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

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 180)


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.


Incommensurate Modulation Underdoped Cuprates Bogoliubov Quasiparticle Break Symmetry State Octet Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We acknowledge and thank all our collaborators: E.-A. Kim, M.J. Lawler, J.W. Alldredge, T. Hanaguri, P.J. Hirschfeld, J.E. Hoffman, E.W. Hudson, Y. Kohsaka, K.M. Lang, C. Lupien, Jhinhwan Lee, Jinho Lee, V. Madhavan, K. McElroy, J. Orenstein, S.H. Pan, R. Simmonds, A. Schmidt, J. Sethna, J. Slezak, H. Takagi, C. Taylor, P. Wahl and M. Wang. Preparation of this manuscript was supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy Sciences under Award Number DE-2009-BNL-PM015. We also acknowledge support during the writing of this article by US DOE under contract DEAC02-98CH10886, as well as by a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan) and the Global Centers of Excellence Program for Japan Society for the Promotion of Science. C.K.K. was supported under the FlucTeam program at Brookhaven National Laboratory under contract DE-AC02-98CH10886. M.H. acknowledges funding the Office of Naval Research under Award N00014-13-1-0047. S.M. acknowledges support from NSF Grant DMR-1120296 to the Cornell Center for Materials Research.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.LASSP, Department of PhysicsCornell UniversityIthacaUSA
  2. 2.CMPMS DepartmentBrookhaven National LaboratoryUptonUSA
  3. 3.Kavli Institute at Cornell for NanoscienceCornell UniversityIthacaUSA
  4. 4.National Institute of Advanced Industrial Science and Technology (AIST)TsukubaJapan
  5. 5.Department of PhysicsUniversity of TokyoBunkyo-kuJapan
  6. 6.School of Physics and AstronomyUniversity of St. AndrewsScotlandUK

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