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