  The role of charge order in the phase diagram of high temperature cuprate
superconductors has been recently re-emphasized by the experimental discovery
of an incipient bi-directional charge density wave (CDW) phase in a class of
underdoped cuprates. In a subset of the experiments, the CDW has been found to
be accompanied by a d-wave intra-unit-cell form factor, indicating modulation
of charge density on the oxygen orbitals sandwiched between neighboring Cu
atoms on the CuO planes (the so-called bond-density wave (BDW) phase). Here we
take a mean field Q_1=(2\pi/3,0) and Q_2=(0,2\pi/3) bi-directional BDW phase
with a d-wave form factor, which closely resembles the experimentally observed
charge ordered states in underdoped cuprates, and calculate the Fermi surface
topology and the resulting quasiparticle Nernst coefficient as a function of
temperature and doping. We establish that, in the appropriate doping ranges
where the low temperature phase (in the absence of superconductivity) is a BDW,
the Fermi surface consists of an electron and a hole pocket, resulting in a low
temperature negative Nernst coefficient as observed in experiments.
