1. STM/S Imaging Studies in the Vortex State Anjan K. Gupta Physics Department, IIT, Kanpur (Tutorial, IVW10 at TIFR)

2. Quantum Tunneling z=d Tunneling Current So, For typical Metals Ref.: J. G. Simmons, J. Appl. Phys. 34, 1793 (1963) I increases ~ 10 times if d decreases by 1

3. Scanning Tunneling Microscope A Fresh Cleaved HOPG (Graphite)

4. STM Schematics Fine XYZ positioner The coarse Approach Sample & Tip holder Vibration isolation Electronics & Software The coarse Approach ~0.25  m step < 0.5  m 5 mm Fine XYZ positioner 0.1 sample Sample holder

5. The First STM 5 cm Ref.: Binnig, Rohrer, Gerber, and Weibel, APL50, 178 (1982)

6. STM at IITK IITK HOPG in ambience

7. Tunneling Current Sample (+ve bias) N sam eV kBTkBT Tip  N ti p filled empty  Tip d Sample V

8. Topography : k ~ 1 Å -1 Spectroscopy : ~ N sam (eV) (T ~ 0) Ref.: J. Bardeen, Phys. Rev. Lett. 6, 57 (1961) Tersoff & Hamann, Phys. Rev. B 31, 805 (1985) Sample (+ve bias) N sam eV kBTkBT Tip  NtNt filled empty  Tunneling Current w~kT eV

9. Tunneling Spectrum Energy Resolution ~ 29  eV Features in electronic DOS within  E << E F (~  can be resolved extremely well with an energy resolution ~ kT Example: BCS gap in a Superconductor Superconductor Normal Metal insulator Vs. Sandwich Junction Tip d Sample STM Junction STS

10. 2) ac-Modulation: + Tip Sample Amp Z-Feedback Lock-In v 0 sin  t Scanning Tunneling Spectroscopy 1) Measure I(V) at each point and differentiate Impractical: 128x128 image takes >2hrs. and >16MB memory (0.5s/spec. & 1kB for 512 of 2 bytes points) Band-widths: Scanning speed: Sampling time >  lock-in > 1/  ~80 s./im (  = 2kHz,  lock-in = 3msec, S.T. = 5msec., 128x128 )

11. STS: Vortex Imaging Ref.: H. F. Hess et.al., Phys. Rev. Lett. 62, 214–216 (1989) 2H-NbSe 2 at T = 1.8K and 1 Tesla, dI/dV at 1.3mV T c =7.2K,  =1meV,  || =8nm,  || =30 200G, 350nm

12. LDOS in Vortex Core Ref.: F. Gygi and M. Schluter, PRB41, 822 (1990); ibid, PRB43, 7609 (1991) B-dG eqns. in vortex core: For lowest E Bound (E  0 ) States LDOS [N(E)] (Flat near E F )

13. STS vs. Theory Anisotropy of periodic potential and magnetic field F. Gygi and M. Schluter, PRB43, 7609 (1991) 200G, 350nm STS Theory Anisotropy 150nm H=500G, 1.3K 0mV Th 0.5mV Th

14. Vortex Imaging (low T c ) Ref.:M. R. Eskildsen, PRL89, 187003 (2002) No bound states ! 0.05T0.2T V 0 /V  MgB 2 4.2K 1.5 T 290nm 150nm Ref.: Y. De Wilde PRL78, 4273 (1997) LuNi 2 B 2 C (4.2 K) Ref.: H. Sakata, PRL84, 1583 (2000) YNi 2 B 2 C (4.2 K) 0.5 T || c Au covered for passivation Ref.: G. J. C. van Baarle, APL82, 1081 (2003) Mo 2.7 Ge 700nm 0.5T 680 nm

15. Vortex Imaging (high T c ) Ref.: I. Maggio-Aprile, PRL75, 2754 (1995) YBCO123 4.2K, 6T (field cooled) Bi 2 Sr 2 CaCu 2 O 8 Ref.: S. H. Pan, PRL85, 1536 (2000) 7.25 T, 4.2K, 7mV 0T, 4.2K, 7mV

16. Ref.: S. Behler, PRL72, 1750 (1994) Vortex Pinning Topography STS, 0.5T,0.5mV STS, 0.1T,0.5mV STS, 4mT,0.5mV Ion irradiated (Au 24+ ) NbSe 2 at 4.2K Topography & tunneling conductance images at various fields

17. Vortex Pinning Ref.: A. M. Troyanovski, Nature399, 665, 1999 NbSe 2, 0.6T, 4.2K, ion (6GeV Pb) irradiated NbSe 2, 0.6T, 4.2K, pristine

18. Magnetic Vortex: SP-STM Xth International Vortex State Studies Workshop STM/S Imaging Studies in the Vortex State Ref.: A. Wachowiak, Science 298, 577. Fe island on W (110) Cr coated W tip, 10K

19. Thank You !