Spectroscopic Imaging STM: Atomic-Scale Visualization of Electronic Structure and Symmetry in Underdoped Cuprates

Abstract

Atomically resolved spectroscopic imaging STM (SI-STM) has played a pivotal role in visualization of 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 types of electronic states are observed when using SI-STM. The first consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor existing in an energy range \(\vert {}E\vert {} \le {}\varDelta _{0}\) and only upon an arc in momentum space (k-space) that terminates close to the lines connecting k \(=\) \(\pm {}(\pi {}/a_{0},0)\) to k \(=\) \(\pm {}(0, \pi {}/a_{0})\). This ‘nodal’ arc shrinks continuously as electron density increases towards half filling. In both phases, the only broken symmetries detected in the \(\vert E\vert \le \varDelta _{0}\) states are those of a d-wave superconductor. The second type of electronic state occurs near the pseudogap energy scale \(\vert E\vert \sim \varDelta _{1}\) or equivalently near the ‘antinodal’ regions k \(=\) \(\pm (\pi /a_{0},0)\) and k \(=\) \(\pm (0, \pi /a_{0})\). These states break the expected 90\(^{\circ }\)-rotational (C\(_{4}\)) symmetry of electronic structure within each CuO\(_{2}\) unit cell, at least down to 180\(^{\circ }\)-rotational (C\(_{2}\)), symmetry. This intra-unit-cell symmetry breaking is interleaved with the incommensurate conductance modulations locally breaking both rotational and translational symmetries. Their wavevector S is always found to be determined by the k-space points where Bogoliubov quasiparticle interference terminates along the line joining \(\mathbf k =(0,\pm \pi /a_{0})\) to \(\mathbf k =(\pm \pi /a_{0},0)\), and thus diminishes continuously with doping. The symmetry properties of these \(\vert E\vert \sim \varDelta _1\) states are indistinguishable in the dSC and PG phases. While the relationship between the \(\vert E\vert \sim \varDelta _1\) broken symmetry states and the \(\vert E\vert \le \varDelta _{0}\) Bogoliubov quasiparticles of the homogeneous superconductor is not yet fully understood, these two sets of phenomena are linked inextricably because the k-space locations where the latter disappears are always linked by the modulation wavevectors of the former.