Session A44: Extending the Twist Paradigm Beyond Bilayer Graphene

Simulating twistronics in acoustic metamaterials

Twisted van der Waals (vdW) heterostructures have recently emerged as a tunable platform for studying correlated electrons. However, these materials require laborious and expensive effort for both theoretical and experimental exploration. Here we numerically simulate twistronic behavior in acoustic metamaterials composed of interconnected air cavities in two stacked steel plates. Our classical analog of twisted bilayer graphene (TBG) perfectly replicates the band structures of its quantum counterpart, including mode localization at a magic angle of 1.12º. However unlike the quantum counterpart, we can simply and continuously tune the thickness of the interlayer membrane to reach a regime of strong interlayer tunneling where the acoustic magic angle appears as high as 6.01º, equivalent to applying 130 GPa to twisted bilayer graphene. In this regime, the localized modes are over five times closer together than at 1.12º, increasing the strength of any emergent non-linear acoustic couplings. Currently, our tunable metamaterial design will allow simulation of a broad class of twisted vdW heterostructures at accessible moiré unit cell sizes. In the longer term, 3D-printed acoustic metamaterials could offer a new way to experimentally simulate complex, multilayer vdW heterostructures with overlapping moiré patterns that exceed all computational capabilities.   

A moire superlattice on the surface of a topological insulator

Twisting two materials produces moiré patterns and can induce correlated many-body states, as seen in twisted bilayer graphene, for example. We investigate the surface state of a topological insulator subject to a moiré superlattice potential. With diagrammatic perturbation theory, lattice model simulations, and ab initio calculations, we uncover the unique aspects of twisting a single Dirac cone with an induced moiré superlattice and the role of bulk topology on the reconstructed bands. The Dirac cone velocity renormalizes, but no gap opens up; instead, a whole ladder of satellite Dirac cones appears, some of which can be made relatively flat with a large nearby density of states. We discuss the implications of our findings to correlated physics and future experiments.   

Emergent Interfacial Superconductivity between Twisted Cuprate Superconductors

We developed a cryogenic assembly technique to fabricate Josephson junctions with an atomically sharp twisted interface between Bi2Sr2CaCu2O8+x crystals. We find that the Josephson critical current density $J_c$ depends sensitively on the twist angle. At small twisting angles,  $J_c$ exhibits the maximum value comparable to that of the intrinsic junctions. Close to 45 degree twisting angle, $J_c$ is greatly suppressed, but it remains finite. Near 45 degree twisted angle, we observe well-developed Fraunhofer patter as well as half-integer Shapiro steps. Theoretical analysis of our data suggests that the remaining superconducting coherence at 45 degree twisted angle indicates the development of dominant second harmonic in the Josephson energy versus phase relation due to the co-tunneling of Cooper pairs, supporting time reversal symmetry broken interfacial superconductivity in this junction.   

Magic angles and current-induced topology in twisted nodal superconductors

Motivated by the recent achievements in the realization of strongly correlated and topological phases in twisted van der Waals heterostructures, we study the low-energy properties of a twisted bilayer of nodal superconductors. It is demonstrated that the spectrum of the superconducting Dirac quasiparticles close to the gap nodes is strongly renormalized by twisting and can be controlled with magnetic fields, current, or interlayer voltage. In particular, the application of an interlayer current transforms the system into a topological superconductor, opening a topological gap and resulting in a quantized thermal Hall effect with gapless, neutral edge modes. Close to the "magic angle," where the Dirac velocity of the quasiparticles is found to vanish, a correlated superconducting state breaking time-reversal symmetry is shown to emerge. Estimates for a number of superconducting materials, such as cuprate, heavy fermion, and organic nodal superconductors, show that twisted bilayers of nodal superconductors can be readily realized with current experimental techniques.   

Moire physics in transition metal dichalcogenides

I will survey recent advances in van der Waals heterostructures formed by stacking two layers of transition metal dichalcogenides (TMD). When the two layers have a small lattice mismatch or rotational misalignment, a long-wavelength moire structure emerges and produces narrow minibands in the electron energy spectrum. Strong electron interaction effects in these minibands give rise to a remarkable variety of quantum states, including Mott/charge transfer insulators, generalized Wigner crystals, and the quantum anomalous Hall state. I will introduce a theoretical description based on generalized Hubbard model to explain these diverse phenomena in a unified way. In particular, the newly discovered quantum anomalous Hall state in MoTe2/WSe2 arises from inverted charge transfer gap in a Mott insulator [1]. Doping charge transfer insulators in TMD moire materials may give rise to pair density wave and unconventional superconducting states [2,3].

[1] T. Devakul and L. Fu, arXiv:2109.13909 (to appear in PRX)   

[2] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)

[3] V. Crépel and L. Fu, Science Advances 7, eabh2233 (2021)