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

Abstract

In light of the new experimental and theoretical important developments in high-Tc superconductivity, we revisit the fermionic hot-spot model relevant to the phenomenology of the cuprates. We extend previous results by means of a complete two-loop order renormalization group (RG) framework. Here, we explicitly study the effect of the charge-density-wave (CDW) order parameter with a d-wave form factor with the experimentally observed modulation (±Q0, 0) and (0, ±Q0) at the infrared-stable nontrivial fixed point obtained previously for this model. Additionally, we proceed to investigate also the so-called pair-density-wave (PDW) order that was recently proposed in the literature as a possible candidate for the "hidden" order to describe the pseudogap phase observed in underdoped cuprates. We confirm that although the above two ordering tendencies are also found to be nearly degenerate both at one-loop and two-loop RG orders and linked by an emergent SU (2) pseudospin symmetry, they turn out to be subleading for weaker couplings in the present model to antiferromagnetism, d-wave bond-density wave (BDW) order with modulation along Brillouin zone diagonals (±Q0, ±Q0), and d-wave singlet superconductivity (SSC). However, as we increase the strength of the initial coupling towards moderate values, we do capture a tendency for the entangled PDW/CDW order to become leading compared to BDW/SSC in the model, which suggests that the former composite order might be indeed a viable concept to describe some cuprate superconductors at high temperatures in the underdoped regime, as has been recently alluded to by many authors in the literature.

Calculation of the magnetotransport for a spin-density-wave quantum critical theory in the presence of weak disorder

“…As a result, its expression can be written as J k /∂k x ∂k y ). In this way, we can conclude that, when the Fermi surface of a given model possesses flat regions -as it happens, e.g., in the so-called hot spot model 10,19,21,23 -both the Hall current and the Hall conductivity σ xy will not have contributions from these specific regions. This fact will be important for the considerations that follow in the present work.…”

“…This happens because of the emergent particle-hole symmetry at the low-energy fixed point in the model and the resulting dynamical nesting of the corresponding renormalized Fermi surface (for explanations about this change of topology of the underlying Fermi surface that was obtained by several RG approaches for the hot spot model, see the Refs. 10,19,21,23 ). This fact underscores the importance of the emergent charge conjugationĈ symmetry at the hot spots in the low-energy effective theory.…”

“…In this respect, we note that a recent groundbreaking experimental work 17 has provided evidence of a novel pair-density-wave in the cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+x using scanned Josephson tunneling microscopy, which was anticipated by theories that assume a crucial role of SDW criticality in those materials 18,19 . In the SDW quantum critical scenario, the underlying mechanism for the formation of Cooper pairs in the superconducting phase of these compounds is rooted in the exchange of antiferromagnetic short-range SDW fluctuations 20 , which are enhanced close to the quantum critical point 10 .…”

“…In the SDW quantum critical scenario, the underlying mechanism for the formation of Cooper pairs in the superconducting phase of these compounds is rooted in the exchange of antiferromagnetic short-range SDW fluctuations 20 , which are enhanced close to the quantum critical point 10 . On the theoretical side, many works have described several aspects of the properties of the Abanov-Chubukov spin-fermion model using various complementary analytical 10,15,19,[21][22][23][24][25][26] and numerical 27 techniques. In this respect, it is now clear that the quasiparticle excitations are destroyed at the socalled hot spots (i.e., the intersection of the underlying Fermi surface with the antiferromagnetic zone boundary) at low energies 19,27 .…”

“…On the theoretical side, many works have described several aspects of the properties of the Abanov-Chubukov spin-fermion model using various complementary analytical 10,15,19,[21][22][23][24][25][26] and numerical 27 techniques. In this respect, it is now clear that the quasiparticle excitations are destroyed at the socalled hot spots (i.e., the intersection of the underlying Fermi surface with the antiferromagnetic zone boundary) at low energies 19,27 . Lastly, we mention that the spinfermion model is expected to provide a good description of many correlated systems both in the normal phase and in the symmetry-broken phases that appear at low temperatures, including of course the d-wave superconducting phase.…”