Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis

Abstract

Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi2Sr2CaCu2O 8+δ by Chatterjee et al. [Nature Physics 6, 99 (2010)], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model consisting of eight points located near the "hot spots" on the Fermi surface which are directly connected by spin density wave ordering wave vector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.

Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors

“…The two-loop-order corrections also implies that the quasiparticle weight Z ψ tends to be nullified at the hot spots in the present model and that both uniform spin and charge susceptibilities tend to become suppressed in the low-energy limit, which was previously obtained in Ref. 47 . This may either point to a partial truncation of the Fermi surface at the hot spots (e.g., Fermi arcs) or it might also lead to a full reconstruction of the Fermi surface into pockets.…”

“…In this section, we describe the two-loop RG approach that we shall apply in the rest of this work. Our discussion here will be relatively concise, since the fieldtheoretical RG methodology was already explained by two of us in great detail in the context of the present model elsewhere 43,47 . Within perturbation theory, if we compute many one-loop quantities, such as, e.g., particleparticle and particle-hole polarization bubbles for several choices of incoming external momenta q and also their corresponding two-loop-order corrections, we obtain several logarithmic divergences of the type ln(Λ 0 /Λ) as we probe the system towards the low-energy limit Λ → 0 (see also Refs.…”

Charge orders, magnetism and pairings in the cuprate superconductors

“…Many suggestions have been made for the formation of axial CDW order. The fact that this wave vector is present as a secondary instability in any weak coupling theory, and stabilized for example, in the presence of additional effect like Coulomb interactions [134,155,156], within both one-loop and two-loop RG [128,129,[157][158][159] or starting from a three band model [152], or invoking the proximity to the van Hove singularity [160] has been outlined in many works, including ours. All these studies are based on the observation that axial CDW is distinct from the formation of the PG state and starts to get formed at the tip of the arcs.…”

Strong competition betweenΘII-loop-current order andd-wave charge order along the diagonal direction in a two-dimensional hot spot model

“…In this respect, an important work by Metlitski and Sachdev 15 consisted in the elegant demonstration that, if the energy dispersion of this model is linearized, an exact emergent SU (2) pseudospin symmetry relating a d-wave singlet superconducting (SSC) order to a d-wave quadrupole-density-wave (QDW) order at wavevectors along the Brillouin zone diagonal (±Q 0 , ±Q 0 ) is verified at the spin-density-wave (SDW) quantum critical point. This degeneracy between these two orders effectively produces a composite order parameter (denoted by QDW/SSC) with both bond order and preformed pairs at high temperatures as shown by Efetov et al 16 and the properties of this state have been explored in connection with the physics of the cuprates using different approaches in many works [28][29][30][31][32][33][34][35][36][37] . In addition to this fact, another emergent SU (2) degeneracy relating two additional orders -a superconducting order with a finite Cooper-pair center of mass momentum (the so-called pair-density-wave (PDW) [38][39][40] ) and a d-wave CDW at the experimentally observed wavevectors Q x and Q yhas also been recently verified in the model in the work by Pépin et al 41 and explored further by Wang et al 42 .…”