Understanding cuprate superconductors with spontaneous nodal gap   generation
  We study the spontaneous gap generation for gapless nodal fermions within an effective gauge field theory of high temperature superconductors. When superconductivity appears, the gauge boson acquires a finite mass via Anderson-Higgs mechanism. Spontaneous nodal gap generation takes place if the gauge boson mass $\xi$ is zero or less than a critical value $\xi_{c}$ but is suppressed by a larger gauge boson mass. The generated nodal gap prohibits the appearance of low-energy fermion excitations and leads to antiferromagnetic order. Using the fact that gauge boson mass $\xi$ is proportional to superfluid density and doping concentration, we build one mechanism that provides a unified understanding of the finite single particle gap along the nodal direction in lightly doped cuprates, the competition and coexistence of antiferromagnetism and superconductivity, and the thermal metal-to-insulator transition from the superconducting state to the field-induced normal state in underdoped cuprates. 
Guo-Zhu Liu and Geng Cheng