Spin polarization and diode effect in thermoelectric current through altermagnet-based superconductor heterostructures

Abstract

The recent advent of a new class of magnetic material named as {\it altermagnet} (AM), characterized by a combination of momentum-dependent spin splitting with zero net magnetization, has opened up promising prospects for spintronic applications. We theoretically explore how the altermagnetic spin splitting affects the thermoelectric quasiparticle current in AM-based superconducting heterostructures. Our setup comprises of a bilayer system where a $d$-wave AM is proximity coupled to an ordinary $s$-wave superconductor (SC). We calculate the thermoelectric current carried by the quasiparticles applying a finite thermal bias across the junction. The behavior of the thermoelectric current with the system's base temperature and chemical potential is very similar to that in traditional SC heterostructures. Remarkably, the dissipative thermoelectric current found in the AM junction is spin split and thus generates finite spin polarization in the AM-based junction, which can approach $100\%$ spin polarization in the strong altermagnetic phase. We further investigate the thermoelectric current in AM-based Josephson junction (JJ) and illustrate how to achieve almost perfect diode effect in this AM-based JJ characterized by its efficiency $\sim 100\%$ with its sign decided by the strength of the AM, enhancing the potential for spin-caloritronics applications.

Figures (14)

• Figure 1: Schematic diagram of thermally biased AM-SC hetero junction. Here, a $d$-wave AM is proximity coupled to a common bulk $s$-wave SC at $x=0$. A temperature gradient $\delta T$ is applied across the junction.
• Figure 2: The behavior of the spin-split thermoelectric current $\mathcal{L}_{\sigma}$ (in units of $ek_{B}/h$) as a function of (a) $t_{1}$ choosing $t_{2}=0$ and (b) junction temperature $T/T_{c}$. The other model parameters are considered as (a) $\mu=200\Delta_0$, $T=0.1T_{c}$, $\Delta_0=0.001$ and (b) $t_{1}=0.4$, $t_{2}=0$, $\mu=200\Delta_0$ and $500\Delta_0$ where $\Delta_0=0.001$.
• Figure 3: A schematic diagram of AM-JJ setup where two $s$-wave SCs with phases $\phi_{\rm{L}}$ and $\phi_{\rm{R}}$ are coupled to a $d$-wave AM at $x=0$ and $x=d$ respectively. These two SCs are maintained at two different temperatures $T+\delta T$ and $T$, respectively, in order to create a temperature gradient $\delta T$ across the JJ setup.
• Figure 4: The spin-dependent thermoelectric quasiparticle currents $\mathcal{L}_{\sigma}$ (in units of $ek_{B}/h$) with respect to the superconducting phase difference $\phi$, for different pairs of AM strengths $t_{1}$ and $t_{2}$ in the JJ. The up-spin current is presented by $\mathcal{L}_{\uparrow}$ and the down-spin current is presented by $\mathcal{L}_{\downarrow}$. Here, we consider the other parameters of the model Hamiltonian as $\mu=200\Delta_{0}, d=0.1\xi, T=0.4 T_{c}, \Delta_{0}=0.001$.
• Figure 5: The spin-dependent thermoelectric currents $\mathcal{L}_{\sigma}$ (in units of $ek_{B}/h$) is displayed for the up-$(\mathcal{L}_{\uparrow})$ and down-spin $(\mathcal{L}_{\downarrow})$ quasiparticles with respect to (a) the AM strength $t_{1}$ and (b) the heterostructure temperature $T$ (in units of $T_{c}$) for different AM strengths $t_{1}$. This result is presented for the normal AM-SC interfaces, considering $t_{2}=0$. We choose temperature $T=0.3T_{c}$ for (a). The other system parameters remain the same as we consider in Fig. \ref{['L_vs_phi']}.