Real-Space Holon Pairing in Underdoped Cuprates

We examine the behavior of a recently developed model for underdoped cuprates [1] in the fluctuation regime above $T_c$. It is characterized by a spin gap and describes sublattice preserving hopping by holons and holon pairs, accompanied by a backflow of spin singlets. The singlets form a short-range valence-bond state which is continuously connected to the correct spin state at half filling. The theory, thus constrained, leads to the correct phase diagram and also explains the two-dimensionality of the metallic states. Superconductivity is due to pair hopping, as holons form real-space pairs at low densities and undergo a Bose-Einstein condensation below $T_c$. The pairs exist up to a temperature $T_p > T_c$, which is consistent with the observed Nernst effect and diamagnetism above $T_c$. The pair spectrum is calculated by identifying poles of the pair Green's function. Here we show that the specific heat of this system is in qualitative agreement with recent measurements [2].\\[4pt] [1] S. K. Sarker and T. Lovorn, Phys. Rev. B {\bf 82}, 014504 (2010); ibid {\bf 85}, 144502 (2012)\\[0pt] [2] H.-H. Wen \textit{et al.}, Phys. Rev. Lett. {\bf 103}, 067002 (2009)