Detection of spin- and valley-polarized states in van der Waals materials via thermoelectric and non-reciprocal transport

Abstract

We predict thermoelectric and current rectification effects in hybrid junctions formed by Ising superconductors and materials hosting valley-polarized states. Both effects originate from the interplay of intrinsic Ising spin-orbit coupling, spin-splitting from an exchange or Zeeman field, and valley polarization. The resulting transport signatures provide experimentally accessible probes of valley-polarized states in van der Waals heterostructures, such as junctions of few-layer transition metal dichalcogenides and twisted bilayer or rhombohedral graphene.

Figures (6)

• Figure 1: Schematic illustration for probing Ising thermopower and rectification. (a) Junction between Ising SC and a spin- and valley-polarized material X with a tunnel barrier. The field $\boldsymbol{h}$, in the SC can be applied with an in-plane external field or via proximity effect with a ferromagnetic insulator. The probe can be an STM tip on which the SC is grown or can be a gate for tuning the superconducting phase, while the bottom gate tunes the electronic state of X. The thermoelectric signal results from a temperature difference, $\delta T$, between the materials, while rectification occurs as a consequence of voltage differences beyond the linear regime. (b) The valley and spin dependence of the tunneling. Only intra-valley tunneling with tunneling amplitude $t$ of the same spin species is allowed. However, due to the valley and spin polarization in X, the tunneling conductance $G_{\sigma v}^{}$ inherits spin, $\sigma$, and valley, $v$, selectivity enabling the probing of valley- and spin-polarized states in the Ising SC.
• Figure 2: Various DOS in Ising SC with in-plane field showing both energy and spectral gap, $\Delta_{\rm}^{}$, symmetries. These DOS are responsible for different transport coefficient, see Eq. \ref{['eq:Transport-coeffs']}. Here, $\Delta_{\rm so}^{}/\Delta_0^{}=1,\, h_{\rm }^{}/\Delta_0^{}=0.2,\, \psi = 0$, and $\Delta_0^{} \equiv \Delta \left( T=0,h=0 \right)$.
• Figure 3: Thermoelectric coefficients in Ising SC. $\alpha_z^{}$ in $h-\Delta_{\rm so}$ space (a) and $h- T$ space (b). (c,d) Same as (a,b) but for $\alpha_x^{}$. Here $\psi=0$, $k_{B}^{}T/\Delta_0^{}=0.3$ in (a,c), and $\Delta_{\rm so}/\Delta_0^{} =1$ in (b,d).
• Figure 4: Seebeck coefficients from Ising SC, $S_{x/z}^{}$ corresponding to the TEs in Fig. \ref{['fig:TE-Coeffs']}.
• Figure 5: Rectification effects from Ising SC. (a) Individual currents, $I_{0,x,z}^{}$, and (b) rectification factors. Here $\Delta_{\rm so}/\Delta_0=h/\Delta_0=1$ and $k_{\rm B}^{}T/\Delta_0 = 0.1$.