Session Z24: Orbital Ordering in Cuprates

Resonant x-ray scattering investigations of orbital/nematic and charge density wave orders in cuprate superconductors

Charge density wave (CDW) order has been established as a generic feature of the cuprate phase diagram, competing and co-existing with superconductivity. In addition to being a modulation of charge density, CDW order couple to orbital degrees of freedom, including (Q_x = Q_y = 0) orbital/nematic order. How these orders manifest and couple to each other can depend on the structure of the material and hole doping, and may play an important role in how CDW order varies amongst the different cuprates. In this talk, we explore the relationship between structural distortions, (Q_x = Q_y = 0)  nematic/orbital order and CDW using equilibrium and pump/probe resonant x-ray scattering measurements in the (La,M)₂CuO₄ family of cuprate superconductors. These measurements demonstrate orbital/nematic order to be coupled to but distinct from CDW order.  We will also show nematic order to be present in underdoped cuprates, but vanish above the pseudogap critical doping, p*, and temperature, T* in overdoped cuprates.

    

Nematic and spin-charge orders driven by hole-doping a charge-transfer insulator

Recent experimental discoveries have brought a diverse set of broken symmetry states and in particular, nematicity in the form of orbital ordering to the center stage of research on cuprate superconductors. Here, we present a thematic understanding of the diverse phenomenology by exploring a strong-coupling mechanism of symmetry breaking driven by frustration of antiferromagnetic order. We achieve this through a combination of numerically exact methods and variational analysis of a three-band model of the CuO₂ plane with Kondo type exchange couplings between doped oxygen holes and classical copper spins. In the resulting spin-fermion model, we find (1) that the symmetry hierarchy of spin stripe, charge stripe, intra-unit-cell nematic order, and isotropic phases are all accessible microscopically within the model, and (2) many symmetry-breaking patterns compete with energy differences within a few meV per Cu atom to produce a rich phase diagram. Finally, we study the tendency to orbital ordering in the various phases and signatures of the resulting nematicity.   

Interplay of nematicity and orbital order with non-Fermi liquid physics

Multiorbital models for correlated quantum materials naturally describe a wealth of broken symmetry phases including nematicity arising from orbital order. We explore the interplay of this nematicity with non-Fermi liquid behavior using generalizations of the Sachdev-Ye-Kitaev model to describe transport and elastotransport. Our results are of broad interest for the cuprates which exhibit oxygen orbital ordering, and the iron chalcogenides with dxz/dyz orbitals.   

Beyond BCS: An Exact Model for Superconductivity and Mottness

The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity described all superconductors until the 1986 discovery of the high-temperature counterpart in the cuprate ceramic materials.  This discovery has challenged conventional wisdom as these materials are well known to violate the basic tenets of the  Landau Fermi liquid theory of metals, crucial to the BCS solution.   Precisely what should be used to replace Landau's theory remains an open question.  The natural question arises: What is the simplest model for a non-Fermi liquid that yields tractable results.  Our work builds[1] on an overlooked symmetry that is broken in the normal state of generic models for the cuprates and hence serves as a fixed point.  A surprise is that this fixed point also exhibits Cooper's instability[2,3].  However, the resultant superconducting state differs drastically[3] from that of the standard BCS theory.  For example the famous Hebel-Slichter peak is absent and the elementary excitations are no longer linear combinations of particles and holes but rather are superpositions of composite excitations.  Our analysis here points a way forward in computing the superconducting properties of strongly correlated electron matter.

[1] E. Huang, G. La Nave, P. Phillips, accepted Nat. Phys., 2021 (https://arxiv.org/abs/2103.03256).

[2] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

[3]J. Zhao, L. Yeo, E. Huang, PWP, https://arxiv.org/abs/2111.14852.

    

Visualization of Intra-Unit-Cell Orbital Ordering in Bi2Sr2CaCu2O8+

The CuO₂ unit cell is the essential element of superconductivity in cuprate. The Coulombic interactions dominating the 3d⁹ and 3d¹⁰ configurations of each copper ion have been the focus of virally all theoretical investigations. However, if Coulombic interactions exist between the electrons of the 2p⁶ orbitals of each planar oxygen atom, the energy degeneracy may be lifted due to orbital ordering. The consequence would be symmetry breaking inside the CuO₂ unit cell and an electronic nematic phase in which the charge transfer energy ε separating each oxygen 2p⁶ orbital from the relevant copper 3d¹⁰ orbital configuration is different for the two oxygen atoms. We developed sublattice resolved imaging of charge transfer energy ε(r) to CuO₂ and successfully detected powerful rotational symmetry breaking of ε(r) inside the unit cell. In fact the energy splitting between the two oxygen atoms on the energy scale of circa 50 meV. Hence a powerful orbitally ordered state occurs in Bi₂Sr₂CaCu₂O₈ at the charge-transfer energy scale. We show that, spatially, this state is arranged in Ising domains that are pinned by the dense dispersal of dopant-ions which render the material superconducting. These data pinpoint the microscopic mechanism for the cuprate nematicity as due to orbital ordering. And such orbital ordering bears striking analogies to the iron d_zx and d_zy orbitals (orbital ordering) well known in iron-based superconductors.