Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials

Abstract

We demonstrate that superconductivity driven by strong quantum-critical fluctuations can emerge near relativistic Mott transitions in twisted two-dimensional materials, taking on a remarkably rich character. In twisted double-bilayer WSe$_2$, all time-reversal-even, gap-opening collective modes promote pairing, whereas time-reversal-odd modes do not. In a Dirac model of twisted bilayer graphene, the Gross-Neveu transition into inter-valley-coherent insulators gives rise to a spectrum of degenerate and nearly degenerate superconducting states. More generally, we show that the richer the Dirac structure, the more readily pairs can form. A crucial ingredient of the theory is that critical fluctuations render the electronic states strongly incoherent, allowing attractive pairing channels to overcome the bare Dirac semi-metal behavior. Finally, we demonstrate a direct relation between boson-mediated pairing and the formation of charge-carrying skyrmionic excitations in the proximate insulating state.

Figures (2)

• Figure 1: Schematic phase diagram for the behavior near the Gross-Neveu mass-generating transition (at $g_c$) of two-dimensional Dirac systems within the approach of Ref. Stangier2025. For systems with a sufficiently large anomalous fermion dimension, $\eta_\psi$, in the electron Green's function $G(k)$, critical boson fluctuations (with propagator $D(q)$) give rise to superconductivity (SC) even in the absence of a sharp Fermi surface or any well-defined charge carriers.
• Figure 2: Top Row: The four possible SC instabilities in double-bilayer WSe$_2$ given in Eqs. (\ref{['eq:pairing WSe2']}), (\ref{['eq:pairing WSe2-1-1']}) and (\ref{['eq:pairing WSe2-1']}) labeled by the D$_6$ irrep. Pairing correlations that are intra-sublattice ($\propto \rho_0$) or inter-sublattice ($\propto \rho_2$) are labeled blue and pink, respectively, with solid (dashed) lines connecting inter-valley pairing of type $\tau_1$ ($\tau_2$). Panels with no lines indicate intravalley pairing that is either in phase ($\propto \tau_0$, indicated with $+$) or out of phase ($\propto \tau_3$, indicated with $-$). Bottom Rows: The six possible SC instabilities in TBG depending on the nature of the insulating state (KIVC or TIVC), as listed in Eqs. (\ref{['eq:pairing_KIVC']}) and (\ref{['eq:pairing_TIVC']}) and labeled by the D$_6$ irrep. In each panel the left and right hexagons are the mini-BZ's associated with opposite valleys, with numbers $1,2$ labeling mini-valleys. The valley pairing is labeled by color (pink for $\tau_1$ and blue for $\tau_2$). The pairing can also mix mini-valleys, with $\mu_1$ (or $\mu_2$) pairing given by solid (or dashed) lines, or be in the same mini-valley, with $+-$ (or $++$) labeling $\mu_z$ (or $\mu_0$) giving the phase. In each case, $\vec{\sigma}$ indicates triplet pairing, with the other cases singlet.