Vortices in superconductors& low temperature STM

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1 Vortices in superconductors& low temperature STM José Gabriel Rodrigo Low Temperature Laboratory Universidad Autónoma de Madrid, Spain (LBT-UAM) Cryocourse, 2011

2 Outline -Vortices in superconductors -Vortices & STM -STM with superconducting tip -Vortices & STM with superconducting tip

3 Superconductors Perfect conductor Meissner effect : gap in the electronic density of states N (E) B = 0 I di dt ρ = 0 5 > 10 yrs T > T T c T < T c EF E Levitating magnets We need vortices

κ(τ)=λ(τ)/ ξ(τ) Penetration depth: λ Coherence length: ξ κ = 1/ 2 κ << 1 : type I κ >> 1 : type II

4 Superconductors and magnetic field Type I - Meissner effect, perfect diamagnetism H Magnetic flux penetration: - energy balance - N-S boundaries - S-outside boundaries Ginzburg-Landau parameter: κ(τ)=λ(τ)/ ξ(τ) Penetration depth: λ Coherence length: ξ κ = 1/ 2 κ << 1 : type I κ >> 1 : type II λ ψ Η ψ Η ξ H ξ λ Type II -vortices Al : λ(0) = 16 nm ξ (0) = 1600 nm NbSe 2 : λ(0) = 240 nm ξ (0) = 8 nm

superconductor: H c 1 H c 2 Φ 0 2 4πλ Φ 4πξ 0 2 The first vortex penetrates the superconductor The

5 Superconductors and magnetic field H T Phase diagram H Type I H H C2 Type II H C N H C N H C1 < 100 G S H C = G 0 0 T T C H C1 S T C T H C2 = G Critical fields in a type II superconductor: H c 1 H c 2 Φ 0 2 4πλ Φ 4πξ 0 2 The first vortex penetrates the superconductor The magnetic flux through a vortex is the quantum flux unit: Vortex cores overlap, everything is Normal Φ 0 = h / 2e 2 mtµm 2

6 What is a vortex? Type II superconductor: λ> ξ Cooper pairs density (order parameter, gap) Φ 0 = h / 2e 2 mtµm 2 Magnetic field N S Supercurrent density d Abrikosov vortex lattice d(nm) 50 / H(T) H

7 How do we see vortices with the STM? N S Variation of the order parameter Superconducting DOS d H E F E E E Vortices can be seen using the STM (tunneling curves) E F S N 2ξ S E F conductance Y axis X axis voltage

8 A flat type II superconductor: NbSe 2 Layered material, atomically flat surfaces easily obtained. Superconductor: T C = 7.2 K, Type II: H c1 <10 mt, H c2 =4.5 T CDW below 30K 3.47 Å λ(0) = 70 nm ξ (0) = 8 nm Schematic plot of the Fermi Surface NbSe 2 Se Nb NbSe Å c b a

Observation of the vortex lattice: STM on

9 Observation of the vortex lattice: STM on NbSe 2 NbSe 2 T C = 7.2 K λ(0) = 240 nm ξ (0) = 8 nm / 0 A B C x/ξ y/ξ E F conductance A B C 1 Tesla, T= 1.8 K Image at V = = 1.3 mv H.F. Hess et al. PRL (1989) voltage 0.02 Tesla, T= 1.85 K Peak: electronic states at the vortex core

10 What happens inside the vortex? N S Variation of the order parameter Superconducting DOS d H E F E E E Similar to the quantum well Particles in a box E F S N S E F 2ξ Electronic bound states Can we see these electronic levels?

11 Bound states: quantum well Electrons in a box Energy levels and wave functions of a particle in a box. Ene ergy Can we see these electronic states? How? E E F λf L 2 E F =10 ev L = 2 nm λ F =0.2 nm E=100 mev x (10 K k B T=1 mev)

12 Bound electronic states: quantum well seen by STM T=4.9K Sample : Ag Tip: W di ) / dv ( E (Bias modulation : 5mV) x Bürgi et al. PRL, 1998

13 Bound electronic states: quantum corral seen by STM Electronic surface states in Cu(111) confined by barriers made of Fe atoms. T=4.2 K Dimensions: 10 nm Corrals: 50 átomos / 0 Crommie, Lutz & Eigler, IBM, Almaden, USA x/ξ y/ξ

