Spectroscopic signatures of intervalley coherence and superconductivity in twisted trilayer graphene

Recent [1,2] scanning tunneling microscopy (STM) experiments suggest that the incommensurate K’ekul’e spiral (IKS) metal is the normal state from which superconductivity emerges in twisted bilayer and trilayer graphene. We explore the pairing instabilities of such IKS metals to identify qualitatively robust trends in the spectroscopic signatures of moiré graphene systems. Using symmetry considerations and self-consistent mean-field analysis, we rationalize the reported [3] evolution between U-shaped (gapped) and V-shaped (nodal) tunneling spectra in twisted trilayer graphene. We further argue that the IKS metal gives rise to a suppression of tunneling density of states at the Fermi level away from integer fillings, reminiscent of a pseudo-gap behavior. Our results shine light on recent experiments and may explain differences in phenomenology between twisted bilayer and trilayer systems.

[1] Nuckolls, K.P., Lee, R.L., Oh, M. et al. Quantum textures of the many-body wavefunctions in magic-angle graphene. Nature 620, 525–532 (2023).

[2] Kim, H., Choi, Y., Lantagne-Hurtubise, É. et al. Imaging inter-valley coherent order in magic-angle twisted trilayer graphene. arXiv:2304.10586 (2023).

[3] Kim, H., Choi, Y., Lewandowski, C. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494–500 (2022)