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

TL;DR

This paper investigates gap formation in the dice model with local interactions, revealing that flat bands catalyze intervalley gap generation at any coupling strength, unlike intravalley gaps which require supercritical conditions.

Contribution

It demonstrates that flat bands in the dice model enable intervalley gap generation at arbitrary coupling, highlighting a novel mechanism for gap formation due to flat band catalysis.

Findings

Intervalley gaps are generated for any small coupling due to flat band effects.

Intravalley gaps require supercritical coupling to form.

Flat bands lead to large gaps proportional to the Brillouin zone area.

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.