot efficiency for $T_{\rm S}=0.25T_c$. More information in the main text.
• Figure S1: Wider representation of $W$ and $\eta$ dependence on $V$ for several regimes. For $E_c=0.03\Delta_0,T_{\rm S}=0.9T_c$, the point $V=2\Delta_0/e$ where $W\sim0.02 G_T(\Delta_0/e)^2$ and $\eta=0.8\eta_C$ is mentioned in the main text. Read this section for more details.