Dynamical Gap Generation For Nodal Quasiparticles In The D-wave Cuprate Superconductors

The cuprate superconductors have a d-wave symmetry,which will leads its properties different to the traditional s-wave superconductors.The existence of four nodal points in d-wave superconductors provide that the quasiparticle excitations is gapless at zero temperature.Recently,some experiments indicate that there maybe an additional gap in the nodal points,which will lead to many observable phenomenon,we will give a mechanism for this gap generation using the method of low dimensional field theory and explain the experiments.It is believed that the t-J model can well describe the d-wave cuprate superconductors. But this model have not an exact solution till now.After the slave boson treatment of the t-J model and considering the fluctuatations,the low energy effective theory is a 2+1 dimensional U(1) gauge field theory.Before studies are mainly focus on the coupling between the fermion and gauge field(QED₃),while the coupling between scalar boson and gauge field(Abelian Higgs model) is often neglected. We studied the dynamical chiral symmetry breaking in(2+1)-dimensional QED in the presence of an Abelian Higgs model(Ginzburg-Landau model) at the leading order of 1/N.In the gauge symmetry broken phase,the gauge boson becomes massive via Anderson-Higgs mechanism.The Dyson-Schwinger equation for fermion self-energy depends on two parameters:the gauge boson mass m_A and the Higgs boson mass m_h. It is found that,in the region of large ratio r=m_h/m_A,m_A and m_h reduces the critical fermion number N_c,below which the massless fermion acquires a dynamical mass. This model can describe the competing and coexistance of the antiferromagnetic order and superconducting order in high temperature superconductors.But the above model will experience huge difficulty in dealing with the mixed state,for the average of the vortex can not be down since the spin and charge is separated after the slave boson treatment.Hence we propose that an excitonic gap can be generated along nodal directions by Coulomb interaction in the mixed state.In a superconductor, the Coulomb interaction usually can not generate any fermion gap since its strength is weakened by superfluidity.It becomes stronger as superfluid density is suppressed by external magnetic field,and is able to generate a gap for initially gapless nodal quasiparticles beyond some critical field H_c.By solving the gap equation,it is found that the nodal gap increases with growing field H,which leads to a suppression of thermal conductivity at zero temperature.This mechanism naturally produces the field-induced thermal metal-insulator transition observed in transport experiments, and this mechanism give an explanation for the antiferromagnetic order observed in the vortex state.