Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation

Bikash Padhi; Chandan Setty; Philip W. Phillips

doi:10.1021/acs.nanolett.8b02033

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation

Bikash Padhi, Chandan Setty, Philip W. Phillips

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Abstract

We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when Î = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for Î = 1, clearly inconsistent with Mott insulation. We compute r_s = E_U/E_K, where E_U and E_K are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 10⁴ and (ii) a transition to a series of Wigner crystalline states exists as a function of Î. We find that, for Î = 1, r_s fails to cross the threshold (r_s = 37) for the triangular lattice, and metallic transport ensues. However, for Î = 2 and Î = 3, the thresholds r_s = 22 and r_s = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (Î = 2) and a kagome (Î = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.

Original language	English (US)
Pages (from-to)	6175-6180
Number of pages	6
Journal	Nano letters
Volume	18
Issue number	10
DOIs	https://doi.org/10.1021/acs.nanolett.8b02033
State	Published - Oct 10 2018

Keywords

Bilayer graphene
Mott insulator
Wigner crystal
magic angle
superconductivity

ASJC Scopus subject areas

Bioengineering
Chemistry(all)
Materials Science(all)
Condensed Matter Physics
Mechanical Engineering

Online availability

10.1021/acs.nanolett.8b02033

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@article{5e64139b100846b9a9dd9126ee5cdaf8,

title = "Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation",

abstract = "We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when {\^I} = 2 or 3 charges occupy a unit moir{\'e} cell, a feature attributed to Mottness per previous work but not for {\^I} = 1, clearly inconsistent with Mott insulation. We compute rs = EU/EK, where EU and EK are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 104 and (ii) a transition to a series of Wigner crystalline states exists as a function of {\^I}. We find that, for {\^I} = 1, rs fails to cross the threshold (rs = 37) for the triangular lattice, and metallic transport ensues. However, for {\^I} = 2 and {\^I} = 3, the thresholds rs = 22 and rs = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb ({\^I} = 2) and a kagome ({\^I} = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.",

keywords = "Bilayer graphene, Mott insulator, Wigner crystal, magic angle, superconductivity",

author = "Bikash Padhi and Chandan Setty and Phillips, {Philip W.}",

note = "Funding Information: *E-mail: bpadhi2@illinois.edu. *E-mail: dimer@illinois.edu. ORCID Philip W. Phillips: 0000-0003-2621-0738 Author Contributions B.P. performed numerous calculations on rs and screening, C.S. contributed to the analysis of screening, and P.P. proposed Wigner crystallization and the hierarchy of density-dependent states. Funding We acknowledge support from the Center for Emergent Superconductivity, a DOE Energy Frontier Research Center, Grant No. DE-AC0298CH1088. We also thank the NSF DMR-1461952 for partial funding of this project. Notes The authors declare no competing financial interest. Publisher Copyright: {\textcopyright} 2018 American Chemical Society.",

year = "2018",

month = oct,

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doi = "10.1021/acs.nanolett.8b02033",

language = "English (US)",

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T1 - Doped Twisted Bilayer Graphene near Magic Angles

T2 - Proximity to Wigner Crystallization, Not Mott Insulation

AU - Padhi, Bikash

AU - Setty, Chandan

AU - Phillips, Philip W.

N1 - Funding Information: *E-mail: bpadhi2@illinois.edu. *E-mail: dimer@illinois.edu. ORCID Philip W. Phillips: 0000-0003-2621-0738 Author Contributions B.P. performed numerous calculations on rs and screening, C.S. contributed to the analysis of screening, and P.P. proposed Wigner crystallization and the hierarchy of density-dependent states. Funding We acknowledge support from the Center for Emergent Superconductivity, a DOE Energy Frontier Research Center, Grant No. DE-AC0298CH1088. We also thank the NSF DMR-1461952 for partial funding of this project. Notes The authors declare no competing financial interest. Publisher Copyright: © 2018 American Chemical Society.

PY - 2018/10/10

Y1 - 2018/10/10

N2 - We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when Î = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for Î = 1, clearly inconsistent with Mott insulation. We compute rs = EU/EK, where EU and EK are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 104 and (ii) a transition to a series of Wigner crystalline states exists as a function of Î. We find that, for Î = 1, rs fails to cross the threshold (rs = 37) for the triangular lattice, and metallic transport ensues. However, for Î = 2 and Î = 3, the thresholds rs = 22 and rs = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (Î = 2) and a kagome (Î = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.

AB - We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when Î = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for Î = 1, clearly inconsistent with Mott insulation. We compute rs = EU/EK, where EU and EK are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 104 and (ii) a transition to a series of Wigner crystalline states exists as a function of Î. We find that, for Î = 1, rs fails to cross the threshold (rs = 37) for the triangular lattice, and metallic transport ensues. However, for Î = 2 and Î = 3, the thresholds rs = 22 and rs = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (Î = 2) and a kagome (Î = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.

KW - Bilayer graphene

KW - Mott insulator

KW - Wigner crystal

KW - magic angle

KW - superconductivity

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SP - 6175

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JO - Nano Letters

JF - Nano Letters

SN - 1530-6984

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ER -

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation

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