Strong Coulomb interactions between electrons on adjacent Cu atoms result in charge localization in the cuprate Mott-insulator state. When a few percent of electrons are removed, both high-temperature superconductivity and exotic charge density modulations appear. Identifying the correct fundamental theory for superconductivity requires confidence on whether a particle-like or a wave-like concept of electrons describes this physics. To address this issue, here we take the approach of using the phase of charge modulations, available only from atomic-scale imaging. It reveals a universal periodicity of the charge modulations of four crystal unit cells. These results indicate that the particle-like concept of strong interactions in real-space provides the intrinsic organizational principle for cuprate charge modulations, implying the equivalent for the superconductivity.
Recent studies establish that the cuprate pseudogap phase is susceptible at low temperatures to forming not only a d-symmetry superconducting (SC) state, but also a d-symmetry form factor (dFF) density wave (DW) state. The concurrent emergence of such distinct and unusual states from the pseudogap motivates theories that they are “intertwined” i.e derived from a quantum composite of dissimilar broken-symmetry orders. Some composite order theories predict that the balance between the different components can be altered, for example at superconducting vortex cores. Here, we introduce sublattice phase-resolved electronic structure imaging as a function of magnetic field and find robust dFF DW states induced at each vortex. They are predominantly unidirectional and co-oriented (nematic), exhibiting strong spatial-phase coherence. At each vortex we also detect the field-induced conversion of the SC to DW components and demonstrate that this occurs at precisely the eight momentum-space locations predicted in many composite order theories. These data provided direct microscopic evidence for the existence of composite order in the cuprates, and new indications of how the DW state becomes long-range ordered in high magnetic fields.
Developing nm-resolved milliKelvin Scanned Josephson microscopy, we directly imaged the pair density wave of the cuprate superconductor Bi2Sr2CaCu2O8 near optimal doping. The superconducting STM tip synthesized from Bi2Sr2CaCu2O8 allowed for Josephson tunneling of d-wave Cooper-pairs, the primary superfluid carriers in the cuprate high temperature superconductors. Nanometer scale imaging capabilities were preserved by the tip synthesis process and allowed for direct visualization of the spatially modulating Cooper-pair density believed to exist in such compounds.
Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic ‘pseudogap’ phenomenonand the more recently investigated density wave state. This state always exhibits wave vector Q parallel to the planar Cu-O-Cu bonds along with a predominantly d-symmetry form factor(dFF-DW). Finding its microscopic mechanism has now become a key objective of this field. To accomplish this, one must identify the momentum-space (k-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualizationof electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the ‘pseudogap’ energy Δ1. Moreover, we demonstrate that the dFF-DW modulations at E=−Δ1 (filled states) occur with relative phase π compared to those at E=Δ1 (empty states). Finally, we show that the dFF-DW Q corresponds directly to scattering between the ‘hot frontier’ regions of k-space beyond which Bogoliubov quasiparticles cease to exist. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of ‘hot frontier’ regions in k-space where the pseudogap opens.
(In preparation for ROPP) A unified review of newly developed theoretical and experimental methods to directly observe heavy fermion physics including formation of heavy quasiparticles and their Cooper pairing.
Direct sublattice-phase-resolved imaging of the electronic structure in both Bi2Sr2CaCu2O8+δ and Ca2-xNaxCuO2Cl2 reveals that the cuprate pseudogap phase exhibits a previously unknown electronic state of matter: a d-symmetry form factor density wave. The density wave requires independent degrees of freedom between the Cu and the O atoms inside each unit cell providing strong evidence that a multiband approach is essential in the explaining the cuprate high temperature superconductors.
Additional Link: Quanta Magazine – http://www.simonsfoundation.org/quanta/20140430-decoding-the-secrets-of-superconductivity/
An abrupt transition in Bi2Sr2CaCu2O8+δ Fermi surface topology from broken ‘arc’ to full closed contour is visualized with SI-STM along the doping phase diagram. The topological transition is also found to occur at the same critical doping level where the translational and intra-unit-cell broken symmetries are restored. The discovery reveals that the momentum space topology transformation is intimately linked to presence of a concealed critical point in the cuprate phase diagram.
Additional Link: Phys.org – http://phys.org/news/2014-05-solution-long-standing-mysteries-cuprate-superconductivity.html
A review of the various theoretical and experimental methods developed to study real and momentum space structure of underdoped cuprates by spectroscopic imaging STM. The article focuses on recent advances to identify broken symmetries at the intra-unit-cell scale.
Zinc impurity states on CuO2 layer of the high temperature cuprate superconductor Bi2Sr2CaCu2O8+δ are located to pico-meter scale by simultaneously registering topographic and spectroscopic data from two different atomic layers. The result demonstrates the high degree of spatial registration between layers and rigorously validates the use of intra-unit-cell Bragg-peak Fourier analysis in determining intra-unit-cell broken symmetry states.
While the effect of non-magnetic defects, known as Kondo holes, in the magnetic lattice of heavy fermion compounds had been studies for decades, there was no clear understanding of how they drastically alter the bulk properties. Introducing the method of heavy fermion hybridization mapping, it was found that Kondo holes send out ripples in the hybridization strength of local f-electrons with the conduction electrons. The random distribution of a very small number of such defects is then found to create intense hybridization disorder explaining the alterations in the bulk properties.
Additional Links: Phys.org – http://phys.org/news/2011-10-impurity-atoms-disorder-exotic-electronic.html
The first direct observation of heavy fermion formation using heavy quasiparticle interference imaging in spectroscopic imaging STM. The real and momentum space electronic structure were determined as a function of temperature and revealed that even the highly complex heavy fermion compound URu2Si2 develops heavy bands as long predicted for simpler materials.
Additional Links: Nature Perspectives – http://www.nature.com/nature/journal/v465/n7298/full/465553a.html