Higher Vortexability: Zero-Field Realization of Higher Landau Levels

Journal Article · Mon Mar 10 00:00:00 EDT 2025 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.134.106502· OSTI ID:2529464

Fujimoto, Manato ^[1]; Parker, Daniel Eric ^[2]; Dong, Junkai ^[3]; Khalaf, Eslam ^[3]; Vishwanath, Ashvin ^[3]; Ledwith, Patrick ^[3]

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1. Harvard University, Cambridge, MA (United States); University of Tokyo (Japan); Harvard University
2. University of California, Berkeley, CA (United States); University of California at San Diego, La Jolla, CA (United States)
3. Harvard University, Cambridge, MA (United States)

The rise of moiré materials has led to experimental realizations of integer and FCIs in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee an Abelian fractional state in a flat band were identified, namely “ideal" or “vortexable" quantum geometry. Such vortexable bands share essential features with the LLL, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at ν = 1/2, 2/5 are known to be competitive. The possibility of realizing these states at zero magnetic field, and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work, we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. Furthermore, periodically strained Bernal graphene is shown to realize such a 1LL structure even in zero magnetic field.

• Research Organization: Harvard University, Cambridge, MA (United States)
• Sponsoring Organization: JSPS KAKENHI; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: AC02-07CH11358
• OSTI ID: 2529464
• Alternate ID(s): OSTI ID: 2533590
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 134; ISSN 0031-9007
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Bilayer graphene
Chern insulators
Fractional quantum Hall effect
Geometric & topological phases
Landau levels
Quantum anomalous Hall effect
Twisted bilayer graphene