TY - JOUR
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 - *E-mail: [email protected]. *E-mail: [email protected]. 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85054136984&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85054136984&partnerID=8YFLogxK
U2 - 10.1021/acs.nanolett.8b02033
DO - 10.1021/acs.nanolett.8b02033
M3 - Article
C2 - 30185049
AN - SCOPUS:85054136984
SN - 1530-6984
VL - 18
SP - 6175
EP - 6180
JO - Nano letters
JF - Nano letters
IS - 10
ER -