Band flatness optimization through complex analysis

Ching Hua Lee

doi:10.1103/PhysRevB.93.155155

Band flatness optimization through complex analysis

2016-04-26

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DOI：10.1103/PhysRevB.93.155155

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Narrow-band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy-fermion systems, and topological phases such as fractional quantum Hall states and their lattice-based cousins, the fractional Chern insulators (FCIs). Here we discuss the problem of designing models with optimal band flatness, subject to constraints on the range of electron hopping. In particular, we show how the imaginary gap, which serves as a proxy for band flatness, can be optimized by appealing to Rouche's theorem, a familiar result from complex analysis. This leads to an explicit construction which we illustrate through its application to two-band FCI models with nontrivial topology (i.e., nonzero Chern numbers). We show how the imaginary-gap perspective leads to an elegant geometric picture of how topological properties can obstruct band flatness in systems with finite-range hopping.

Keyword:

WANNIER FUNCTIONS

GROUND-STATES

HUBBARD-MODEL

GAP STATES

FERROMAGNETISM

ELECTRON

Band flatness optimization through complex analysis

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