Kekule Spirals in Twisted Graphene Multilayers

One of the major challenges in the study of magic angle twisted bilayer graphene (MATBG) has been the understanding the insulating states that arise as a result of inter-electron interaction. A combination of recent theoretical [1,2,3,4] and experimental [5,6] work has now established the presence of a new type of order which we call "Incommensurate Kekule Spiral" (IKS) order. This order spontaneously breaks both the valley-charge conservation and moiré translation symmetries, but preserves a modified translation symmetry which simultaneously shifts the spatial coordinates and rotates the U(1) angle which characterizes the spontaneous inter-valley coherence. This type of order appears ubiquitous in the presence of miniscule amounts of strain at temperatures above the superconducting transitions. In this talk I will give an introduction to the physics of MATBG emphasizing the strong coupling approximations. I will then turn to the Hartree-Fock calculations we used to predict the IKS order and I will explain the physics that drives the system towards this ground state. I will also briefly discuss the experiments that have observed this phase, the competing phases that are observed in ultra-small strain samples, as well as the closely related physics of magic angle trilayer graphene.

[1] Yves H. Kwan, Glenn Wagner, Tomohiro Soejima, Michael P. Zaletel, Steven H. Simon, Siddharth A. Parameswaran, Nick Bultinck, Phys. Rev. X 11, 041063 (2021)

[2] Glenn Wagner, Yves H. Kwan, Nick Bultinck, Steven H. Simon, S. A. Parameswaran, Phys. Rev. Lett. 128, 156401 (2022)

[3] Yves H. Kwan, Glenn Wagner, Nick Bultinck, Steven H. Simon, Erez Berg, S. A. Parameswaran, arXiv:2303.13602

[4] Tianle Wang, Daniel E. Parker, Tomohiro Soejima, Johannes Hauschild, Sajant Anand, Nick Bultinck, and Michael P. Zaletel, PRB accepted (2023)

[5] Kevin P. Nuckolls et al, Nature 620, 525-532 (2023)

[6] Hyunjin Kim, et al, arXiv:2304.10586