Title: Magic angle hierarchy in twisted graphene multilayers

Abstract

When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of "magic angles" where correlation effects can induce a host of exotic phases. Here we study a class of related models of n-layered graphene with an alternating relative twist angle ±θ which exhibits magic angle flat bands coexisting with several Dirac dispersing bands at the moiré K point. Remarkably, we find that the Hamiltonian for the multilayer system can be mapped exactly to a set of decoupled bilayers at different angles, revealing a remarkable hierarchy mathematically relating all these magic angles to the TBG case. For the trilayer case (n=3), we show that the sequence of magic angle is obtained by multiplying the bilayer magic angles by $$\sqrt{2}$$, whereas the quadrilayer case (n=4) has two sequences of magic angles obtained by multiplying the bilayer magic angles by the golden ratio φ=($$\sqrt{5}$$+1)/2≈1.62 and its inverse. We also show that for larger n, we can tune the angle to obtain several narrow (almost flat) bands simultaneously and that for n → ∞, there is a continuum of magic angles for θ ≲ 2°. Furthermore, we show that tuning several perfectly flat bands for a small number of layers is possible if the coupling between different layers is different. Furthermore, the setup proposed here can be readily achieved by repeatedly applying the "tear and stack" method without the need of any extra tuning of the twist angle and has the advantage that the first magic angle is always larger than the bilayer case.

Authors:

Khalaf, Eslam ^[1]; Kruchkov, Alex J. ^[1]; Tarnopolsky, Grigory ^[1]; Vishwanath, Ashvin ^[1]

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+ Show Author Affiliations

1. Harvard Univ., Cambridge, MA (United States)

Publication Date:

2019-08-02

Research Org.:

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1572042

Alternate Identifier(s):

OSTI ID: 1546832

Grant/Contract Number:  

AC02-05CH11231; W911NF-14-1-0003; SC0007870; SC0019030

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review B

Additional Journal Information:

Journal Volume: 100; Journal Issue: 8; Journal ID: ISSN 2469-9950

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY