Spectroscopic Imaging Scanning Tunneling Microscopy Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High-T-c Superconductors

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. These are detected below a lower energy scale vertical bar E vertical bar Delta(0) and only upon a momentum space (k-space) arc which terminates near the lines connecting k = +/-(pi/a(0), 0) to k = +/-(0, pi/a(0)). Below optimal doping, this "nodal" arc shrinks continuously with decreasing hole density. In both the dSC and PG phases, the only broken symmetries detected in the vertical bar E vertical bar <= Delta(0) states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale vertical bar E vertical bar similar to Delta(1) which is associated conventionally with the "antinodal" states near k = +/-(pi/a(0), 0) and k = +/-(0, pi/a(0)). We find that these states break the expected 90 degrees-rotational (C-4) symmetry of electronic structure within CuO2 unit cells, at least down to 180 degrees-rotational (C-2) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C4 symmetry breaking coexists at vertical bar E vertical bar <= Delta(1) with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The characteristic wavevector Q of the latter is determined, empirically, by the k-space points where Bogoliubov quasiparticle interference terminates, and therefore evolves continuously with doping. The properties of these two classes of vertical bar E vertical bar <= Delta(1) states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales vertical bar E vertical bar similar to Delta(1) and vertical bar E vertical bar <= Delta(0), and to understand how this impacts the electronic phase diagram and the mechanism of high-T-c superconductivity, represents one of a key chall(enges for cuprate studies.)