The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

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From quantum matter to high-temperature superconductivity in copper oxides

The search for the coexistence between superconductivity and other collective electronic states in many instances promoted the discovery of novel states of matter. The manner in which the different types of electronic order combine remains an ongoing puzzle. 1T-TaS(2) is a layered material, and the only transition-metal dichalcogenide (TMD) known to develop the Mott phase. Here, we show the appearance of a series of low-temperature electronic states in 1T-TaS(2) with pressure: the Mott phase melts into a textured charge-density wave (CDW); superconductivity develops within the CDW state, and survives to very high pressures, insensitive to subsequent disappearance of the CDW state and, surprisingly, also the strong changes in the normal state. This is also the first reported case of superconductivity in a pristine 1T-TMD compound. We demonstrate that superconductivity first develops within the state marked by a commensurability-driven, Coulombically frustrated, electronic phase separation.

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From Mott state to superconductivity in 1T-TaS2

In the high-transition-temperature (high-T(c)) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO(2) unit cell. We analyse spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi(2)Sr(2)CaCu(2)O(8 +) (delta) and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90 degrees -rotational symmetry within every CuO(2) unit cell.

Intra-unit-cell electronic nematicity of the high- T c copper-oxide pseudogap states

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.

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Ubiquitous Interplay between Charge Ordering and High-Temperature Superconductivity in Cuprates

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classicalnematicsgenerally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

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Nematic Fermi Fluids in Condensed Matter Physics

Removing electrons from the CuO2 plane of cuprates alters the electronic correlations sufficiently to produce high-temperature superconductivity. Associated with these changes are spectral-weight transfers from the high-energy states of the insulator to low energies. In theory, these should be detectable as an imbalance between the tunneling rate for electron injection and extraction-a tunneling asymmetry. We introduce atomic-resolution tunneling-asymmetry imaging, finding virtually identical phenomena in two lightly hole-doped cuprates: Ca(1.88)Na(0.12)CuO(2)Cl2 and Bi2Sr2Dy(0.2)Ca(0.8)Cu2O(8+delta). Intense spatial variations in tunneling asymmetry occur primarily at the planar oxygen sites; their spatial arrangement forms a Cu-O-Cu bond-centered electronic pattern without long-range order but with 4a(0)-wide unidirectional electronic domains dispersed throughout (a(0): the Cu-O-Cu distance). The emerging picture is then of a partial hole localization within an intrinsic electronic glass evolving, at higher hole densities, into complete delocalization and highest-temperature superconductivity.

https://science.sciencemag.org/content/sci/315/5817/1380.full.pdf

An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.

How Cooper pairs vanish approaching the Mott insulator in Bi 2 Sr 2 CaCu 2 O 8+δ

In conventional superconductors, the critical temperature goes to zero as the density of charge carriers falls due to increased scattering. But in high-temperature superconductors, the scattering rate as a function of charge carriers was unknown, until now.

Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi2Sr2CaCu2O8+|[delta]|

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C. Taylor

Papers

An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates

How Cooper pairs vanish approaching the Mott insulator in Bi 2 Sr 2 CaCu 2 O 8+δ

Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi2Sr2CaCu2O8+|[delta]|

Evolution of the electronic excitation spectrum with strongly diminishing hole-density in superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$