Pressure-Driven Quantum Criticality in An Iron-Selenide Superconductor

Abstract

The discovery of superconductivity of about 30 K in iron selenides with very
large magnetic moments simulates the examination of completing orders. Here we
report a finding of pressure- induced suppression of the superconducting
transition temperature Tc and enhancement of the temperature of the resistance
hump TH through charge transfer between two iron sites with different
occupancies. The activation energy for the electric transport of the
high-temperature resistance is observed to go to zero at a critical pressure of
8.7 GPa, at which superconductivity tends to disappear and the
semiconductor-to-metal transition takes place. Beyond the critical point, the
resistance exhibits a metallic behavior over the whole temperature range
studied. All these features indicate the existence of quantum criticality in
iron-selenide superconductors.

Full text

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arXiv:1101.0092v2 [cond-mat.supr-con] 12 Apr 2011
Pressure-Driven Quantum Criticality in An Iron-Selenide Superconductor
Jing Guo,1, ∗Xiao-Jia Chen,2, ∗Chao Zhang,1Jiangang Guo,1Xiaolong Chen,1Qi Wu,1Dachun
Gu,1Peiwen Gao,1Xi Dai,1Lihong Yang,1Ho-kwang Mao,2Liling Sun,1, †and Zhongxian Zhao1, ‡
1Institute of Physics and Beijing National Laboratory for Condensed Matter Physics,
Chinese Academy of Sciences, Beijing 100190, China
2Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015, USA
(Dated: April 13, 2011)
The discovery of superconductivity of about 30 K in iron selenides with very large magnetic
moments simulates the examination of completing orders. Here we report a finding of pressure-
induced suppression of the superconducting transition temperature Tc and enhancement of the
temperature of the resistance hump TH through charge transfer between two iron sites with different
occupancies. The activation energy for the electric transport of the high-temperature resistance
is observed to go to zero at a critical pressure of 8.7 GPa, at which superconductivity tends to
disappear and the semiconductor-to-metal transition takes place. Beyond the critical point, the
resistance exhibits a metallic behavior over the whole temperature range studied. All these features
indicate the existence of quantum criticality in iron-selenide superconductors.
PACS numbers: 74.70.Xa, 74.25.Dw, 74.62.Fj
The recent discoveryof superconductivityin
K0.8Fe2Se2 [1] with a transition temperature (Tc)
above 30 K has generated considerable interest because
its isostructure KFe2As2 only has a Tc of about 3 K
and the former is more environmentally friendly than
the latter. Since then, superconductivity was also found
in other AxFe2−ySe2 (A =Rb, Cs, or Tl substituted
K, Rb) [2–4]. A very small amount of carriers in these
superconductors were identified to be electrons from the
measurements of optical spectroscopy [5], Hall effect [6],
and angle-resolved photoemission spectroscopy [7–9].
This is quite different from pnictide superconductors
which have both electron and hole pockets at Fermi sur-
face [10]. This difference is important for understanding
the issue regarding whether the pairing symmetry in
both selenide and pnictide superconductors or in FeSe
is the same [11, 12].Superconductivity of such iron
selenides was reported to coexist with antiferromag-
netism with ordering temperatures as high as ∼550 K
[13–17] but large magnetic moments of 3.3 µB for each
Fe atom [13, 17]. Theoretical [18] and experimental [13]
studies on K0.8Fe1.6Se2 reveal that the ground state of
this superconductor is in reality a quasi-two-dimensional
blocked checkerboard antiferromagnetic semiconductor.
The Fe vacancy has been proposed to be a major player
of the observed superconductivity and many interesting
physical properties [17, 19, 20].
A striking feature of these newly discovered supercon-
ductors [1–4, 16, 17, 21] is the appearance of a hump in
the resistance curve showing a transition at temperature
TH from the high-temperature semiconducting to low-
temperature metallic behavior in the temperature range
between Tc and TN. Changing the doping x and/or y
of AxFe2−ySe2can affect significantly TH [16, 21], while
leaving both Tcand TN almost unchanged [16, 17]. Al-
though the Fe vacancy was also suggested to account for
the TH shift upon dopant [16, 21], a complete under-
standing of this interesting feature and the regularities of
changes of Tcand THhas not been achieved. The system-
atic suppression of Tcin K0.8Fe2−xCoxSe2 was reported
[22] with the substitution of Co into Fe site. The sub-
stituted magnetic impurities could also introduce cation
distortion, which brings about difficulties in distinguish-
ing the different effects on superconductivity. Compared
with chemical substitution, pressure is a clean parameter
in tuning the lattice and electronic properties. Investiga-
tions of the pressure effects on Tcand TH may shed an
important insight on the underlying mechanism of super-
conductivity in iron selenides.
In this Letter, we report an experimental discovery
of pressure-driven quantum criticality in newly discov-
ered iron-selenide superconductor K0.8Fe1.7Se2 through
resistance and structure measurements. We find that su-
perconductivity is gradually suppressed with the applied
pressure and eventually disappears at a critical point
around 8.7 GPa at which the activation energy for the
electronic transport of the high-temperature resistance
approaches to zero and a semiconductor-metal transition
is achieved. The presence of such quantum phase tran-
sitions classifies iron-selenide superconductors into the
quantum matter with quantum criticality, although they
possess very large magnetic moments.
High-pressure electric resistance measurements on
K0.8Fe1.7Se2 single crystals detailed previously [1] were
carried out in a diamond-anvil-cell made from Be-Cu al-
loy in a house built refrigerator. Diamond anvils of 600
and 300 µm flats were used with 300 µm and 100 µm di-
ameter sample holes in Re gaskets, respectively, for two
runs. Insulation from the rhenium gasket was achieved
by a thin layered mixture of c-BN (cubic boron nitride)
powder and epoxy. The crystal was placed on the top
anvil and then pressed into the insulating gasket hole

