Electron correlation effects near Van Hove singularities: Application to twisted bilayer graphene and supermetal
e-mail: kato@issp.u-tokyo.ac.jp
Electron correlation decorates the condensed matter physics, bringing symmetry breaking and ordered phases. It becomes vital when many electrons are active, namely near a Van Hove singularity (VHS) where the density of states (DOS) diverges. Since a VHS accompanies the topological transition of the Fermi surface, tunable materials are desirable to observe VHS-related behaviors, for example, by strain or pressure. The seminar focuses on moiré superstructures made of van der Waals materials; twisted bilayer graphene allows band dispersion design by the stacking angle, and correlated insulating and superconducting states are observed near the so-called magic angle.
First, we introduce a theory that describes a possible mechanism for correlated insulating and superconducting states in twisted bilayer graphene [1]. Our analysis of a hot-spot model shows that d- or p-wave superconductivity and charge/spin-density wave emerge from Coulomb repulsion near VHS. We further investigate the tunable nature of twisted bilayer graphene, which invokes the notion of a high-order VHS [2]. We show that tuning a single tuning parameter, such as a twist angle of a moiré material, pressure, and strain, realizes a high-order VHS realizes a power-law divergence in the DOS in two dimensions, unlike the usual logarithmic one. We could attribute the origin of the so-called magic angle to the high-order VHS. Finally, we discuss correlation effects at a high-order VHS [3]. We perform a renormalization-group analysis to find a nontrivial metallic state, where various divergent susceptibilities coexist, but no long-range order appears. We term such a metallic state as a supermetal. Our controlled analysis at the interacting fixed point reveals that an interacting supermetal is a non-Fermi liquid.
[1] H. Isobe and L. Fu, Phys. Rev. Research 1, 033206 (2019).[2] N. F. Q. Yuan, H. Isobe, and L. Fu, Nat. Commun. 10, 5769 (2019).
[3] H. Isobe, N. F. Q. Yuan, and L. Fu, Phys. Rev. X 8, 041041 (2018).
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