KIT – University of the State of Baden-Württemberg and
National Large-scale Research Center of the Helmholtz Association www.kit.edu
Superconductor-insulator transition
in disordered FeSe thin films
R. Schneider1, A.G. Zaitsev1, D. Fuchs1, H. von Löhneysen1,2
Karlsruhe Institute of Technology
1Institut für Festkörperphysik and 2Physikalisches Institut
Thin Films and Interfaces
Outline
overview of iron-based superconductors
FeSe thin films: preparation and properties
ordered FeSe thin films: excess conductivity and BKT transition
disordered FeSe thin films: superconducting and insulating phases,
superconductor-insulator transition
disordered FeSe thin films in a magnetic field
summary
Material classes of superconducting FePn / Ch
11 FeTe1-xSex Tc = 15K for x = 0.5 and Tc = 8K for x = 1
122* A1-xFe2-ySe2 Tc 32K (A = K, Rb, Cs, (Tl,K), (Tl,Rb))
122 BaFe2As2 Tc = 38K in Ba0.6K0.4Fe2As2
111 LiFeAs Tc = 18K
1111 ReFeAsO1-xFx Tc = 25 - 56K
21311 Sr2VO3FeAs Tc = 37K „(n+1)n(3n-1)22
„
Unit cells and structural motif
J. Paglione, R.L. Greene, Nature phys. 6, 645 (2010) F. Wang, D.-H. Lee, Science 332, 200 (2011)
11
111 122
1111
32522
β - FeSe
Pressure effect
50 49.73 49.34 at% Se
concentration range of the b-phase very small
tetragonal phase turns to orthorhombic below 90 K
structural transition not accompanied by magnetic ordering
superconductivity sensitive to composition
largest among Fe Pn/Ch
Tc increase to 37 K at 4 GPa
connected with decreasing Se height
superconductivity sensitive to structure
T.M. McQueen et al., Phys. Rev. B 79, 014522 (2009)
Y. Mizuguchi, Y. Takano, J. Phys. Soc. Jpn. 79, 102001 (2010)
FeSe thin films: deposition and optimization
8°
S
2 cm
0 500 1000 1500 20000
5
10
15
20
25
experimental simulated Fe signal Se signal
Backscattering Y
ield
(C
ounts
x 1
0-3)
Energy (keV)
Se
Fe
Mg
O
2 MeV 4He
+ FeSe / MgO
350 400 450 500 550 6000
4
8
120
50
100
150
200
250
1
2
3
4
5
6
TC (
K)
TS (°C)
0 (
µ
cm
)
RR
R
optimized substrate temperature
optimized sputtering power
R. Schneider et al., Supercond. Sci. Technol. 26, 055014 (2013)
20 40 60 80 1001
10
100
1000
10000
100000
Inte
nsity (
co
un
ts/s
)
2 (deg)
(001)
(101)
(002)
(200) MgO
(003)(004)
(303)
(400) MgO
*
*
a=b=0.3789 nmc=0.5526 nm
6 8 10
0
5000
10000
15000
20000
25000
30000
Inte
ns
ity
(c
ou
nts
/s)
(deg)
(001)
FWHM = 0.22°
Surface and orientation
SEM
500 nm thick film
smooth
free of precipitates
aligned grains
rectangular shape
sizes 100 to 400 nm
lattice mismatch
minimized to 5%
XRD
(00l) Bragg reflections
[001] FeSe ‖ [001] MgO
a film > a bulk
small value of FWHM
good growth quality
fourfold rotational
symmetry
[100] FeSe ‖ [110] MgO
A.G. Zaitsev et al., J. Phys. Conf. Ser. 507, 012054 (2014)
Excess conductivity
0 50 100 150 200 250 3000
100
200
300
400
500
600
(
µ
cm
)
T (K)
495 °C
480 °C
510 °C
4 8 12 160
1
2
Rs (
k
)
T (K)
TMF
TBKT
1211109.59.25
T (K)
expt.
