The intriguing idea that strongly interacting electrons can generate spatially inhomogeneous electronic liquid-crystalline phases is over a decade old 1-5 , but these systems still represent an unexplored frontier of condensed-matter physics. One reason is that visualization of the many-body quantum states generated by the strong interactions, and of the resulting electronic phases, has not been achieved. Soft condensed-matter physics was transformed by microscopies that enabled imaging of real-space structures and patterns.

A possible explanation for the existence of the cuprate "pseudogap" state is that it is a d-wave superconductor without quantum phase rigidity. Transport and thermodynamic studies provide compelling evidence that supports this proposal, but few spectroscopic explorations of it have been made. One spectroscopic signature of d-wave superconductivity is the particle-hole symmetric "octet" of dispersive Bogoliubov quasiparticle interference modulations. Here we report on this octet's evolution from low temperatures to well into the underdoped pseudogap regime.

Although solid helium-4 ( 4He) may be a supersolid, it also exhibits many phenomena unexpected in that context. We studied relaxation dynamics in the resonance frequency f(T) and dissipation D(T) of a torsional oscillator containing solid 4He. With the appearance of the "supersolid" state, the relaxation times within f(T) and D(T) began to increase rapidly together. More importantly, the relaxation processes in both D(T) and a component of f(T) exhibited a complex synchronized ultraslow evolution toward equilibrium.

Superconducting excitations-Bogoliubov quasiparticles-are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). Depending on the applied voltage bias in scanning tunneling microscope (STM) one can sample the particle and hole content of such a superconducting excitation. Recent STM experiments offer a unique insight into the inner workings of the superconducting state of superconductors. We propose a new observable quantity for STM studies that is the manifestation of the particle-hole dualism of the quasiparticles.

In solid-state physics two different paradigms are typically applied. The first is a local picture, in which one visualizes the quantum states of electrons in atomic orbitals or at impurity atoms in real space (r-space). The second is the momentum or reciprocal space (k-space) picture, where electrons are viewed as de Broglie waves completely delocalized throughout the material.

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.

Coulomb interactions between the carriers may provide the mechanism for enhanced unconventional superconductivity in the copper oxides. However, they simultaneously cause inelastic quasiparticle scattering that can destroy it. Understanding the evolution of this balance with doping is crucial because it is responsible for the rapidly diminishing critical temperature as the hole density p is reduced towards the Mott insulating state.

Many theoretical models of high-temperature superconductivity focus only on the doping dependence of the CuO2-plane electronic structure. However, such models are manifestly insufficient to explain the strong variations in superconducting critical temperature, Tc, among cuprates that have identical hole density but are crystallographically different outside of the CuO2 plane.

One of key challenges in high-Tc superconductivity research is to identify a predominant mechanism controlling superconductivity at atomic scale.

High-transition-temperature (high-Tc) superconductivity is ubiquitous in the cuprates containing CuO2 planes, but each cuprate has its own character. The study of the material dependence of the d-wave superconducting gap (SG) should provide important insights into the mechanism of high-Tc superconductivity. However, because of the pseudogap phenomenon, it is often unclear whether the energy gaps observed by spectroscopic techniques really represent the SG. Here, we use scanning tunnelling spectroscopy to image nearly optimally doped Ca2xNaxCuO2Cl2(Na-CCOC) with Tc≤25-28K.