Recent transport properties on the stripe phase in La$_{text{1.875}}$Ba$_{text{01.25}}$CuO$_{text{4}}$ by Li textit{et al.} found 2-dimensional superconductivity over a wide temperature range including a Berezinski-Kosterlitz-Thouless transition at a
temperature T=16K, with 3-dimensional superconducting (SC) ordering only at T=4K. These results contradict the long standing belief that the onset of superconductivity is suppressed by stripe ordering and suggest coexistence of stripe and SC phases. The lack of 3-D superconducting order above T=4K requires an antiphase ordering in the SC state to suppress the interlayer Josephson coupling as proposed by Berg textit{et al.}. Here we use a renormalized mean field theory for a generalized t-J model to examine in detail the energetics of the spin and charge stripe ordered SC states including possible antiphase domains in the SC order. We find that the energies of these modulated states are very close to each other and that the anisotropy present in the low temperature tetragonal crystal structure favors stripe resonating valence bond states. The stripe antiphase SC states are found to have energies very close,but always above, the ground state energy which suggests additional physical effects are responsible for their stability.
Recent angle resolved photoemission cite{yang-nature-08} and scanning tunneling microscopy cite{kohsaka-nature-08} measurements on underdoped cuprates have yielded new spectroscopic information on quasiparticles in the pseudogap phase. New features o
f the normal state such as particle-hole asymmetry, maxima in the energy dispersion and accompanying drops in the spectral weight of quasiparticles agree with the ansatz of Yang textit{et al.} for the single particle propagator in the pseudogap phase. The coherent quasiparticle dispersion and reduced asymmetry in the tunneling density of states in the superconducting state can also be described by this propagator.
Magnetic field induced antiferromagnetic phase of the underdoped cuprates is studied within the t-t-J model. A magnetic field suppresses the pairing amplitude, which in turn may induce antiferromagnetism. We apply our theory to interpret the recently
reported quantum oscillations in high magnetic field in ortho-II YBa2Cu3O6.5 and propose that the total hole density abstracted from the oscillation period is reduced by 50% due to the antiferromagnetism.
Recent scanning tunneling microscopy on BSCCO 2212 has revealed a substantial spatial supermodulation of the energy gap in the superconducting state. We propose that this gap modulation is due to the superlattice modulations of the atoms in the struc
ture, and hence the parameters in a microscopic model of the CuO2 plane. The gap modulation is estimated using renormalized mean field theory for a t-t-J model on a superlattice. The results compare well with experiment.
