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Breakdown of Fermi liquid behavior at the (π,π)=2k_F spin-density wave quantum-critical point: the case of electron-doped cuprates

Many correlated materials display a quantum critical point between a paramagnetic and a SDW state. The SDW wave vector connects points (hot spots) on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here we consider the case where pairs of hot spots coalesce, and the wave vector (π,π) of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility and the self-energy at the hot spots are found using the Two-Particle-Self-Consistent theory and specific numerical examples worked out for parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudo-nesting conditions lead to drastic modifications to the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξscales like 1/T, i.e. z=1 instead of the naive z=2, the (π,π) static spin susceptibility χlike $1/\sqrt T$, and the imaginary part of the self-energy at the hot spots like $T^{3/2}$. The correction $T_1^{-1}\sim T^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless SDW fluctuations interacting with fermions. The imaginary part of the fermionic self-energy close to the hot spots scales as $-ω^{3/2}\logω$. This is less singular than earlier predictions of the form $-ω\logω$. The difference arises from the effects of umklapp terms that were not included in previous studies.