Gap generation and flat band catalysis in dice model with local interaction

Abstract

The gap generation in the dice model with local four-fermion interaction is studied. Due to the presence of two valleys with degenerate electron states, there are two main types of gaps. The intra- and intervalley gap describes the electron and hole pairing in the same and different valleys, respectively. We found that while the generation of the intravalley gap takes place only in the supercritical regime, the intervalley gap is generated for an arbitrary small coupling. The physical reason for the absence of the critical coupling is the catalysis of the intervalley gap generation by the flat band in the electron spectrum of the dice model. The completely quenched kinetic energy in the flat band when integrated over momentum in the gap equation leads to extremely large intervalley gap proportional to the area of the Brillouin zone.

arXiv comment15 pages, 6 figures

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• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Electrical and thermal transport through $\alpha -T_3$ NIS junction
• Emergence of Cascading Flat Bands in Breathing Superlattices
• Zigzag dice lattice ribbons: Distinct edge morphologies and structure-spectrum correspondences
• p-wave superconductivity and the axi-planar phase of triple-point fermions
• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Current distribution and group velocities for electronic states on $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Flat and almost flat bands in the quasi-one-dimensional Josephson junction array
• Pseudospin-one particles in the time-periodic dice lattice: A new approach to transport control