The Specific Heat of Co-doped BaFe2As2

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Nov 15, 2013 (3 years and 7 months ago)

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The
Low
-
Temperature
Specific
Heat of
Chalcogen
-
based
FeSe


J.
-
Y. Lin
,
1

Y
. S. Hsieh,
1

D. Chareev,
2

A. N. Vasiliev,
3

Y. Parsons,
4

and H
. D.
Yang
4


1

Institute of Physics/National
Chiao

Tung University,
Hsinchu

30010,
Taiwan

2
Institute of Experimental Mineralogy,
Cherngolovka
, Moscow Region
142432, Russia

3
Department of Low temperature Physics, Moscow State University,
Moscow 119991, Russia

4
Department of Physics, University of California, Santa
Babara
, CA 93106,
USA

4
Department
of Physics, National Sun
Yat
-
sen

University, Kaohsiung 804,
Taiwan


Contents


Introduction to Fe
-
based superconductors



Specific heat as a probe of
the
superconducting order
parameter



Experiments and results



Conclusions

A brief introduction to iron
-
based
superconductors

Structure

80
90
100
110
0
50
100
150


T
c
(K)
Year of discovery
70

Nb
3
Ge


MgB
2

Metallic alloys

LSCO

YBCO

TI
-

cuprate

Hg
-

cuprate

Cuprates

e
-
doped LaOFeP

e
-
doped LaOFeAs

e
-
doped SmOFeAs

Fe
-
based

superconductors

The Race to Beat Cuprates?

The crusade of Room Temperature superconductors?




The

order

parameter

in

Fe
-
based

superconductors

remains

elusive
.

To

get

insight

into

the

pairing

mechanism,

it

is

crucial

to

determine

the

gap

structure

in

the

superconductors

like

FeSe

or

pnictides
.



Though

with

lower

T
c
,

FeSe

has

the

simplest

structure
,

and

this

very

simplicity

could

provide

the

most

appropriate

venue

of

understanding

both

the

order

parameter

and

the

superconducting

mechanism

of

Fe
-
base

superconductors
.



Motivation

Johnston, 2010

(
Subedi

et al., 2008
)

Specific heat as the probe


Revealing the superconducting order
parameter from the specific heat



Information from
k
-
space integration.
Non phase
-
sensitive.



Surprisingly selective if well
excuted

FeSe

single crystals

FeSe

single crystal


0
5
10
15
0
500
1000
1500
(a)
FeSe
H
=0


C
(mJ/mol K)
T
(K)
FeSe

single crystal


0
5
10
15
0
20
40
60
80
100


C
/
T
(mJ/mol K
2
)
T
(K)
FeSe
(a)

0
20
40
60
80
100
0
10
20
30
40
50
60

H
=0

H
=0.5 T

H
=1 T

H
=2 T

H
=3 T

H
=5 T

H
=7 T

H
=9 T


C
/
T
(mJ/mol K
2
)
T
2
(K
2
)
FeSe
H
//
c

0
20
40
60
80
100
0
10
20
30
40
50
60

H
=0

H
=0.5 T

H
=1 T

H
=2 T

H
=3 T

H
=5 T

H
=7 T

H
=9 T


C
/
T
(mJ/mol K
2
)
T
2
(K
2
)
FeSe
C
n
=5.73
T
+0.4208
T
3

n
=5.73
mJ
/mol K
2


=210 K

nearly identical to the results of
polycrystals

from
T.
M. McQueen et al. (2009)


0
20
40
60
80
100
0
10
20
30
40
50
60

H
=0

H
=0.5 T

H
=1 T

H
=2 T

H
=3 T

H
=5 T

H
=7 T

H
=9 T


C
/
T
(mJ/mol K
2
)
T
2
(K
2
)
FeSe
C
n
=5.73
T
+0.4208
T
3
(b)
0
2
4
6
8
10
-6
-4
-2
0
2
4
6
8
10



C
(=
C
-
C
n
)/
T
(mJ/mol K
2
)
T
(K)
0
2
4
6
8
10
-15
-10
-5
0

S


(
mJ/mol K
2
)
T
(K)

C
/

n
T
c
=1.65

Weak limit BCS isotropic
s
-
wave:

C
/

n
T
c
=1.43


C. P. Sun et al. (2004)


=

0
cos2


0
2
4
6
8
10
12
14
16
0.0
0.5
1.0
0
2
4
6
8
10
12
14
16
0.0
0.5
1.0


d
-wave
2

0
/k
T
c
=5.51



(a)
0.0
0.2
0.4
0.6
0.8
-2
-1
0
1
2
DF

(
mJ/mol K
2
)
T
/T
c
(b)


extended
s
-wave
2

e
/k
T
c
=3.59



=0.64


0.0
0.2
0.4
0.6
0.8
-2
-1
0
1
2
DF

(
mJ/mol K
2
)
T
/T
c
(c)

s
-wave
2

L
/k
T
c
=4.43

71%

s
-wave
2

S
/k
T
c
=1.28 29%


C
es
/T
(
mJ/mol K
2
)
T/T
c
0.0
0.2
0.4
0.6
0.8
-2
-1
0
1
2
DF


(
mJ/mol K
2
)
T
/T
c
(d)



s
-wave
2

0
/k
T
c
=3.82 33%
E.
s
-wave
2

e
/k
T
c
=3.22

67%

=0.78


0.0
0.2
0.4
0.6
0.8
-2
-1
0
1
2
DF

(
mJ/mol K
2
)
T
/T
c

=

e
(1+

cos2

)

Nicholson et al. (2011)

0.00
0.05
0.10
0.15
0.20
0.25
0.0
0.5
1.0
1.5
2.0

d
-wave
s
-wave + extended
s
-wave

s
-wave +
s
-wave


C
es
/T
(
mJ/mol K
2
)
T/T
c
FeSe
0
2
4
6
8
10
0
2
4
6

H
//
c

H
//
ab
C
=

T
+

T

2
+

T

3



(
H
) (mJ/mol K
2
)
H
(T)
FeSe

n
H
c2
=13.1 T?


/

n
=0~0.69

Quasi
-
linear

(
H
)

in high H was also observed in 122. (J. S. Kim et al. 2010)

0
1
2
0
5

H
=0

H
=0.5 T

H
=1 T

H
=2 T

H
=3 T

H
=5 T

H
=7 T

H
=9 T


C
/
T
(mJ/mol K
2
)
T
(K)
FeSe
H
//
c
0
2
4
6
8
10
0
2
4
6

H
//
c

H
//
ab



(
H
) (mJ/mol K
2
)
H
(T)
FeSe

n
(a)

n

(
mJ
/mo
l K
2
)

Ө
D

(K)


C
/

n
T
c



H
c2
,
H
//c

(T)

H
c2
,
H

c

(T)

5.73

210

1.65

1.55

13.1

27.9

Bang, 2010

Anisotropic H
c2

6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
0
5
10
0
2
4
6
8
0
5
10
15
20


H
(T)
T
(K)
FeSe

H
//
c

H
//
ab


H
(T)
T
(K)
(b)
STM on
FeSe

C. L. Song et al., 2011

Comparison between
FeSe

and Fe(
Se,Te
)

FeSe

Song et al., 2011

Fe(
Se,Te
)

Hanaguri

et al., 2010

The fitting parameters

Conclusions for
FeSe


Existence

of

low
-
energy

excitations

more

than

in

an

isotropic

s
-
wave
.



Gap

anisotropy
.

S

+

exntended

s
.

Probably

No

accidental

nodes
.



Existence

of

an

isotropic

s
-
wave
.



H
c
2
,
H//c

13
.
1

T

and

H
c
2
,
H

c

27
.
9

T
.

The

anisotropy

in

H
c
2

is

about

2
.
1
.



0
2
4
6
8
10
0
2
4
6

H
//
c



H

0.55
±
0.03

H
//
ab



H

0.60
±
0.05
C
=

T
+

T

2
+

T

3



(
H
) (mJ/mol K
2
)
H
(T)
FeSe

n
0
5
10
15
20
25
30
35
-30
-20
-10
0
10
20
30


(
C
(x=0.08)-

n
T
-
f
s
*C
lat
) /
T

n
=27.02

C/

n
T
c
=1.13
f
s
=
1.0345
C
e
/T
(mJ/mol K
2
)
T
(K)
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
-180
-160
-140
-120
-100
-80
-60
-40
-20
0



S

T
(K)
Fig. 4 The specific heat of MgB
2
. The dashed lines are determined by
the conservation of entropy around the anomaly and used to
estimate
Δ
C/
T
c
. Inset: Entropy difference
Δ
S
by integration of
Δ
C/T
.

0.0
0.5
1.0
1.5
-30
-20
-10
0
10
20
30
40
50
60


d-wave
2

S
/k
B
T
c
=2.70
55%
s-wave
2

L
/k
B
T
c
=4.18
45%
C
e
/T
(mJ/mol K
2
)
T/T
c
0
2
4
6
8
10
12
14
16
-3.0x10
-4
-2.5x10
-4
-2.0x10
-4
-1.5x10
-4
-1.0x10
-4
-5.0x10
-5
0.0
5.0x10
-5


magnetic moment (emu)
Temperature (K)
H
=20 Oe
ZFC
FC