theor. 2D
theor. 3D
TMF
= 8.8 K
5
1
0.1
G
s (
10
-4
-1)
0.40.10.03
n
s s s
s s
1n
s
G G G
G 1 R
G a bT
2
s
25 1
MF
MF MF
e 1G
16
e1.52 10
16
T T Tln
T T
2D Aslamazov-Larkin theory:
L.G. Aslamazov, A.I. Larkin
Phys. Lett. A 26, 238 (1968)
t = 500 nm
linear at low T
parabolic with negative curvature
at high T
rounding of the transition
sR = c
Excess sheet conductance
per Fe-Se layer:
c=0.55 nm
c=3 nm
R. Schneider et al., J. Phys.: Condens. Matter 26, 455701 (2014)
2D character of the superconducting fluctuations
BKT transition and Gi
B.I. Halperin , D.R. Nelson, J. Low Temp. Phys. 36, 599 (1979)
V I a(T)
jump in a to 3 at TBKT ≈ 4.7 K
T>TBKT a=1
T<TBKT a>3
2D Ginzburg - Levanyuk number Gi :
TBKT = 5.5 K TMF = 8.8 K → Gi = 5 x 10-2
A. Larkin, A. Varlamov
Theory of Fluctuations in Superconductors
N.Y.: Oxford University Press (2005)
comparable to YBa2Cu3O7-x
large m and low ns favor large Gi
2D superconducting fluctuations
important in the layered FeSe
compound
V.L. Berezinskii, Sov. Phys. JETP 34, 610 (1972)
J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)
0
200
400
600
800
1
2
3
4
5
100 10000
4
8
12
0 (
µ
cm
)
RR
R
TC (
K)
t (nm)
Tc exp(-1/ t)
High sensitivity to disorder
0 10 20 30 40 5010
1
102
103
104
105
106
RS (
)
T (K)
1300800263
95
80
64
292019
10
21
t (nm)
Thickness threshold at 300 nm
bulklike features for t > 300 nm
increase of 0
decrease of RRR
decrease of Tc with decreasing t < 300 nm
Fanlike set of curves
20 nm < t < 300 nm
Rs(1.2K) 0
Rs(0) 0
19 nm < t < 20 nm
horizontal separatrix indicating SIT
t < 19 nm
Rs(T,t)/T < 0 R. Schneider et al., Phys. Rev. Lett. 108, 257003 (2012)
Disorder driven SIT
0 2 4 6 8 10
101
102
RS (
k
)
T (K)
t (nm)
2
10
19
20
29
64
tc
t < tc
t > tc
1 10 100
104
105
8 K 6 K 4 K 2 K
RS (
)
t (nm)
Rs exp(-t)
Rs 1/ tR
c = 19.8 k
tc = 19.5 nm
1 2 4 6 8 10
15
20
25
30
35
- R
S /
t | t C
(
102
/ n
m)
T (K)
z = 2.33 0.03
c
st
Rlog | =
t
1 log T + constz
c
s c 1 z
t tR = R f
T
z dynamical critical exponent
correlation-length exponent
Boson localization
M.P.A. Fisher, Phys. Rev. Lett. 65, 923 (1990)
finite-size scaling of Rs
linear log-log plot provides z
z=1: =7/3 consistent with universality class of quantum percolation
Isotherms Rs(t,T=const.)
crossing point (tc,Rc)
strong exponential decrease of Rs with increasing t
crossover to weak 1/t decrease
R. Schneider et al., Phys. Rev. Lett. 108, 257003 (2012)
Quantum percolation
a-InOx films z = 2.2
D.-H. Lee et al., Phys. Rev. Lett. 70, 4130 (1993)
plateau transitions
in quantum Hall
liquids
M.A. Steiner et al., Phys. Rev. B 77, 212501 (2008)
X. Leng et al., Phys. Rev. Lett. 107, 027001 (2011)
Ultrathin YBa2Cu3O7-x films
Magnetic-field induced SIT
1 2 3 4 5
14.0 T 13.0 T 12.0 T 11.0 T 10.5 T 9.8 T 9.3 T 8.9 T 8.5 T 7.0 T 5.0 T 3.0 T 1.0 T 0.0 T
RS (
k)
T (K)
9
9.5
10
10.5
4 6 8 10 12 14
1.2 K 1.3 K 1.4 K 1.5 K 1.6 K 1.7 K 1.8 K 1.9 K 2.0 K
RS (
k)
B (T)
Bc = 8.92 T
Rc = 10.4 k
9.8
10.0
10.2
10.4
10.6
RS / R
C
B-BC/ T
1/z (T / K
0.43)
B < BC
B > BC
0.01 0.1 1 10
1.0
0.9 Bc = 8.92 T
z = 2.33
Rs(B,T) = R
cf(B-B
c / T
1/z)
t=30 nm
B┴
Scaling of Rs(B,T)
collapse of the branches B<Bc and B>Bc onto a single curve
scaling prediction of the Bose-glass model independently confirmed
Isotherms Rs(B,T=constant)
crossing point (Bc,Rc)
no magnetoresistance peak below 14 T
R. Schneider et al., Phys. Rev. Lett. 108, 257003 (2012)
Different tuning parameters
a - Bi
thickness d tuned SIT
z ≈ 1.2
universality class of classical percolation in 2D
describes SIT in a 2D disordered system
magnetic field B tuned SIT
z ≈ 0.7
universality class of 3D XY model
describes SIT in a 2D ordered system
N. Marković et al., Phys. Rev. Lett. 81, 5217 (1998)
Summary
reproducible synthesis of superconducting b-FeSe thin films by sputtering
excess conductivity, BKT transition, large Gi
- 2D character of superconductivity
- importance of thermal fluctuations
high sensitivity to disorder results in a thickness-driven SIT
SIT also driven with magnetic field
finite-size scaling according to the Bose-glass model
universality class of quantum percolation
Temperature-doping phase diagrams
Fe-based superconductors Cuprate superconductors
Cho (2010)
Magnetism and superconductivity
TC and structural details
Huang (2010)
Bellingeri (2010)
Resistance tails
0 5 10 15 2010
1
102
103
104
Rs (
)
T(K)
800 1300 nm263
95
80
64
29
20
0 4 8 120
1
2
3
4
5
0 4 8 12 16
5
10
15
Rs (k
)
263 nm
95 nm
expt.
theor.