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2
0
50
100
150
200
250
300
0
5
10
15
Resistance (Ω)
0.5 GPa
0.8 GPa
1.2 GPa
1.7 GPa
2.6 GPa
3.3 GPa
4.1 GPa
5.0 GPa
6.1 GPa
6.6 GPa
7.4 GPa
8.0 GPa
8.5 GPa
9.2 GPa
0 1020 30 40
50
Temperature (K)
0.0
0.5
1.0
1.5
2.0
2.5
Resistance (Ω)
0.5
0.8
1.2
1.7
2.6
3.3
4.1
5.0
6.1
6.6
7.4
8.0
8.5
9.2
P (GPa)
(a)
(b)
TH
TC
FIG. 1: (color online). Temperature dependence of the elec-
trical resistance of a K0.8Fe1.7Se2 single crystal measured at
different pressures up to 9.2 GPa and in the temperature
range of 4 and 300 K (a) and of 4 and 50 K (b). The arrow
in (a) shows a transition temperature TH of the resistance in
a hump shape from its high-temperature semiconducting to
low-temperature metallic behavior. The arrow in (b) denotes
the superconducting transition temperature Tc.
with leads.
medium. The pressure was determined by the ruby fluo-
rescence method [23]. The standard four-probe technique
was adopted in measurements. Electric resistance mea-
surements at ambient pressure but with magnetic fields
were performed on a Quantum Design Physical Property
Measurement System. Powder x-ray diffraction was used
to obtain the structural information by using a MAC
SCIENCE-MXT18AHF diffractometer with Cu Kα ra-
diation based on the powders from the cleaved pieces of
crystals. Rietveld refinements were performed by using
the FULLPROF package [24].
Figure 1(a) shows the temperature dependence of the
in-plane resistance of a K0.8Fe1.7Se2single crystal mea-
sured at various pressures up to 10 GPa. The super-
conducting transition occurs at 32.5 K and reaches zero
resistance at 30.6 K at ambient pressure. A remarkable
feature of this superconductor is that its resistance ex-
hibits a large hump showing a transition at TH. This
NaCl powders were employed as pressure
024
6
8 10
Pressure (GPa)
0
10
20
30
40
TC (K)
K0.8Fe1.7Se2
FIG. 2: (color online). Pressure dependence of the super-
conducting transition temperature Tc of a K0.8Fe1.7Se2 single
crystal.
hump phenomenon is absent in FeAs-based superconduc-
tors, for which their resistance behavior is metallic. Inter-
estingly, the maximum resistance at TH is dramatically
reduced when pressure is applied. Meanwhile. the Tc
is suppressed with pressure and disappeared at 9.2 GPa
(Fig. 1(b)). Releasing pressure from 9.2 GPa, both the
Tcand the resistive hump go back together. These follow
that the intrinsic factors control the resistance hump and
superconductivity together.
Figure 2 shows the pressure dependence of Tc of
K0.8Fe1.7Se2. The Tc exhibits a systematic reduction
with pressure till approaching zero at 9.2 GPa. Con-
sidering the fact that pressure enhances Tcin a FeSe su-
perconductor [25], our observed suppression and disap-
pearance of superconductivity in K0.8Fe1.7Se2with pres-
sure suggest that the driving force of superconductivity
in these two similar systems are probably different. It
was noticed that superconductivity can be suppressed in
FeAs-based superconductors through some modification
of cation substitution or pressure. The suppression of the
superconductivity can be correlated to the modification
of the Fermi surface, resulting in the collapse of the nest-
ing [10]. However, for K0.8Fe2−ySe2, the Fermi surface
nesting is absent [7, 8]. Therefore, the mechanism for the
suppression of superconductivity in iron selenides may be
different from the case of the FeSe superconductors.
The structural determination is used to understand the
origin of the resistance hump at TH. Figure 3(a) shows
the x-ray diffraction patterns at selected temperatures
down to 60 K and at ambient pressure. The refined data
demonstrate that the sample has a tetragonal ThCr2Si2-
type structure with space group I4/m over the temper-
ature range crossing TH. No structural transition can
be detected. As expected, the lattice parameters a and
c decrease with decreasing temperature (Figs. 3(b) and
3(c)). Our data offer clear evidence in supporting that

