Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys. $\bf{9}$, 1745 (2013)].The CDW is sensitive to the shape of the Fermi surface in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.Comment: 15 pages, 15 figures, final version + typo corrected in Eq. (12

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with the special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic (AF) quantum critical point (QCP) in two dimensions, in which preemptive orders in the charge and superconducting (SC) sectors emerged, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SU(2) pairing fluctuations are dominant and argue that they are unstable towards the formation of a Resonant Peierls Excitonic (RPE) state at the pseudogap (PG) temperature $T^{*}$. We discuss the implications of this scenario for a few key experiments.Comment: 16 pages, 17 figure

Resistivity near a nematic quantum critical point: impact of acoustic phonons

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOWe revisit the issue of the resistivity of a two-dimensional electronic system tuned to a nematic quantum critical point (QCP), focusing on the nontrivial impact of the coupling to the acoustic phonons. Due to the unavoidable linear coupling between the electronic nematic order parameter and the lattice strain fields, long-range nematic interactions mediated by the phonons emerge in the problem. By solving the semiclassical Boltzmann equation in the presence of scattering by impurities and nematic fluctuations, we determine the temperature dependence of the resistivity as the nematic QCP is approached. One of the main effects of the nematoelastic coupling is to smooth the electronic nonequilibrium distribution function, making it approach the simple cosine angular dependence even when the impurity scattering is not too strong. We find that at temperatures lower than a temperature scale set by the nematoelastic coupling, the resistivity shows the T-2 behavior characteristic of a Fermi liquid. This is in contrast to the T-4/3 low-temperature behavior expected for a lattice-free nematic quantum critical point. More importantly, we show that the effective resistivity exponent alpha(eff)(T) in rho(T) - rho(0) similar to T-alpha eff(T) displays a pronounced temperature dependence, implying that a nematic QCP cannot generally be characterized by a simple resistivity exponent. We discuss the implications of our results to the interpretation of experimental data, particularly in the nematic superconductor FeSe1-xSx.10011110FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO2017/16911-3We would like to thank A. Chubukov, A. Coldea, A. Klein, E. Miranda, H. Freire, I. Paul, and A. Schofield for stimulating discussions. V.S.d.C. is grateful for the financial support from FAPESP under Grant No. 2017/16911-3. R.M.F. is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0012336