2024/08/26 by Penghao Zhu, Shi Feng, Zhu, Penghao +3
Mathematics · #FOS: Physical sciences #Geometry and complex manifolds #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2408.14533
openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the abundance of symmetry breaking states in magic-angle twisted bilayer graphene and other two-dimensional materials, we study superconducting (SC) and charge orders in two-dimensional topological flat bands in the strong correlation regime. By relating the half-filled 2D topological flat bands to the surface states of 3D topological insulators in symmetry class AIII, we reveal the topological obstruction to the formation of gapped SC and inter-valley charge orders without intrinsic topological orders, in the presence of the anti-unitary particle-hole symmetry at half filling. This is a generalization of the Li-Haldane arguments for nodal superconductivity to strongly interacting electrons. In contrast to the ℤ-valued obstruction derived from the non-interacting band topology, the topological obstruction of interacting electrons in half-filled flat bands has a ℤ8 classification, depending on the charge (valley) Chern number of the superconducting (inter-valley charge) orders. This is demonstrated by an interacting Hamiltonian for half-filled flat bands with a net Chern number C=4, where superconductivity and ℤ2 topological order coexist in a gapped ground state with particle-hole symmetry.