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Suppression of superconductivity at nematic critical point in underdoped cuprates

A nematic quantum critical point is anticipated to exist in the superconducting dome of some high-temperature superconductors. The nematic order competes with the superconducting order and hence reduces the superconducting condensate at $T = 0$. Moreover, the critical fluctuations of nematic order can excite more nodal quasiparticles out of the condensate. We address these two effects within an effective field theory and show that superfluid density $ρ^s(T)$ and superconducting temperature $T_c$ are both suppressed strongly by the critical fluctuations. The strong suppression of superconductivity provides a possible way to determine the nematic quantum critical point.