Abstract

The SU(2) slave-boson mean-field theory for the ${\mathrm{tt}}^{\ensuremath{'}}J$ model is analyzed. The role of next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ on the phase diagram is studied. We find a pseudogap phase in hole-doped (HD) materials (where ${t}^{\ensuremath{'}}<0).$ The pseudogap phase is a U(1) spin liquid (the staggered-flux phase) with a U(1) gauge interaction and no fractionalization. This agrees with experiments on HD samples. The same calculation also indicates that a positive ${t}^{\ensuremath{'}}$ favors a ${Z}_{2}$ state with true spin-charge separation. The ${Z}_{2}$ state that exists when ${t}^{\ensuremath{'}}\ensuremath{\gtrsim}0.5J$ can be a candidate for the pseudogap phase of electron-doped (ED) cuprates (if such a phase exists). The experimental situation in ED materials is also addressed.

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