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 !