Superconducting and charge-density-wave orders in the spin-fermion model: A comparative analysis

Abstract

We present a comparative analysis of superconducting and charge-density-wave orders in the spinfluctuation scenario for the cuprates. That spin-fluctuation exchange gives rise to d-wave superconductivity is well known. Several groups recently argued that the same spin-mediated interaction may also account for charge-density-wave order with momenta (Q, 0) or (0, Q), detected in underdoped cuprates. This has been questioned on the basis that charge-density-wave channel mixes fermions from both nested and anti-nested regions on the Fermi surface, and fermions in the anti-nested region do not have a natural tendency to form a bound state, even if the interaction is attractive. We show that anti-nesting is not an obstacle for charge order, but to see this one needs to go beyond the conventional Eliashberg approximation. We show that in the prefect nesting/antinesting case, when the velocities of hot fermions are either parallel or antiparallel, the onset temperatures in superconducting and charge-density-wave channels are of comparable strength for any magnetic correlation length ξ. The superconducting Tsc is larger than T cdw , but only numerically. When the velocities of hot fermions are not strictly parallel/antiparallel, T cdw progressively decreases as ξ decreases and vanishes at some critical ξ.

Characterizing featureless Mott insulating state by quasiparticle interference: A dynamical mean field theory view

“…This feature is correct in the atomic limit of the Hubbard model 7 , but in general the electron self energy should depend on the momentum whenever t/U is non-zero. Nevertheless, since we are mainly interested in the Mott insulating state in which t/U is a small parameter, the momentum-dependence of the electron self energy should be very weak in the Mott insulating state, which has been discussed in previous studies [31][32][33][34][35][36] . As a result, the predicted re-entry of the non-interacting QPIs at a critical bias voltage should be robust even as the momentum dependence of the electron self energy is considered.…”

Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems

“…The full quantum-critical pairing problem is more complicated 23,25,[39][40][41][42][43][44][45] in the sense that (i) bosonic and fermionic self-energies and vertex corrections can have non-analytic behavior and generally cannot be neglected, (ii) the Eliashberg approximation which confines the important fermionic degrees of freedom to the vicinity of the FS is generally invalid, and (iii) the contribution from non-ladder diagrams is generically comparable to that from the ladder diagrams. These issues have been studied and addressed in previous works 24,25,40,42,43,[45][46][47][48] for different quantum critical pairing problems within a large-N f framework, where N f corresponds to the number of fermionic flavors. In particular, it was found that the Eliashberg approximation and the ladder approximation become exact in the N f → ∞ limit.…”

Real-space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations

“…2,[25][26][27][28][29][30][30][31][32][33][34][35] One line of reasoning starts with fermions interacting with antiferromagnetic spin fluctuations peaked at wave vector K (see Fig. 1).…”