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

摘要

We describe the enhanced magnetic transition temperatures $T_c$ oftwo-component fermions in three-dimensional layered Lieb lattices, which arecreated in cold atom experiments. We determine the phase diagram athalf-filling using the dynamical mean-field theory. The dominant mechanism ofenhanced $T_c$ gradually changes from the (delta-functional) flat-band to the(logarithmic) Van Hove singularity as the interlayer hopping increases. Weelucidate that the interaction induces an effective flat-band singularity froma dispersive flat (or narrow) band. We offer a general analytical framework forinvestigating the singularity effects, where a singularity is treated as oneparameter in the density of states. This framework provides a unifieddescription of the singularity-induced phase transitions, such as magnetism andsuperconductivity, where the weight of the singularity characterizes physicalquantities. This treatment of the flat-band provides the transition temperatureand magnetization as a universal form (i.e., including the Lambert function).We also elucidate a specific feature of the magnetic crossover in magnetizationat finite temperatures.