On left absolutely flat bands

Topological flat bands from dipolar spin systems.

We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S=1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hard-core bosons, namely, the dressed spin flip...

Superfluidity in topologically nontrivial flat bands.

Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applic...

Flat - Bands on Partial Line Graphs — Systematic Method for Generating Flat - Band Lattice Structures —

We introduce a systematic method for constructing a class of lattice structures that we call “partial line graph”s. In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge. This method can be applied to twoand three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for...

On Left Regular Bands and Real Conic-line Arrangements

An arrangement of curves in the real plane divides it into a collection of faces. Already in the case of line arrangements, this collection can be given a structure of a left regular band and one can ask whether the same is possible for other arrangements. In this paper, we try to answer this question for the simplest generalization of line arrangements, that is, conic–line arrangements. Invest...

On Absolutely Continuous Transformations