Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities

TL;DR

This paper investigates how flat-band and Van Hove singularities in a three-dimensional layered Lieb lattice enhance magnetic transition temperatures, providing a unified analytical framework for understanding singularity-induced phase transitions.

Contribution

It introduces a general analytical framework for analyzing singularity effects on phase transitions, including magnetism and superconductivity, in layered Lieb lattices.

Findings

Enhanced $T_c$ due to flat-band and Van Hove singularities.

A unified analytical description of singularity effects on phase transitions.

Identification of a magnetic crossover feature at finite temperatures.

Abstract

We describe the enhanced magnetic transition temperatures $T_c$ of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold atom experiments. We determine the phase diagram at half-filling using the dynamical mean-field theory. The dominant mechanism of enhanced $T_c$ gradually changes from the (delta-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.