Spectroscopic Imaging Scanning Tunneling Microscopy Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High-T_{\text{c}} Superconductors

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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 |E|=\Delta_{0} and only upon a momentum space (\mathbf{k}-space) arc which terminates near the lines connecting \mathbf{k}=\pm(\pi/a_{0},0) to \mathbf{k}=\pm(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 |E|\leq\Delta_{0} states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E|\sim \Delta_{1} which is associated conventionally with the ``antinodal'' states near \mathbf{k}=\pm(\pi/a_{0},0) and \mathbf{k}=\pm(0,\pi/a_{0}). We find that these states break the expected 90°-rotational (C_{4}) symmetry of electronic structure within CuO2 unit cells, at least down to 180°-rotational (C_{2}) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C_{4} symmetry breaking coexists at |E|\sim\Delta_{1} with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The characteristic wavevector \mathbf{Q} of the latter is determined, empirically, by the \mathbf{k}-space points where Bogoliubov quasiparticle interference terminates, and therefore evolves continuously with doping. The properties of these two classes of |E|\sim\Delta_{1} states are indistinguishable in the dSC and PG phases. To explain this segregation of \mathbf{k}-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales |E|\sim\Delta_{1} and |E|\leq\Delta_{0}, and to understand how this impacts the electronic phase diagram and the mechanism of high-T_{\text{c}} superconductivity, represents one of a key challenges for cuprate studies.
2012-01-15

Spectroscopic Imaging Scanning Tunneling Microscopy Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High-T_{\text{c}} Superconductors

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