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=(2pi/3,0) and Q_2=(0,2pi/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.
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