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Repeated observations of inhomogeneity in cuperate superconductors[1-5] makeone immediately question the existance of coherent quasiparticles(qp's) and theapplicability of a momentum space picture. Yet, obversations of interferenceeffects[6-9] suggest that the qp's maintain a remarkable coherence underspecial circumstances. In particular, quasi-particle interference (QPI) imagingusing scanning tunneling spectroscopy revealed a highly unusual form ofcoherence: accumulation of coherence only at special points in momentum spacewith a particular energy dispersion[5-7]. Here we show that nematic quantumcritical fluctuations[10], combined with the known extreme velocityanisotropy[11] provide a natural mechanism for the accumulation of coherence atthose special points. Our results raise the intriguing question of whether thenematic fluctuations provide the unique mechanism for such a phenomenon.

Interference of nematic quantum critical quasiparticles: a route to the octet model