Topological Chiral Superconductivity Mediated by Intervalley Antiferromagnetic Fluctuations in Twisted Bilayer WSe$_2$

Abstract

Motivated by the recent observations of superconductivity in twisted bilayer WSe$_2$ (tWSe$_2$), we theoretically investigate the superconductivity driven by electronic mechanism. We first demonstrate that the multi-band screened Coulomb interaction within the random phase approximation is insufficient to induce observable pairing instability. Nevertheless, by further including the intervalley antiferromagnetic fluctuations, the pairing interaction is substantially enhanced, yielding superconductivity with critical temperature $T_c$ of hundreds of millikelvin at van Hove singularities. The predicted $T_c$ increases with increasing the displacement field and corresponds to a doubly-degenerate $d$-wave-like pairing, which evolves into topological chiral $d \pm id$ superconductor below $T_c$. The interplay between superconductivity and intervalley antiferromagnetism results in a phase diagram consistent with experimental observations.These findings establish intervalley fluctuations as the primary pairing glue in tWSe$_2$.

Figures (5)

• Figure 1: (a) The $K$-valley first morié band along high-symmetry lines of the MBZ. The vertical arrows mark the saddle points for three different values of $V_z$. The inset depicts the Fermi surfaces of $K$ and $K'$ valleys for $V_z = 15$ meV at the VHS. (b) DOS versus the filling fraction $\nu$ and $V_z$.
• Figure 2: (a) RPA bubble diagram summation, where the light and bold wave lines denote the bare and screened Coulomb interactions, respectively. (b),(c) Diagrammatic representations of the linearized gap equation for (b) pairing instability and (c) IVA order. The filled triangle and semicircle denote the SC and IVA order parameters, respectively. The dashed rectangles in (b) and (c) denote series summation of the ladder diagrams, representing IVA fluctuations induced by the RPA screened interaction illustrated in panel (a).
• Figure 3: (a) Phase diagram showing the regions of the superconductivity (SC) (red-filled) and IVA order (gray-filled). The dotted line traces the VHSs as functions of $\nu$ and $V_z$. (b) SC critical temperature $T_c$ and the IVA critical temperature $T_{\text{IVA}}$ plotted as functions of $\nu$ along the dashed line shown in panel (a), with $V_z = 17.56$ meV. (c) $T_c$ and $T_{\text{IVA}}$ at VHSs, extracted from panel (a) along the doted line.
• Figure 4: (a),(b) $\bm{k}$-space structure of the doubly-degenerate order parameters $\Delta_{1,\bm{k}}$ and $\Delta_{2,\bm{k}}$ at the phase point indicated by the open arrow in Fig. \ref{['fig:figure3']}(b). The while lines denote the FS, and the overlaid dots mark the sampling points along the FS, which are equally spaced in angular coordinate $\phi$ with respect to the MBZ center. (c),(d) Angular dependence of the FS-sampled profiles $\Delta_{1,2}(\phi)$, extracted from (a) and (b), and normalized by their respective maximum magnitudes $|\Delta_{m}|$. (e),(f) Fourier decompositions of $\Delta_{1,2}(\phi)$, where $C_n$ denotes the Fourier coefficient of the $n$-th angular momentum channel.
• Figure 5: (a) Temperature dependences of the MBZ-averaged magnitudes of the nematic ($\Delta_{1,2}(\bm{k})$) and chiral ($\Delta_{\pm}(\bm{k}) = \Delta_{1}(\bm{k}) \pm i \Delta_{2}(\bm{k})$) superconducting order parameters. (b) Temperature dependences of the superconducting condensation energies ($E_c$) of the nematic and chiral states. (c),(d) Magnitude and phase of $\Delta_{+}(\bm{k})$ at zero temperature, with the dashed curve denoting the FS. (d) Berry curvature $\Omega_{\bm{k}}$ for $\Delta_{+}(\bm{k})$ pairing state, where $a_m=a_0/\theta$ is the morié period. These results are obtained by solving the self-consistent gap equation with $V_z = 17.56$ meV and $\nu = \nu_{\text{VHS}} + 0.0067$, as marked by the open arrow in Fig. \ref{['fig:figure3']}(b).