OUTLOOK

Despite significant progress in revealing the exotic flat-band physics in twisted graphene superlattice, several key challenges remain. A primary obstacle is that the electronic states in twisted graphene are susceptible to twist angle inhomogeneity and strain, leading to difficulties in reproducing these states in different devices. A reliable control of the twist angle and the suppression of twist-angle disorder is therefore of high importance for the ongoing experimental studies of twisted graphene.

The microscopic superconducting pairing mechanism of twisted graphene remains enigmatic. Recent studies showed that when a metallic gate, bilayer graphene or SrTiO₃ dielectric substrates with a large in-situ tunable dielectric constant are placed close to TBG to enhance the screening effect and reduce Coulomb interactions, the correlated insulating phases are suppressed while superconductivity remains robust, suggesting that superconducting states are independent of and probably competing with the nearby correlated insulators [119–122]. Such behaviors are distinct from high temperature cuprate superconductors where the antiferromagnetic Mott insulator is a “parent” state of superconductivity. Indeed, more and more results suggest that superconducting states and correlated insulators in twisted graphene may slightly differ such as in the specific IVC quantum textures [25]. One interpretation for the decoupled superconductivity and correlated insulator is that electron–phonon coupling, amplified by the enhanced density of states in flat bands, plays a central role in the superconducting pairing mechanism [123,124]. While in TBG/SrTiO₃ devices, superconducting pairing mechanism is found to arise from Coulomb interactions given the complete suppression of superconductivity with increasing dielectric screening strength [123]. These experimental results, together with the discussed non-BCS pairing behaviors hint that the microscopic superconducting pairing mechanism in twisted graphene is complex, and both electron-phonon coupling and electron–electron interactions are important for superconducting pairing. Examining the response of superconducting critical temperature _T_C to carbon isotope effect where substitution of 12C with heavier 13C shifts the phonon spectrum without altering the electronic structure, would provide direct evidence for the role of electron–phonon coupling in the superconducting pairing mechanism.

On the other hand, experimental signatures of anisotropic superconducting gap pose an urgent requirement for a thorough investigation into the symmetry of superconducting order parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mathrm{\Psi }} = |\Delta ( k )|{{e}^{i\phi ( k )}}$\end{document}, which is typically subject to the lattice symmetry, spin structure and Coulomb interactions. This requires momentum-resolved and phase-sensitive probes to detect the momentum dependence of superconducting gap Δ ( k ) and phase change ϕ ( k ) at a sub-millielectronvolt energy and micrometer spatial scale, imposing great challenges to the traditional spectroscopy techniques. Cryogenic QTM in this context, and phase-sensitive global transport measurements including Little-Parks oscillations in mesoscopic rings, phase-sensitive SQUID interferometry, etc., are hoped to provide more insight.

The future of twisted graphene superlattice also lies in further leveraging designable freedoms with tailored correlations and topology. By integrating tunable strain strength, researchers can control the competing orders and band topology that are linked to quantum textures of many-body wavefunctions [32]. Twisted graphene superlattice holds great promise for exploring quantum phase transitions and exotic quantum criticality beyond conventional paradigms with its flexible in-situ tuning knobs. In addition, incorporating exotic graphene stacking order, moiré periodicity and layer symmetry to expand the family of twisted graphene, opens exciting prospects to investigate the unexplored quantum states. The recently investigated twisted rhombohedral graphene provides such opportunities to explore high integer Chern number or novel fractional Chern insulating states outside the traditional Landau-level framework [125–128]. We believe continuous exploration of twisted graphene superlattices promises to uncover surprising physical phenomena and provide new routes toward correlated and topological quantum matter.