14 Bound electronic states: the vortex core / 0 ( r) = 0 tanh( r / ξ ) Quantized levels, E L x/ξ y/ξ E 9/2 E 7/2 Wave function E L E 5/2 E 3/2 E 1/2 Low E ξ= 10 nm = 1 mev E F =1 ev E 2 h mξ 2 0 E F High E E=1 µev (1 K k B T=0.1 mev) h vf ξ = π Shore et al. PRL 1989

15 Bound electronic states: the vortex core. STM on NbSe 2 H.F. Hess et al. PRL (1990) T= 0.3 K Energy resolution: 0.1 mv / 0 x/ξ y/ξ

16 Observation of the vortex lattice: STM on NbSe 2 Reducing temperature, increasing resolution H.F. Hess et al. PRL (1990) / 0 T= 0.3 K Resolution: 0.1 mv x/ξ y/ξ

Observation of the vortex lattice: STM on NbSe 2 Conductance patterns around the vortex Six-fold star-like pattern: ( r) = 0 tanh( r / ξ ) Intinsic phenomenom of the vortex?

17 Observation of the vortex lattice: STM on NbSe 2 Conductance patterns around the vortex Six-fold star-like pattern: ( r) = 0 tanh( r / ξ ) Intinsic phenomenom of the vortex? Anisotropy of the order parameter? Effect of the vortex lattice? ( r, θ) = 0 (1 + bcos(6θ ) tanh( r / ξ ) N. Hayashi, M. Ichioka, and K. Machida, PRL77, LBT-UAM T= 0.3 K

18 Other superconductors, other symmetries of the order parameter N. Nishida, Tokio Institute of Technology, 2000

19 Other superconductors, other symmetries of the order parameter YNi 2 B 2 C T= 0.46 K 0.3 Tesla 0.07 Tesla Bi 2 Sr 2 CaCu 2 O x 4.2 K 14.5 T N. Nishida, Tokio Institute of Technology, 2004 Important: the symmetry of the order parameter & Fermi surface are reflected in the vortex core and lattice

origin at atomic scale, related to the orientation of the crystal lattice. side = 8.3 nm side =250 nm, T=0.3K, H=0.

20 Observation of the vortex lattice: STM on NbSe 2 To correlate the observed variations in (r,θ) to variations of the order parameter in Fermi Surface, (k F,θ), we must check if these macroscopic scale (100 nm) observations have an origin at atomic scale, related to the orientation of the crystal lattice. side = 8.3 nm side =250 nm, T=0.3K, H=0.2T d v-v = 112 nm Image at E= Image at E=E F The vortex lattice and the atomic lattice always present the same orientation.

21 Observation of the vortex lattice: STM on NbSe 2 side = 250 nm The bound states at a E F (the rays) are alwaysrotated 30º relative to the atomic lattice directions. What happens if the vortex is not part of a lattice? -Isolated vortex, -Let s produce a disordered vortex lattice.

22 Observation of the vortex lattice: STM on NbSe 2 side= 250 nm The bound states at a E F (the rays) are alwaysrotated 30º relative to the atomic lattice directions. H = 0.2 T T = 0.3 K G side = 380 nm side = 250 nm Distorted vortex lattice due to large scale defects of the sample surface.

23 How is Fermi surface in NbSe 2? NbSe 2 2-band superconductor Gap vs T Huang et al, PRB 76 (2007); Yokoya et al., Science 294 (2001); Rodrigo and Vieira, Physica C 404 (2004) Boaknin et al., PRL 90 (2003) Fermi surface 0.3K 6K

24 How are tunneling curves in NbSe 2? R N = 10 MΩ Pb -NbSe 2 T=0.3 K NbSe 2 2-band superconductor Gap distribution Normalized c conductance Voltage (mv) Pb = 1.35 mv NbSe 2 S = 0.7 mv L = 1.2 mv 80% from band with large gap 20% from band with small gap

25 Double well in the vortex in NbSe 2? Cooper pairs density, (OP, ) ( r, θ) Magnetic field L Supercurrent density ξ S ~ 1/ S (r) ξ L ~ 1/ L S ξ S > ξ L ξ L r ξ S

