This content will become publicly available on December 1, 2022
 Award ID(s):
 1849751
 Publication Date:
 NSFPAR ID:
 10323610
 Journal Name:
 Nature Communications
 Volume:
 12
 Issue:
 1
 ISSN:
 20411723
 Sponsoring Org:
 National Science Foundation
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The defining characteristic of holedoped cuprates is d wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strongcoupling meanfield theory of cuprates, to model the atomicscale electronic structure of an eightunitcell periodic, d symmetry form factor, pair density wave (PDW) state coexisting with d wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states N r , E is predicted at the terminal BiO surface of Bi 2 Sr 2 CaCu 2 O 8 and compared with highprecision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunitcell structure and periodic modulations of N r , E , the modulations of the coherence peak energy Δ p r , and the characteristics of Bogoliubov quasiparticle interference in scatteringwavevector space q  space . Consistency between all these predictions and the corresponding experiments indicates that lightly holedoped Bi 2 Sr 2 CaCu 2 O 8 does contain a PDW + DSC state. Moreover,more »

High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electronpair density wave (PDW). To search for evidence of a fieldinduced PDW, we visualized modulations in the density of electronic states N ( r ) within the halo surrounding Bi 2 Sr 2 CaCu 2 O 8 vortex cores. We detected numerous phenomena predicted for a fieldinduced PDW, including two sets of particlehole symmetric N ( r ) modulations with wave vectors Q P and 2 Q P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary fieldinduced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO 2 unitcell periodicity and coexisting with its secondary CDWs.

The CuO 2 antiferromagnetic insulator is transformed by holedoping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic densityofstates D ( E ) for energies  E  < Δ * , where Δ * is the PG energy. Unanticipated brokensymmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite Q densitywave (DW) state and a Q = 0 nematic (NE) state. Sublatticephaseresolved imaging of electronic structure allows the doping and energy dependence of these distinct brokensymmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures T DW and T NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy Δ * . Moreover, no new energygap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of openingmore »

Abstract The proximity of many strongly correlated superconductors to densitywave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantumcritical (QC) fluctuations of the corresponding order parameter. Here we study anisotropic
s wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the nonlinear gap equation for the pairing gap and show that its angular dependence strongly varies below$$\Delta (\theta ,{\omega }_{m})$$ $\Delta \left(\theta ,{\omega}_{m}\right)$ . We show that this variation is a signature of QC pairing and comes about because there are multiple$${T}_{{\rm{c}}}$$ ${T}_{c}$s wave pairing instabilities with closely spaced transition temperatures . Taken alone, each instability would produce a gap$${T}_{{\rm{c}},n}$$ ${T}_{c,n}$ that changes sign$$\Delta (\theta ,{\omega }_{m})$$ $\Delta \left(\theta ,{\omega}_{m}\right)$ times along the Fermi surface. We show that the equilibrium gap$$8n$$ $8n$ is a superposition of multiple components that are nonlinearly induced below the actual$$\Delta (\theta ,{\omega }_{m})$$ $\Delta (\theta ,{\omega}_{m})$ , and get resonantly enhanced at$${T}_{{\rm{c}}}={T}_{{\rm{c}},0}$$ ${T}_{c}={T}_{c,0}$ . This gives rise to strong temperature variation of the angular dependence of$$T={T}_{{\rm{c}},n}\ <\ {T}_{{\rm{c}}}$$ $T={T}_{c,n}\phantom{\rule{0ex}{0ex}}<\phantom{\rule{0ex}{0ex}}{T}_{c}$ . This variation progressively disappears away from a QC point.$$\Delta (\theta ,{\omega }_{m})$$ $\Delta \left(\theta ,{\omega}_{m}\right)$ 
We present a valence transition model for electron and holedoped cuprates, within which there occurs a discrete jump in ionicity Cu2+ > Cu1+ in both families upon doping, at or near optimal doping in the conventionally prepared electrondoped compounds and at the pseudogap phase transition in the holedoped materials. In thin films of the T' compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutraltoionic transition in mixedstack organic chargetransfer solids. Doped cuprates have negative chargetransfer gaps, just as rareearth nickelates and BaBiO3. The unusually high ionization energy of the closed shell Cu1+ ion, taken together with the dopingdriven reduction in threedimensional Madelung energy and gain in twodimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small dp electron hoppings ensure that the systems behave as effective 1/2filled Cu band with the closed shell electronically inactive O2 ions in the undoped state, and as correlated twodimensional geometrically frustrated 1/4filled oxygen hole band, now with electronically inactive closedshell Cu1+ ions, in the doped state. The model thus gives microscopic justification for themore »