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We calculate the Pauli-limited upper critical field and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) instability for dirty d -wave superconductors within the quasiclassical theory using the self-consistent t -matrix approximation for impurities. We find that the phase diagram depends sensitively on the scattering rate and phase shift of nonmagnetic impurities. The transition into the superconducting state is always second order for weak (Born) scattering, while in the unitarity (strong) scattering limit a first-order transition into both uniform and spatially modulated superconducting states is stabilized. Contrary to general belief, we find that the FFLO phase is robust against disorder and survives impurity scattering equivalent to a Tc suppression of roughly 40%. Our results bear on the search of FFLO states in heavy-fermion and layered organic superconductors. © 2008 The American Physical Society.

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Physical Review B - Condensed Matter and Materials Physics