High-T c Superconductor Surface State 15/20/2015 Group member: 陈玉琴、郭亚光、贾晓萌、刘俊义、刘晓雪 彭星星、王建力、王鹏捷 ★ 、喻佳兵 ★ :Group Leader & Speaker

Foreword 2

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 3

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 4

General Concept Disappearance of Resistance (H.K.Onnes,Commun.Phys.Lab.12,120(1911) Meissner Effect (Meissner, W, Naturwissenschaften 21 (44): 787–88.(1933) BCS Theory (Physical Review 97 (6): 1724–1725.) Two electrons with opposite spin and momentum combine a Cooper pair, the coherence length is about cm which can be unimpeded form current. Energy gap In order to break a pair, one has to change energies of all other pairs. This means there is an energy gap for single-particle excitation, unlike in the normal metal. 5

General Concept Critical Field/Temperature/Current McMillan Limit (PRB. 16,643(1977)) 6

Scanning Tunneling Spectrum 7 Rev. Mod. Phys. 79, 353 (2007)

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 8

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 9

Crystal Structure 10 Fig.(a) Bi 2 Sr 2 CaCu 2 O 8 Fig.(b) YBa 2 Cu 3 O 6 Fig.(c) Schematics of the dx 2 −y 2 superconducting gap in the unit-cell coordinate system. Rev. Mod. Phys. 79, 353 (2007)

STM Topography and Spectroscopy of a cleaved Bi 2 Sr 2 CaCu 2 O 8 thin film 11 Rev. Mod. Phys. 79, 353 (2007)

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 12

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 13

From Conventional SC to High- T c SC 14 Rev. Mod. Phys. 79, 353 (2007)

Pseudogap on different SC Materials 15 Rev. Mod. Phys. 79, 353 (2007)

Conflicts from Y123 &Nd Rev. Mod. Phys. 79, 353 (2007)

Two Scenarios of the Mechanism 1. The scenario of preformed pairs.(Fig. (a)) 2. The scenario of a non-superconducting related pseudogap. (Fig. (b)) 17 Rev. Mod. Phys. 79, 353 (2007)

Recently Research 18 Nature Physics 9, 442–446 (2013) 02 June 2013

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 19

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 20

Vortex in High-T c Superconductor 21

Vortex Measurement 22 Illustration of the vortex-lattice imaging by STM: (a) Local SIN junction with typical BCS s-wave characteristics when the tip is between vortices. (b) Local NIN junction with a constant conductance for a dirty BCS superconductor when the tip is positioned over a vortex core. Rev. Mod. Phys. 79, 353 (2007)

Difference between 2 kind of SC Conventional SuperconductorHigh-T c Superconductor 23 Left: Phys. Rev. Lett. 62, 214 (1989)Right: Rev. Mod. Phys. 79, 353 (2007)

Difference between 2 kind of SC Conventional SuperconductorHigh-T c Superconductor 24 Left: Phys. Rev. Lett. 62, 214 (1989)Right: Rev. Mod. Phys. 79, 353 (2007)

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 25

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 26

27 Two different types of spatial variations have been seen by STS: a.Large but irregular spatial variations of the gap, with typical lengths scales of the order of 3–10 nm, in samples which are not specially treated for homogeneity; b.Weaker but spatially periodic LDOS modulations with a wavelength of about 1.6–2 nm. Local Electronic Modulations

The Experiment about Periodic Modulations 1.The first indication of the presence of such periodic spatial modulations was the observation that around the center of a vortex there is a modulation of the LDOS. 2. Subsequently, Howald, Eisaki, Kaneko, Greven,and Kapitulnik 2003 found that charge modulations were also present in the absence of a magnetic field. They reported that the structure appeared at an energy around 25 meV and that the superperiod did not disperse with energy. 3. Hoffman, McElroy, et al reported similar zero-field electronic modulations, but in contrast to Howald, Eisaki, Kaneko, Greven, and Kapitulnik 2003 they found that these modulations disperse with energy,energy. They successfully interpreted their findings in terms of quasiparticle interference due to scattering from impurities and other inhomogeneities. 4.More recently Vershinin, Misra, Ono, et al observed electronic modulations in the pseudogap phase above T. 28

29 Quasiparticle Interference Oscillations In the Superconducting State Rev. Mod. Phys. 79, 353 (2007)

Quasiparticle Interference Oscillations In the Superconducting State 30 Representation of the quasiparticle energy along the Fermi surface. q A and q B are two possible vectors connecting quasiparticle states with identical energies, giving rise to interference patterns. Science 279, 353 (2007)

Recently Research 31 Nature 462, (2009)

Recently Research 32 Nature 462, (2009)

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 33

Contents I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 34

Summary I.General Concept II.Crystal Structure III.Pseudogap in High-T c Superconductor IV.Vortex in High-T c Superconductor V.Local Electronic Modulations Observed by STM VI.Summary 35