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

Abstract

Many correlated materials display a quantum critical point between a paramagnetic and a spindensity wave (SDW) state. The SDW wave vector connects points, so-called 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-SelfConsistent theory and specific numerical examples worked out for band and interaction 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 of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξ scales like 1/T , namely z = 1 instead of the naive z = 2, the (π, π) static spin susceptibility χ like 1/ √ T , and the imaginary part of the self-energy at the hot spots like T 3/2 . The correction T −1 1 ∼ 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 collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as −ω 3/2 log ω. This is less singular than earlier predictions of the form −ω log ω. The difference arises from the effects of umklapp terms that were not included in previous studies.

Enhancement of superconductivity at the onset of charge-density-wave order in a metal

“…4. We compute basonic and fermionic self-energies in a selfconsistent fashion, like it was done in the earlier works on the spin-fermion model 11,52,55 . Namely, we first evaluate one-loop bosonic self-energy (the bosonic polarization operator) using free fermions and show that it has the form of Landau damping, then use the full dynamical bosonic propagator to calculate one-loop fermionic self-energy and show that it is strong but predominantly depends on frequency, and then verify that frequency dependent fermionic self-energy does not affect the Landau damping.…”

“…At the first stage we put aside the issue what causes CDW order, assume that this order develops below some critical doping, and consider a semiphenomenological model of fermions interacting by exchanging soft CDW fluctuations with momenta Q. This model is quite similar to the spin-fermion model, considered in earlier studies of spin-mediated superconductivity for cuprates, Fe-pnictides, and other correlated materials [34][35][36][37][38][39] , and we dub this model the "charge-fermion model". The charge-fermion and spin-fermion models are similar but differ in detail because of the difference between the CDW momentum Q and antiferromagnetic momentum (π, π), and also because of the difference in the spin structures of charge-mediated and spin-mediated interactions (spin Kronecker δ functions vs spin Pauli matrices).…”

Direct probe of Fermi surface evolution across a pressure-induced quantum phase transition

“…Angle-resolved photo-emission spectroscopy (ARPES) requires samples in vacuum with well-prepared surfaces [5][6], while de Haas-van Alphen (dHvA) and Shubnikov-de Haas quantum oscillation techniques require large magnetic fields, which can result in structural or electronic changes to the system. 2k F -density wave systems have been discussed extensively as a class of materials for studying continuous quantum phase transitions and related quantum critical behavior [7][8][9][10]. These systems encompass many types of Fermi surface instability, such as nesting [11], saddle points [12] and hot spots [7][8][9][10], and could even extend to quasi-particle interference in high-T c cuprates, where the ordering wave vector at a given energy is strongly dependent on the detailed dispersion of the band structure near the Fermi surface [13].…”

“…2k F -density wave systems have been discussed extensively as a class of materials for studying continuous quantum phase transitions and related quantum critical behavior [7][8][9][10]. These systems encompass many types of Fermi surface instability, such as nesting [11], saddle points [12] and hot spots [7][8][9][10], and could even extend to quasi-particle interference in high-T c cuprates, where the ordering wave vector at a given energy is strongly dependent on the detailed dispersion of the band structure near the Fermi surface [13]. In general, incommensurate charge and spin order [14] can arise from local entities, through mechanisms such as electron-phonon coupling [15][16][17] and Ruderman-KittelKasuya-Yosida (RKKY) exchange interactions [18].…”

“…The Fermi surfaces of these 2k F systems at ambient pressure are often calculable with ab initio band structure calculations [6,25,26] and directly measureable through techniques such as ARPES [5,6]. The pressure evolution of the incommensurate ordering wave vectors can be measured directly using diffraction techniques [24,27,28] to reflect features on the Fermi surface [7][8][9][10][19][20][21].…”