Flat bands with higher Chern number in pyrochlore slabs

Abstract

A large number of recent works point to the emergence of intriguing analogs of fractional quantum Hall states in lattice models due to effective interactions in nearly flat bands with Chern number C=1. Here, we provide an intuitive and efficient construction of almost dispersionless bands with higher Chern numbers. Inspired by the physics of quantum Hall multilayers and pyrochlore-based transition-metal oxides, we study a tight-binding model describing spin-orbit coupled electrons in N parallel kagome layers connected by apical sites forming N-1 intermediate triangular layers (as in the pyrochlore lattice). For each N, we find finite regions in parameter space giving a virtually flat band with C=N. We analytically express the states within these topological bands in terms of single-layer states and thereby explicitly demonstrate that the C=N wave functions have an appealing structure in which layer index and translations in reciprocal space are intricately coupled. This provides a promising arena for new collective states of matter.

5+3 pages. Title extended, as published

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two

Cited by in corpus (4)

• Topological flat band models with arbitrary Chern numbers
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Distant-Neighbor Hopping in Graphene and Haldane Models
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum