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)