Hard superconductivity of soft quantum films
M Murat Özer
Oak Ridge National Laboratory
Special thanks to
H Hanno Weitering & James R Thompson
M.M. Özer et al, Phys. Rev. B 72, 113409 (2005)
M.M. Özer et al, Nature Phys. 2, 173 (2006)
M.M. Özer et al, Phys. Rev. B 74, 235427 (2006)
M.M. Özer et al, Science 316, 1594 (2007)
Funded by NSF DMR-0244570
Phys. 555/342:ch.10a (2008)
Motivation
¾
Superconductivity in the quantum regime
does it survive…?
Outline
¾
Quantum size effects and self-assembly of ultrathin Pb films
¾
Thermodynamics and non-equilibrium critical state properties of
two-dimensional quantum-confined Pb superconductors
¾
Tuning the Fermi contour in quantum alloys:
Quantum growth mode of Pb-Bi alloys and multi-subband
superconductivity
Phys. 555/342:ch.10a (2008)
Electron confinement by film thickness gives quantization,
like a “particle-in-a-box”
Ψ(z) ~ sin(nπz/d)
λn = 2d/n
En = n2h2/8md2
Amorphous Ge “cap”
Pb Film
Substrate
d
: One Dimensional Confinement
gives quantization
|| : Bloch waves (2-D Subbands)
d = few monolayers (ML);
1 ML = 0.286 nm in Pb (111)
Phys. 555/342:ch.10a (2008)
Electron confinement by film thickness gives quantization,
like a “particle-in-a-box”
Amorphous Ge “cap”
Pb Film
d
Substrate
: One Dimensional Confinement
gives quantization
|| : Bloch waves (2-D Subbands)
d = few monolayers (ML);
1 ML = 0.286 nm in Pb (111)
Surface Energy
d
λF/2
δ
For Pb (111), 2 ML ≈ 3 × λF/2
5-7-9-11-13 14-16-18-20-22 25…ML
Özer et. al. PRB 72 113409 (2005)
Phys. 555/342:ch.10a (2008)
Phys. 555/342:ch.10a (2008)
Re-entrant bilayer-by-bilayer growth
Pb on Si(111)(√3×√3)R30˚-Pb(α)
Phys. 555/342:ch.10a (2008)
Re-entrant bilayer-by-bilayer growth
Pb on Si(111)(√3×√3)R30˚-Pb(α)
⇑
Pb on Ge(111)(√3×√3)R30˚-Pb(α)
⇑
Pb on Si(111)7x7
Phys. 555/342:ch.10a (2008)
Superconductivity
Heike Kamerlingh Onnes
Nobel Prize in Physics 1913
"for his investigations on the properties of matter at low temperatures
which led, inter alia, to the production of liquid helium"
Phys. 555/342:ch.10a (2008)
almost 100 years later…
SC in reduced dimensionality….?
• Film thickness << size of the Cooper pairs
→
2D superconductivity
• Fluctuations (entropy) suppress or inhibit superconductivity in 2D
• Disorder disrupts quantum coherence, particularly in reduced dimensions
Phys. 555/342:ch.10a (2008)
Generic phase diagram for a Type II
superconductor
1.0
H c1 =
H/Hc2
0.8
0.6
0.4
Hc1
0.0
0.0
normal
state
vortex or
mixed
state
Jc = 0
Hc2 =
Jc > 0
0.2
Φ0
ln(κ )
4πλ 2
Φ0
2πξ 2
Meissner state; B=0
0.2
0.4
0.6
0.8
1.0
T/Tc
Phys. 555/342:ch.10a (2008)
Vortices
15 Sept 2004; GEOS satellite
http://cimss.ssec.wisc.edu/tropic/tropic.html
Phys. 555/342:ch.10a (2008)
In mixed state, electric currents generate forces on vortices
B
J = current/area
E
v || force F
¡ F = (1/c)J×B Lorentz-like force on vortices;
¡ if vortices move at velocity v = F/ηdrag , the motion creates
an electric field E = (1/c)B×v with E || J.
¡ This dissipates power/volume P = J ·E as heat.
¡ One must immobilize vortices for loss-free
current conduction, using dopants or “dirt”.
¡ Dirt suppresses superconducting coherence
Phys. 555/342:ch.10a (2008)
Engineering nanoscale barriers for
vortex motion:
“Dirty up a thin superconductor cleanly”
Phys. 555/342:ch.10a (2008)
Inductive (i.e., contactless) measurements of the critical
current Jc via SQUID magnetometry
r
15 ΔM
Jc =
r
0.0
-0.3
-10
0.3
9 ML Mesas
m (memu)
m (memu)
0.3
ΔM
-5
0
Ha (G)
5
10
9 ML Voids
ΔM
0.0
-0.3
-10
-5
0
5
10
Ha (G)
Strong vortex pinning
Phys. 555/342:ch.10a (2008)
Hard and Soft Superconductivity
• DC magnetization loops with voids (“blind nanoholes”) are “hard”
-> strong pinning
• Loops with mesas are “softer” as Jc falls off with field.
Phys. 555/342:ch.10a (2008)
0 DC
Add
5 ML
-5
9 ML
DC Field
18 ML
-10
2
m' (μemu)
0
0
9 ML
1800 G
200 G
-5
4
6
T(K)
5G
2
4
T(K)
6
8
18 ML
13 ML
9 ML
6
Obtain
Tc*
Hc2 (kG)
m' (μemu)
AC Magnetization Measurements: Tc(HDC = 0) and Hc2(T)
4
2
0
T*C TC
2
3
T (K)
4
5
6
Phys. 555/342:ch.10a (2008)
Key Length Scales: GL and BCS
Bulk Material:
Coherence Length ξ
o
⇒ ξGL = 200 A
ξ
BCS
Bulk
o
Tc (d )
.
