If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps Δi(k →) should appear on the different electronic bands i. Here, we introduce intraband Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of Δi(k→) in such materials, focusing on lithium iron arsenide (LiFeAs).

One of the key motivations for the development of atomically resolved spectroscopic imaging scanning tunneling microscopy (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor.

Replacing a magnetic atom by a spinless atom in a heavy-fermion compound generates a quantum state often referred to as a "Kondo-hole". No experimental imaging has been achieved of the atomic- scale electronic structure of a Kondo-hole, or of their destructive impact [Lawrence JM, et al. (1996) Phys Rev B 53:12559-12562] [Bauer ED, et al. (2011) Proc Natl Acad Sci. 108:6857-6861] on the hybridization process between conduction and localized electrons which generates the heavy-fermion state.

We study the coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi 2Sr 2CaCu 2O 8+δ. By visualizing their spatial components separately, we identified 2π topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra-unit-cell nematicity revealed strong empirical evidence for a coupling between them.

We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-STM) to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E = Δ0.

Using a high-sensitivity torsional oscillator (TO) technique, we mapped the rotational and relaxational dynamics of solid helium-4 (4He) throughout the parameter range of the proposed supersolidity. We found evidence that the same microscopic excitations controlling the torsional oscillator motions are generated independently by thermal and mechanical stimulation. Moreover, a measure for the relaxation times of these excitations diverges smoothly without any indication for a critical temperature or critical velocity of a supersolid transition.

In the high-transition-temperature (high-Tc) 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 CuO2 unit cell.

Within a Kondo lattice, the strong hybridization between electrons localized in real space (r-space) and those delocalized in momentum-space (k-space) generates exotic electronic states called Ä€̃ heavy fermionsÄ€™. In URu 2 Si 2 these effects begin at temperatures around 55 K but they are suddenly altered by an unidentified electronic phase transition at T o = 17.5 K. Whether this is conventional ordering of the k-space states, or a change in the hybridization of the r-space states at each U atom, is unknown.

The mechanism of high-temperature superconductivity in the newly discovered iron-based superconductors is unresolved. We use spectroscopic imaging-scanning tunneling microscopy to study the electronic structure of a representative compound CaFe1.94Co0.06As2 in the "parent" state from which this superconductivity emerges. Static, unidirectional electronic nanostructures of dimension eight times the inter-iron-atom distance αFe-Fe and aligned along the crystal α axis are observed.

This chapter is a progress report on the challenging yet promising frontier of quantum phase transitions (QPTs) in strongly correlated systems from the perspective of modern local probes and recent theoretical developments. The focus will be on our latest developments at this frontier. An outlook based on opportunities and questions emerging from these latest developments concludes the discussion. © Taylor & Francis Group.