Lower pseudogap phase of Mott insulators: A spin/vortex liquid state

The pseudogap phase is considered to be a new state of matter in the phase string model of the doped Mott insulator, which is composed of two distinct regimes known as the upper and lower pseudogap phases, respectively. The former corresponds to the formation of spin-singlet pairing, the magnetic characterizations of which have been recently studied [Phys. Rev. B 72, 104520 (2005)]. The latter, as a low-temperature regime of the pseudogap phase, is systematically explored in this work, which is characterized by the formation of the Cooper pair amplitude and described by a generalized Ginzburg-Landau theory. Elementary excitation in this phase is a charge-neutral object carrying spin-$1∕2$ and locking with a supercurrent vortex, known as a spinon-vortex composite. Such a lower pseudogap phase can be regarded as a vortex liquid state due to the presence of free spinon vortices. Here thermally excited spinon vortices destroy the phase coherence and are responsible for the nontrivial Nernst effect and diamagnetism. The transport entropy and core energy associated with a spinon vortex are determined by the spin degrees of freedom. Such a spontaneous vortex liquid phase can be also considered as a spin liquid with a finite correlation length and gaped $S=1∕2$ excitations, where a resonancelike nonpropagating spin mode emerges at the antiferromagnetic wavevector $(\ensuremath{\pi},\ensuremath{\pi})$ with a doping-dependent characteristic energy. The superconducting phase is closely related to the lower pseudogap phase by a topological transition with spinon vortices and antivortices forming bound pairs and the emergence of fermionic quasiparticles as holon-spinon-vortex bound objects. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined. Comparisons with experiments are also made.