Penetration Depth λ
φ0
Hc =
∝ Tc (bulk ) ≈ Tc (film)
2 2πλξ
o
⇒ λ f ≈ 1600 A
|Δ|
j
0.5
2ξ
λ
0.0
= 905 A,
T
BCS
BCS
ξFilm
= ξBulk
× c0
J(r), |Δ| (normalized)
φ0
Hc2 =
≈ 8000 G (9 ML)
2
2πξ
1.0
-1
0
r/λ
1
Mean free path l
{
ξGL (T = 0, d ) ≅ 0.739 ξ 0−2 + 0.882 [ξ 0 × l (d )]−1}
−1/ 2
and find l ≈ 2×d
Depairing Current Density JDEPAIR
Finally, J DEPAIR ≈
Hc
λf
≈ 20 MA/cm 2
Phys. 555/342:ch.10a (2008)
80
40
400
mG AC Amplitudes
325
250
175
100
0
2
4
T (K)
Jc = 1.03 hac/d
6
3.0
Jc (MA cm-2)
m'' (μemu)
Out of phase AC response: Jc
9 ML Voids
9 ML Mesas
7 ML Voids
7 ML Mesas
2.5
2.0
1.5
1.0
0.5
0.0
2
3
4
T (K)
5
6
7
Phys. 555/342:ch.10a (2008)
vortex is attracted to void
Strong Vortex Pinning by Voids
Δd
d
Pb film
Maximum vortex pinning force:
f pin
ε 0 Δd
= −∇U 0 ≈
ξ
and balancing “Lorentz” force gives
Scale of vortex line energy
per unit length:
2
⎛ Φ0 ⎞
ε0 = ⎜
⎟
4
πλ
⎝
⎠
Vortex pinning energy:
U 0 = ε 0 Δd
f pin = c−1JcΦ0d
yielding estimated current density
J c ≈ J DEPAIR ( Δ d
d
) ≈ 4 MA/cm 2
Experimentally (T = 2 K):
Jc = [2.0 (dc) – 2.8 (ac)] MA/cm2.
Phys. 555/342:ch.10a (2008)
Bi-Alloying
¾
Tailoring the Fermi contour of
“Quantum alloys”
¾
Altering the quantum growth mode.
¾
Tuning SC parameters.
Phys. 555/342:ch.10a (2008)
Bi-Alloying modifies Quantum Growth Mode;
Changes Beating Period
Pb:
4 5-7-9-11-13 14-16-18-20-22 25…ML
13 ML
~9 ML
In free e- model: kF ~ n1/3
For 11% Bi:
~13 ML
k F → 1.0091 k F
λbeat =
3λF − 4d
M.M. Özer et al, Science 316,
1594 (2007)
4-6 7-9-11-13-15-17-19 20…ML
n → 1.0275 n
λF
Pb + 11% Bi:
≅ 12.7 ML
Pb + 20% Bi:
Excessive scattering
washes out QSE
Phys. 555/342:ch.10a (2008)
Bi-Alloying: Effects on Superconductivity
General:
120
100
Electron-Phonon
coupling and N(E)
increase,
A = 2d
Pb
Pb + 11% Bi
Pb + 20% Bi
1/ A = 1/ A Pb + 1/ A imp
MFP (Å)
80
⇒ Tc ↑
60
1/ A = 1/ A Pb + 1/ A′imp
40
Hc2 ↑ ⇒ ξ ↓ ⇒
A
↓
20
0
0
10
20
30
40
50
60
70
d (Å)
{
ξGL (T = 0, d ) ≅ 0.739 ξ + 0.882 [ξ0 × A(d )]
−2
0
−1
}
−1/ 2
Agrees well with ρ ⋅ A
estimation
Phys. 555/342:ch.10a (2008)
Bi-Alloying: Tc* Dilemma
0.5
(Tb-T*c)/Tb
0.4
0.3
0.2
% 20 Bi
% 10 Bi
Pure Pb
0.1
0.0
0.00
0.01
0.02
0.03
1/MFP (Å-1)
0.04
0.05
Phys. 555/342:ch.10a (2008)
Multiband Superconductivity?
MgB2
π and σ bands
2 SC
gaps
Different intraband
scattering rates
Pb Film
multiple bands
multiple gaps?
Scattering rate
~ n2
16
14
12
Hc2 (kG)
10
5 ML Voids
9 ML Voids
13 ML Voids
18 ML Mesas
8
6
4
A Gurevich et al.
SC Sci Tech, 17
278 (2004)
2
0
Tc
T*c
-2
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
T (K)Phys. 555/342:ch.10a
(2008)
Conclusions
¾
Quantum confined Pb films are extremely robust
superconductors. Critical currents can be calculated
from known pinning geometry.
It only takes a few atomic layers to sustain
macroscopic supercurrents of order ~ 100 mA.
¾
Quantum engineering of low-dimensional
superconductors and quantum alloys.
¾
Bi-alloying modifies quantum growth mode and Tc as
expected; anomalous Hc2 behavior qualitatively
consistent with multi-subband superconductivity.
Phys. 555/342:ch.10a (2008)