• Open Access

Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling

Nick Bultinck, Eslam Khalaf, Shang Liu, Shubhayu Chatterjee, Ashvin Vishwanath, and Michael P. Zaletel
Phys. Rev. X 10, 031034 – Published 12 August 2020
PDFHTMLExport Citation

Abstract

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)×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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 26 February 2020
  • Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031034

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nick Bultinck1,†, Eslam Khalaf2,†, Shang Liu2, Shubhayu Chatterjee1, Ashvin Vishwanath2, and Michael P. Zaletel1,*

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

  • *mikezaletel@berkeley.edu
  • N. B. and E. K. contributed equally to this work.

Popular Summary

Twisted bilayer graphene, in which a one-atom-thick sheet of carbon atoms is placed askew atop another, has garnered a lot of attention in recent years as a platform for exploring novel electronic behaviors. When the relative twist angle between the two graphene layers is close to a “magic angle” of about one degree, electrons are robbed of much of their kinetic energy and experience strong interactions that drastically change the system’s overall properties, including an insulating behavior that is difficult to explain. Here, we numerically and analytically identify a symmetry breaking in twisted bilayer graphene that may be responsible for this insulating behavior.

When two sheets of graphene are stacked atop one another and twisted, the interplay between the honeycomblike arrangements of atoms in each sheet creates a moiré pattern, which provides a periodic arrangement of cells in which electrons can gather. The insulating behavior appears only when these cells are filled with an integer number of electrons. Our numerical and analytical work suggests that when these cells have an even number of electrons, a pattern of alternating circulating currents can arise, which leads to a magnetic density wave that breaks certain symmetries in the system but preserves others. This symmetry breaking, we argue, can explain the observed insulating behavior.

This insulator could serve as a “parent” state for superconducting phases observed in the same moiré devices, when, on average, there are a noninteger number of electrons per cell. It therefore provides an interesting starting point for studies of the origin of superconductivity in moiré systems. The newly identified symmetry breaking is subtle, so directly detecting it will be a challenge.

Key Image

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand
Issue

Vol. 10, Iss. 3 — July - September 2020

Subject Areas
Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×