Electronic Specific Heat and Dissipative Viscosity of Hole-Doped Cuprates

We investigate a d-density wave (DDW) mean field model Hamiltonian in the momentum space suitable for the hole-doped cuprates, such as YBCO, in the pseudo-gap phase to obtain the Fermi surface(FS)topologies, including the elastic scattering by disorder potential ($\vert $v$_{0}\vert )$. For the chemical potential $\mu =-$ 0.27 eV (at 10{\%} doping level), and $\vert $v$_{0}\vert \quad \ge \quad \vert $t$\vert $ (where $\vert $t$\vert $ = 0.25 eV is the first neighbor hopping), at zero/non-zero magnetic field (B) the FS on the first Brillouin zone is found to correspond to electron pockets around anti-nodal regions and barely visible patches around nodal regions. We next relate our findings regarding FS to the entropy per particle(S), the electronic specific heat C$_{el}$ and the dissipative viscosity ($\eta )$. The magneto-quantum oscillations in C$_{el}$ are shown to take place in the moderate disorder regime ($\vert $v$_{0}\vert \quad \sim $0.2 eV) only for B $\sim $ 40 T. For the density of viscosity $\eta $(\textbf{k}) on the first Brillouin zone, we find that whereas the negative contribution arises from the electron pockets in the anti-nodal region, the positive contributions are from the hole-pockets in the nodal region. The KSS bound ($\eta $/S $\ge $ h/4$\pi $k$_{B })$is easily satisfied for the moderately strong disorder potential. The viscosity is found to be proportional to the magnetic field up to B $\sim $ 50 T.