26 STM/S of the vortex core Superconducting DOS Let s use a superconducting tip. Why? -Enhanced energy sensitivity. We probe with a sharp DOS. (Is it well defined?) -We have 2 superconductors: Josephson current. Atomic scale probe of the superconducting condensate of the sample (without interference of the electronic bound states from quasiparticle tunneling) -Sensitive to magnetic field -But is it still a good STM tip? Can we see atoms? E F E

27 Using the STM with a superconducting tip. How good is the tip? Normalize ed conductance Tunneling resistance : R N = 10 MΩ Pb Voltage (mv) phonons R Q Josephson current: E J = 4 R N If the tunneling resistance is reduced, E J increases, and the Josephson signal will increase. (compare E J with kt!!) Pb-Pb 300mK Normalized conductan nce Josephson current Multiple Andreev reflections Voltage (mv) Gap, 2 contact R N < 10 kω Jump to atomic contact R N 10 kω tunneling R N : 10MΩ.. 100kΩ

28 Using the STM with a superconducting tip. How good is the tip? The Pb nanotip remains superconducting, with a well defined DOS at 100 mt S N S N H<Hc,bulk: both electrodes are superconducting. S-S curves H>Hc,bulk: Only the nanotip remains superconducting. N-S curves conductance (Mo ohm-1) 0-10 Normalized condu uctance Pb-Pb 300mK 7nova6.1..7nova6.283 H (mt) mt Hc, bulk 75 mt Rodrigo et al.,eur. Phys. J. B 40, 483 (2004) Rodrigo et al., Physica C 468 (2008) voltage (mv) Voltage (mv)

29 Using the STM with a superconducting tip. How good is the tip? Pb tip: Atomic resolution on NbSe 2 T=0.3 K R N = 10 MΩ R N = 75 kω 12 nm 4 nm Apparent heights: -Atoms : 0.10 angstrom -CDW : 0.15 angstrom -Hole : 0.30 angstrom

30 Using the STM with a superconducting tip. How good is the tip? NbSe 2 2-band superconductor T c =7.2 K Pb-NbSe 2 Rn=50 kohm 300 mk tip + sample Josephson current MAR Huang et al, PRB 76 (2007); Yokoya et al., Science 294 (2001); Rodrigo and Vieira, Physica C 404 (2004) Boaknin et al., PRL 90 (2003)

31 Studying the vortex in NbSe 2 with the superconducting tip. NbSe L = 1.3 mv JC profile (blue), compared to L profile (red) ξ S ~ 1/ S ξ L ~ 1/ L ξ S > ξ L Delta (mv) S = 0.8 mv distancia (nm) Josephson (au) distancia (nm) 1.5 Delta (mv) 1 I will follow the spatial evolution of the electronic bound states distancia (nm) 80% from band with large gap 20% from band with small gap

32 Studying the vortex in NbSe 2 with the superconducting tip. tip tip + L tip tip + L Con nductance (MΩ -1 ) Voltage (mv) BS at E F Conductance (MΩ -1 ) JC Voltage (mv)

33 Studying the vortex in NbSe 2 with the superconducting QP, V=E F JC BQP: spatial evolution of the peak 20 nm 220 nm Profile of the L potential well Profile of the S potential well

34 Studying the vortex in NbSe 2 with the superconducting tip. Conductance image at V= tip = E F sample (Lowest E bound state) Conductance image at V= 0, Josephson current (Profile of the L potential well) The hexagonal shape of the potential well is observed

35 Studying the vortex in NbSe 2 with the superconducting tip. The double vortex (mv) 10 nm 30 nm A vortexisnota simple object: Studying a vortex, at low temperatures, with a superconducting tip, we get information about the gap and Fermi surface. (2-band SC)

36 LBTUAM (Low Temperature Laboratory) is associated to the ICMM of the CSIC. Work supported by the Spanish MICINN and MEC: - Consolider Ingenio Molecular Nanoscience CSD program, - FIS ) and by the Comunidad de Madrid through program Nanobiomagnet.

Superconductivity and Superfluidity

Superconductivity and Superfluidity Contemporary physics, Spring 2015 Partially from: Kazimierz Conder Laboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland Resistivity