Optimal superconductivity in twisted bilayer WSe$_2$ where the Van Hove singularity crosses half-filling

Abstract

The recent discovery of unconventional superconductivity has pointed to twisted WSe$_2$ bilayer as a versatile platform for studying the correlated and topological phases of matter. Here we analyze the effect of the displacement field and electron interactions on the formation of a topological paired state in twisted WSe$_2$. Our approach is based on the effective single band $t$-$J$-$U$ model supplemented with intersite Coulomb interaction term and treated within the Gutzwiller approximation. We show that the superconducting phase is stabilized in a small range of displacement fields where the Van Hove singularity crosses half-filling, which is in qualitative agreement with recent experimental data. According to our analysis, such a circumstance comes as a result of a subtle interplay between the large density of states of the Van Hove singularity, in combination with the renormalization effects that appear in the weak-to-moderate correlations regime. The two factors create favorable conditions for the SC pairing only in a small area of the phase diagram.

Figures (4)

• Figure 1: (a) Phase factor $\phi$ as a function of displacement field, $D$, together with spin-up (blue) and spin-down (red) Femi surfaces at half-filling for selected values of D (inset). In the upper right corner we provide the $\nu_{ij}=\pm 1$ factor corresponding to the six nearest neighbors [c.f. Eq. (\ref{['eq:Hamiltonian_start']})]. (b) Density of states at the Fermi level as a function of band filling for selected values of the displacement field $D_l\in\{0.05,~0.2,~0.3,~0.45,~0.6\}$ V/nm, for $l=1,2,3,4,5$, respectively.
• Figure 2: Symmetry resolved superconducting gap amplitudes corresponding to the obtained mixed spin-singlet $d+id$ and spin-triplet $p-ip$ paired state as a function of band filling $n$ and and displacement field $D$ for gradually increasing value of the intersite Coulomb repulsion $V$. The onsite Coulomb repulsion and the exchange interaction parameters are set to $U=80$ meV and $J=4t^2/U$, respectively. The solid blue line in (e) and (j) mark the evoulution of the van Hove singularity across the phase diagram. The white dashed line is a guide to the eye denoting the stability range of the SC state.
• Figure 3: The $g_v^2$ (a) and $\lambda_s^4$ (b) factors which renormalize the intersite Coulomb interaction term and the exchange interaction term [cf. Eq. (\ref{['eq:J_V_expectation_value']})], respectively, as a function of $n$ and $D$. The blue line marks the Van Hove singularity evolution across the phase diagram. The black dashed line correspond to the stability of the SC state as in Fig. \ref{['fig:diagrams_DnV_dep']} (e,j). Note, that SC phase is located at the crossing of the Van Hove singularity line and the area where the renormalization is the strongest. (c) The SC gap as a function of $U$ and $n$ for $D=0.35$ V/nm with $J=4t^2/U$, $V=U/3.635$. We provide only the singlet component since the triplet one shows the same behavior but is approximately twice smaller.
• Figure 4: Symmetry resolved gap amplitudes of the mixed singlet-triplet solution as a function of $n$ for $D=0.35$ V/nm and for two selected values of the onsite Coulomb repulsion, $U=80$ meV (a) and $U=120$ meV (b). In both cases we keep $J=4t^2/U$ and $V=U/3.635$.