Fig. 3: Chiral \(f\pm {{{{{{{\rm{i}}}}}}}}{f}^{{\prime} }\) superconductivity at 30∘ twist.
a Basis functions f1,p(k0), f2,p(k0) of the projected pair wavefunctions in band p = 2 along the circular Fermi surface of twisted-double layer at μ = 2.9t with momentum radius ∣k0∣ ≃ 0.11 Å−1 shown in Fig. 2d. \({\phi }_{{{{{{{{{\bf{k}}}}}}}}}_{0}}\) is the polar angle of k0 in the 2D plane. A relative shift of \(\delta {\phi }_{{{{{{{{{\bf{k}}}}}}}}}_{0}}=\pi /6\) is found between f1,p(k0) and f2,p(k0) due to 30∘-twist. b Phase diagram of a twisted double-layer spin-triplet valley-singlet (STVS) superconductor in the μ-θ plane. A robust chiral \(f\pm {{{{{{{\rm{i}}}}}}}}{f}^{{\prime} }\) phase (regions depicted in blue) is found over the entire chemical potential range for θ ≃ 30∘. c Evolution of phase dependence of the superconducting free energy \({{{{{{{{\mathcal{F}}}}}}}}}_{{{{{{{{\rm{SC}}}}}}}}}(\varphi )\) as a function of twist angle θ at μ = 2.9t. Unit of y-axis set in eV. d Phase diagram in the T-θ plane obtained at μ = 2.9t and coupling constant U0 = 0.013t, corresponding to critical temperature Tc ≃ 3K. e–g Bulk Bogoliubov excitation gap at (e) θ = 29. 5∘, (f) θ = 30. 0∘, and (g) θ = 30. 5∘, corresponding to dots A, B, and C in (b), respectively. Δ0 = 1 meV is used here in line with values of μ, U0 used in (d).
