Theory for cuprate high-temperature superconductors in the underdoped regime: the singlet-bond superconductivity

In the large U Hubbard model, the singlet-bond state (the two-electron bound state) different from the resonating valence bond (RVB) state is found to exist. Upon doping holes into the half-filled Hubbard model, the singlet-bond state changes from the immobile state to the translationally mobile state and the coherent singlet-bond superconducting state develops below the disordered immobile singlet-bond insulating phase. The superconducting phase has the doubled-size sublattice symmetry similar to the antiferromagnetic phase. The sublattice quasiparticle energy dispersions of the singlet-bond superconducting state can explain the experimentally observed unusual small hole-like Fermi pockets around $$(\pm \frac{\pi }{2},\pm \frac{\pi }{2})$$ ( ± π 2 , ± π 2 ) and are consistent with the ARPES spectra observed in the zone-face and the zone-diagonal directions. The superconducting transition temperature is determined as $$k_{B}T_{c}(\delta )=\frac{3}{\ln \gamma (\delta )}J\delta $$ k B T c ( δ ) = 3 ln γ ( δ ) J δ , where $$\delta $$ δ is doping, $$J\equiv \frac{4t^{2}}{U}$$ J ≡ 4 t 2 U , and $$\frac{3}{\ln \gamma (\delta )}$$ 3 ln γ ( δ ) varies monotonically from 3.77 for $$\delta =0$$ δ = 0 to 2.42 for $$\delta =0.2$$ δ = 0.2 . Graphical abstract