Nematic Enhancement of Superconductivity in Multilayer Graphene via Quantum Geometry

Abstract

Multilayer graphene materials have recently emerged as a fascinating versatile platform for correlated electron phenomena, hosting superconductivity, fractional quantum Hall states, and correlated insulating phases. A particularly striking experimental observation is the recurring correlation between nematicity in the normal state -- manifested by spontaneous breaking of the underlying $C_3$ symmetry -- and the stabilization of robust superconducting phases. Despite its ubiquity across different materials, devices and experiments, this trend has thus far lacked a clear microscopic explanation. In this work, we identify a concrete mechanism linking nematic order to enhanced superconductivity. We demonstrate that $C_3$-symmetry breaking strongly reshapes the Bloch wavefunctions near the Fermi level, producing a pronounced enhancement and redistribution of the so-called quantum metric. This effect drastically amplifies superconducting pairing mediated by the quantum geometric Kohn-Luttinger mechanism [G. Shavit \it{et al.}, \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.176001}{Phys. Rev. Lett. 134, 176001 (2025)}]. Our analysis reveals that nematicity naturally boosts the superconducting coupling constant in experimentally relevant density regimes, providing a compelling explanation for observed correlations. These results establish the central role of geometric effects in graphene superconductivity and highlight nematicity as a promising avenue for engineering stronger unconventional superconducting states.

Figures (4)

• Figure 1: Nematicity enhances quantum geometric superconductivity in bilayer graphene. Plot of the maximal superconducting coupling constant $\lambda^*$ (see Sec. \ref{['sec:QGpairing']}) as a function of single-flavor density $n_\alpha$. Green dots represent the case for $C_3$-symmetric normal state (three equal energy trigonal warping pockets in the band structure), and purple represents the nematic normal state (two out of three pockets below the Fermi level). Dashed purple is for the nematic state, in the absence of quantum geometric underscreening, i.e., geometric form-factors in Eq. \ref{['eq:staticpol']} are all set to unity. Notice that the superconducting critical temperature $T_c\propto e^{-1/\lambda^*}$, such that the differences in $T_c$ can be enormous. The parameters used in this figure (see text for details): $U=60$ meV, $d=20$ nm, $\epsilon=4$.
• Figure 2: Quantum metric and $C_3$ breaking in BLG. (a) Trace of the quantum metric plotted for the lowest lying valence band of Bernal bilayer graphene, Eqs. \ref{['eq:hblgschematic']}--\ref{['eq:hblgspecific']}. (b) The same quantity plotted for the scenario with $C_3$ symmetry breaking [see Eq. \ref{['eq:blgnemmodification']}], where a total of two out of three pockets are occupied. (Here, $\phi=\phi_{2\rm p}=\pi$, and $\epsilon_{\rm nem}=20$ meV.) For both panels the black contours represent the Fermi surfaces at the top of the band, plotted in 1 meV intervals, and we use $U=60$ meV. (c) Fermi-surface averaged quantum metric as a function of single-flavor density $n_\alpha$ for the normal case appearing in panel (a) (red), and for the nematic state in panel (b) (blue).
• Figure 3: Quantum geometry in symmetry-broken RnG. (a) Trace of the quantum metric plotted for the conduction band with $n=5$ layers. The quantum metric is peaked in the shape of a rotationally symmetric ring. (b) The quantum metric redistributes when nematicity takes place. It gets both enhanced and concentrated in a narrow sector of the Brillouin zone. For illustrative purposes, the black contours depict the Fermi surface at the bottom of the band, where the Fermi energy is modified by consecutive 1 meV intervals. Here, $u_{\rm nem}=60$ meV nm. (c) Fermi-surface averaged quantum metric as a function of electronic density and symmetry-breaking order parameter. The nematicity-geometry correlation is apparent. (d) Two horizontal cuts of panel (c), with values corresponding to panels (a) and (b). Throughout this figure we use $U=25$ meV.
• Figure 4: Quantum geometric underscreening in BLG. (a) Bare Coulomb repulsion between different segments of the Fermi surface at one of the trigonal warping pockets in BLG. (b) The RPA screened interaction in one of the Fermi pockets of the $C_3$-symmetric normal state. (c) The RPA screened interaction For the nematic state. (d) Same as (c), with all form-factors set to unity in the calculation of $\Pi_{\bf q}$ [Eq. \ref{['eq:staticpol']}]. For all panels, the interactions are normalized such that the value on the diagonal of the interaction matrix is unity. Here, $n_\alpha=10^{11}$ cm$^{-2}$, $\epsilon=4$, and $d=20$ nm. For the nematic plots we used $\phi=\phi_{2\rm p}=\pi$ and $\epsilon_{\rm nem}=20$ meV.