STM/S Imaging Studies in theVortex State

Anjan K. GuptaPhysics Department, IIT, Kanpur

(Tutorial, IVW10 at TIFR)

Quantum Tunneling

z=d

Tunneling Current

d

mVI

22

exp~

11~

2 Am

So,

eV4~For typical Metals

Ref.: J. G. Simmons, J. Appl. Phys. 34, 1793 (1963)

I increases ~ 10 times if d decreases by 1 A

Scanning Tunneling Microscope

A

Fresh Cleaved HOPG (Graphite)

STM Schematics

• Fine XYZ positioner• The coarse Approach• Sample & Tip holder• Vibration isolation• Electronics & Software

The coarse Approach~0.25m step

< 0.5m

5 mm

Fine XYZ positioner

0.1 A

sam

ple

Sam

ple

hold

er

The First STM

5 cmRef.: Binnig, Rohrer, Gerber, and Weibel, APL50, 178 (1982)

STM at IITK

IITK

HOPG in ambience

Tunneling Current

dNfeVNeVf

eVNeVfNfeGI

tipsam

samtipkd

])}(1{

)}(1{[20

Sample(+ve bias)

Nsam

eV kBT

Tip

Ntip

filled

empty

dNeVNfeVfeG tipsamkd

20

Tip

dSample

V

deVNNeVffeGI tipsamkd

20

Topography : k ~ 1 Å-1

deVfNVdV

dIsam

)()()(Spectroscopy :

~ Nsam (eV) (T ~ 0)

Ref.: J. Bardeen, Phys. Rev. Lett. 6, 57 (1961) Tersoff & Hamann, Phys. Rev. B 31, 805 (1985)

dNeVNfeVfeGI tipsamkd

20

Sample(+ve bias)

Nsam

eV kBT

Tip

Nt

filled

empty

Tunneling Current

w~kT

eV

Tunneling Spectrum

Energy Resolution ~ 29 eV

Features in electronic DOS within E << EF (~ can be resolved extremely well with an energy resolution ~ kT

)()( eVNVdV

dIsam

Example: BCS gap in a Superconductor

22sup )(

E

EENN F

Superconductor

Normal Metal

insulator Vs.

Sandwich Junction

Tip

dSample

STM Junction STS

tdV

Idtv

dV

dIVItvVI

VV

2cos14

1sinsin

2

2

00

2) ac-Modulation:

+

Tip

Sample

Amp

Z-Feedback

Lock-In

v0 sin t

Scanning Tunneling Spectroscopy1) 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:

ampfeedback

)(1

Scanning speed:

Sampling time > lock-in > 1/

~80 s./im (= 2kHz, lock-in = 3msec, S.T. = 5msec., 128x128 )

STS: Vortex Imaging

Ref.: H. F. Hess et.al., Phys. Rev. Lett. 62, 214–216 (1989)

2H-NbSe2 at T = 1.8K and 1 Tesla,dI/dV at 1.3mV

Tc=7.2K, =1meV, ||=8nm, ||=30

200G, 350nm

LDOS in Vortex Core

Ref.: F. Gygi and M. Schluter, PRB41, 822 (1990); ibid, PRB43, 7609 (1991)

r

r tanh0

0)(2

rvrruEEAep F

0)(*2 rurrvEEAep F

B-dG eqns. in vortex core:

For lowest E

Bound (E<0) & Scattering (E>0) States

LDOS [N(E)]

iiiiiS EErvEEruErA 222),(

k

kN EEErA 2),( (Flat near EF)

i

iiii eVEfrveVEfrudV

VrdI)()(

),( 22

STS vs. Theory

Anisotropy of periodic potential and magnetic field

F. Gygi and M. Schluter, PRB43, 7609 (1991)

200G, 350nmSTS

Theory

Anisotropy

150nm

H=500G, 1.3K

0mV

Th

0.5mV

Th

Vortex Imaging (low Tc)

Ref.:M. R. Eskildsen, PRL89, 187003 (2002)No bound states !

0.05T 0.2T

V0/V

MgB2

4.2K

1.5 T

290nm 150nm

Ref.: Y. De Wilde PRL78, 4273 (1997)

LuNi2B2C (4.2 K)

Ref.: H. Sakata, PRL84, 1583 (2000)

YNi2B2C (4.2 K)

0.5 T || c

Au covered for passivation Ref.: G. J. C. van Baarle, APL82, 1081 (2003)

Mo2.7Ge700nm

0.5T 0.5T

680

nm

Vortex Imaging (high Tc)

Ref.: I. Maggio-Aprile,PRL75, 2754 (1995)

YBCO123

4.2K, 6T (field cooled)

Bi2Sr2CaCu2O8

Ref.: S. H. Pan, PRL85, 1536 (2000)

7.25 T, 4.2K, 7mV0T, 4.2K, 7mV

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 (Au24+) NbSe2 at 4.2K

Topography & tunneling conductance images at various fields

Vortex Pinning

Ref.: A. M. Troyanovski, Nature399, 665, 1999

NbSe2, 0.6T, 4.2K,

ion (6GeV Pb) irradiated

NbSe2, 0.6T, 4.2K,

pristine

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

Thank You !