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

We study in a mean-field approximation 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, , where 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. We show that the chemical potential lies always inside the gap for wavevectors in a proximity of whatever is the doping concentration. The spectrum gets a characteristic flat shape as a result of hybridization effect in the vicinity of two different SP's. The shape of the spectrum as a function of and the angle dependence of the gap have a striking similarity with the features observed in the normal state of the underdoped high- cuprates. We discuss also details about the phase diagram and the behaviour of the density of states. Received 9 June 1999