Unified energy law for fluctuating density wave orders in cuprate pseudogap phase

The quantum origin of the cuprate pseudogap is a central conundrum of condensed matter physics. Although many symmetry-broken scenarios were previously proposed, universal quantitative relationships have been rarely studied. Here, we report a unified energy law underlying the pseudogap, which determines the scattering rate, pseudogap energy, and its onset temperature, with a quadratic scaling of the wavevector of density wave order (DWO). The law is validated by data from over one hundred samples, and a further prediction that the master order of pseudogap transforms from fluctuating spin to charge DWO is also confirmed. Furthermore, the energy law enables our derivation of the well-known linear scalings for the resistivity of the strange metal phase and the transition temperature of the superconducting phase. Finally, it is concluded that fluctuating orders provide a critical bridge linking microscopic spectra to macroscopic transport, showing promise for the quantification of other strongly correlated materials.

Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap $${\Delta }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$$ Δ P ( r ) in real-space, and a characteristic quasiparticle scattering interference (QPI) signature $${\Lambda }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{q}}}}}})$$ Λ P ( q ) in wavevector space. By studying strongly underdoped Bi2Sr2CaDyCu2O8 at hole-density ~0.08 in the superconductive phase, we detect the 8a0-periodic $${\Delta }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$$ Δ P ( r ) modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature $$\Lambda ({{{{{\boldsymbol{q}}}}}})$$ Λ ( q ) that is predicted specifically for the temperature dependence of an 8a0-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi2Sr2CaDyCu2O8 pseudogap phase.

Translation-Invariant Bipolarons and Charge Density Waves in High-Temperature Superconductors

A correlation is established between the theories of superconductivity based on the concept of charge density waves (CDWs) and the translation invariant (TI) bipolaron theory. It is shown that CDWs are originated from TI-bipolaron states in the pseudogap phase due to the Kohn anomaly and form a pair density wave (PDW) for wave vectors corresponding to nesting. Emerging in the pseudogap phase, CDWs coexist with superconductivity at temperatures below those of superconducting transition, while their wave amplitudes decrease as a Bose condensate is formed from TI bipolarons, vanishing at zero temperature.

Pseudogap Isotope Effect as a Probe of Bipolaron Mechanism in High Temperature Superconductors

A theory of a pseudogap phase of high-temperature superconductors where current carriers are translation invariant bipolarons is developed. A temperature of T* a transition from a pseudogap phase to a normal one is calculated. For the temperature of a transition to the pseudogap phase, the isotope coefficient is found. It is shown that the results obtained, in particular, the possibility of negative values of the isotope coefficient, are consistent with the experiment. New experiments on the influence of the magnetic field on the isotope coefficient are proposed.

Vanishing nematic order beyond the pseudogap phase in overdoped cuprate superconductors

During the last decade, translational and rotational symmetry-breaking phases—density wave order and electronic nematicity—have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant X-ray scattering in a cuprate high-temperature superconductor La1.6−xNd0.4SrxCuO4 (Nd-LSCO) to navigate the cuprate phase diagram, probing the relationship between electronic nematicity of the Cu 3d orbitals, charge order, and the pseudogap phase as a function of doping. We find evidence for a considerable decrease in electronic nematicity beyond the pseudogap phase, either by raising the temperature through the pseudogap onset temperature T* or increasing doping through the pseudogap critical point, p*. These results establish a clear link between electronic nematicity, the pseudogap, and its associated quantum criticality in overdoped cuprates. Our findings anticipate that electronic nematicity may play a larger role in understanding the cuprate phase diagram than previously recognized, possibly having a crucial role in the phenomenology of the pseudogap phase.

Unified energy law for fluctuating density wave orders in cuprate pseudogap phase

The origin of the pseudogap and its relationship to symmetry-broken orders in cuprates have been extensively debated. Here, we report a unified energy law underlying the pseudogap, which determines the scattering rate, pseudogap energy, and its onset temperature, with a quadratic scaling of the wavevector of density wave order (DWO). The law is validated by data from over one hundred samples, and a further prediction that the master order of pseudogap transforms from fluctuating spin to charge DWO is also confirmed by independent measurements. Furthermore, the energy law enables our derivation of the well-known linear scalings for the resistivity of the strange metal phase and the transition temperature of the superconducting phase, shedding light on the universal origin of various phases. Finally, it is concluded that fluctuating orders provide a critical bridge linking microscopic spectra to macroscopic transport in cuprates, showing promise for the quantification of other strongly correlated materials.

Magnetic monopole mechanism for localized electron pairing in HTS

Recent effective field theory of high-temperature superconductivity (HTS) captures the universal features of HTS and the pseudogap phase and explains the underlying physics as a coexistence of a charge condensate with a condensate of dyons, particles carrying both magnetic and electric charges. Central to this picture are magnetic monopoles emerging in the proximity of the topological quantum superconductor-insulator transition (SIT) that dominates the HTS phase diagram. However, the mechanism responsible for spatially localized electron pairing, characteristic of HTS, remains elusive. Here we show that real-space, localized electron pairing is mediated by magnetic monopoles and occurs well above the superconducting transition temperature Tc. Localized electron pairing promotes the formation of superconducting granules connected by Josephson links. Global superconductivity sets in when these granules form an infinite cluster at Tc, which is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way to tailoring materials with elevated superconducting transition temperatures.