• 文献标题:   Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling
  • 文献类型:   Article
  • 作  者:   BULTINCK N, KHALAF E, LIU S, CHATTERJEE S, VISHWANATH A, ZALETEL MP
  • 作者关键词:  
  • 出版物名称:   PHYSICAL REVIEW X
  • ISSN:   2160-3308
  • 通讯作者地址:   Univ Calif Berkeley
  • 被引频次:   13
  • DOI:   10.1103/PhysRevX.10.031034
  • 出版年:   2020

▎ 摘  要

In magic angle twisted bilayer graphene (TBG), electron-electron interactions play a central role, resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question, and it is potentially linked to the relatively high-temperature superconductivity observed in the same devices. Here, we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation, which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state, which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC order exhibits a pattern of alternating circulating currents that triples the graphene unit cell, leading to an "orbital magnetization density wave." Although translation and time-reversal symmetry are broken, a combined "Kramers" time-reversal symmetry is preserved. Our analytic arguments are built on first identifying an approximate U(4) x U(4) symmetry, resulting from the remarkable properties of the TBG band structure, which helps select a low-energy manifold of states that are further split to favor the K-IVC state. This low-energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry-lowering perturbations can stabilize other insulators and the semimetallic state, and we discuss the ground state at half-filling and give a comparison with experiments.