Some aspects of electronic topological transition in 2D system on a square lattice. Excitonic ordered states

TL;DR

This paper investigates excitonic ordered states near a quantum critical point in a 2D square lattice system, revealing unique spectral features and phase behavior relevant to high-Tc cuprates.

Contribution

It demonstrates how excitonic order parameters and spectral gaps evolve near the ETT with extended hopping, differing from conventional behavior.

Findings

Order parameter and gap increase with distance from QCP

Spectral gap opens at hot spots and extends to saddle points

Spectrum exhibits flat shape similar to underdoped cuprates

Abstract

We study the ordered "excitonic" states which develop around the quantum critical point (QCP) associated with the electronic topological transition (ETT) in a 2D electron system on a square lattice. We consider the case of hopping beyond nearest neighbors when ETT has an unusual character. We show that the amplitude of the order parameter (OP) and of the gap in the electron spectrum increase with increasing the distance from the QCP, \delta_c - \delta, where \delta = 1-n and "n" is an electron concentration. Such a behavior is different from the ordinary case when OP and the gap decrease when going away from the point which is a motor for instability. The gap opens at "hot spots" and extends untill the saddle points (SP) whatever is the doping concentration. The spectrum gets a characteristic flat shape as a result of hybrydization effect in the vicinity of two different SP's. The shape of the spectrum and the angle dependence of the gap have a striking similarity with the features observed in the normal state of the underdoped high-T$_c$ cuprates. We discuss also details about the phase diagram and the behaviour of the density of states.