Rs (k
)
T (K)
64 nm
29 nm
T (K)
FeSe / MgO
granular Pb
A. Frydman, Physica C 391,189 (2003)
s s
0
TR T R 0 exp
T
evolution of resistance tails
described by „Inverse Arrhenius law“
L. Merchant et al., Phys. Rev. B 63, 134508 (2001)
typical for granularity
R. Schneider et al., Eur. Phys. J. B 88, 14 (2015)
Granularity and weak links
10-5
10-3
10-1
0
20
40
60
Re
sis
tan
ce
(
)
Current (A)
Voltage (
V)
10-4
100
10-4
10-2
Current (A)
T=4.2 K
20-nm-thick film at the edge of the superconducting phase
individual crystallites
structureless homogeneous matrix
nonlinearities in the V(I) characteristics
current-dependent resistance R=V/I
weak links with a broad distribution of low critical currents
Theory of boson localization
Fisher (1990)
predicts a continuous SIT at T=0 as a result of the interplay of the attractive electron-electron interaction and
the long-range coulomb repulsion
SIT is a Quantum Phase Transition (QPT): Transition at T=0 between competing ground states of a quantum
system when a parameter x in the Hamiltonian crosses a critical value
Value of the critical sheet resistance Rc is universal (independent of the material system and the
microscopic details) and is equal to the quantum resistance Rq of electron pairs.
0 Quantum ordered phase
Bose Metal with Rc = Rq = h / (2e)2
Quantum disordered phase X Xc
Superconductor Insulator
Condensed Cooper pairs, localized vortices Condensed vortices, localized Cooper pairs
Disorder Bound vortex-antivortex pairs Unbound vortex-antivortex pairs
Magnetic Field
Insulating phase
0 50 100 150
Rs (
k
)
T(K)
20
100
400
nm
19
10
2
1
1 2
0s 0
T G A exp
T
1 3
1s 1
TG A exp
T
As 2
B
EG =A exp
k T
10 nm
soft Coulomb gap constant DOS hard gap
strong localization
sequence of exponential Gs (T) dependencies
(a) T<4K Efros-Shklovskii VRH
A.L. Efros, B.I. Shklovskii, J. Phys. C 8, L49 (1975)
(b) 4K<T<50K Mott VRH
N.F. Mott, J. Non-Cryst. Solids 1, 1 (1968)
(c) 50K<T<160K Arrhenius
R. Schneider et al., Eur. Phys. J. B 88, 14 (2015)
Superconducting phase in a magnetic field
1 2 3 4 5 6 7 8 9
U(B) B-2
U(B)= U0ln(B
0/B)
U (
K)
B (T)
0.01
0.1
1 2 3 4 5
Rs (
k
)
T (K)
0 T
1 T
3 T
5 T
7 T8.5 T8.9 T
9
9.5
10
10.5
RS (k
)
1/T (1/K)0.2 0.4 0.6 0.8 1.0
9
9.5
10
10.5
RS= R
0exp(-U(B)/T)
5 4 3 2 1.5 1
0 T
1 T
3 T
5 T
7 T8.5 T8.9 T
T (K)
t=30 nm
t=2 µm
superconducting side of the
B-SIT
P.H. Kes et al.,
Supercond. Sci. Technol.
1, 242 (1989)
U(B)
TR R es 0
comparison with
„bulklike“ FeSe film
A.G. Zaitsev et al.,
J. Phys. Conf. Ser.
507, 012054 (2014)
logarithmic field dependence (U0=0.098 K, B0=8.85 T)
possible creep-type dissipation mechanism
small values of U, low pinning barriers
power-law fit definitely fails
R. Schneider et al., J. Low Temp. Phys. 178, 118 (2015)
Insulating phase in a magnetic field
1 2 3 4 5
Rs (
k
)
T (K)
10.5 T
11 T
12 T
13 T
14 T
10.4
10.5
10.6
10500
10550
10600
10650
Rs (
)
T (K)
1.2 1.4 1.6 1.8 2.0
Rs=R0ln(T0/T) + Rb
10.5 T
11 T
12 T
13 T14 T
10 11 12 13 14
10520
10560
10600
10640
Rs (
)
B(T)
T=1.2 K
t=30 nm
weakly localized Cooper pairs (Bose glass)
vortices in a quantum liquid phase
crossover from ln to exp T - dependence
in line with bosonic description of SIT
R. Schneider et al., J. Low Temp. Phys. 178, 118 (2015)
weak localization
D. Das, S. Doniach, Phys. Rev. B 57, 14440 (1998)