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3
8.62
14.10
8.63
8.64
8.65
8.66
a (Å)
0 2040
60
80
2Θ (Degree)
0 100200300
Temperature (K)
13.90
13.95
14.00
14.05
c (Å)
60 K
90 K
150 K
250 K
298 K
Intensity (Arb. units)
K0.8Fe1.7Se2
(b)
(c)
(a)
FIG. 3: (color online). (a) X-ray diffraction patterns of a
K0.8Fe1.7Se2 single crystal collected at different temperatures
and ambient pressure. (b) and (c) The refined lattice param-
eters a and c as a function of temperature.
the hump is irrelevant to any structural transition.
Figure 4 shows the temperature dependence of resis-
tance of K0.8Fe1.7Se2at magnetic fields of 0, 3, and 7 T .
As seen, the TH keeps nearly unchanged when the mag-
netic field is applied. This indicates that the resistance
hump is probably not controlled by the antiferromagnetic
order. The resistance at THis enhanced with the applied
magnetic field, yielding a positive magnetoresistance. Al-
though the carrier scattering mechanism is unknown, the
iron vacancy ordering must be the competitive player for
this hump feature. It has been shown [21] that doping
more Fe in KxFe2−ySe2can significantly enhance THbut
leaving Tc unchanged. Neutron diffraction studies [17]
revealed that the Fe vacancies form a
structure in each Fe plane and the magnetic moments of
the four irons in each√5 ×√5 unit cell align ferromag-
netically along the c axis, thus forming a checkerboard
antiferromagnetic shape. The magnetic patterns are al-
most independent on the spin orientation of the vacant
Fe ions in the refinements, implying their minor effect on
antiferromagnetic order. The enhanced THwith pressure
is thus a result of the reduced vacancy ordering of the
partially occupied Fe ions. Meanwhile, pressure-induced
increase in THcan also be understood by the delocaliza-
tion of electrons from Fe ions.
Now that the pressure-induced increase in TH might
mainly result from the increased occupancy of the va-
cant Fe site, one may wonder where this filled charge
comes from. Since iron valence is found to be +2 [17],
and theoretical calculations reveal an insulating behavior
of K0.8Fe1.6Se2with an energy gap of 0.6 eV [18], indi-
cating that each Fe is in spin 2 state. To maintain the
constant Fe valence, the increased occupancy of the va-
cant Fe site must come from the reduced occupancies of
the fully occupied Fe sites, i.e., pressure-induced charge
√5 ×√5 super-
0 100200300
Temperature (K)
0
0.5
1
1.5
2
2.5
3
Resistance (Ω)
0 T
3 T
7 T
26
28303234
T (K)
0
0.5
1
R/R35 K
0 T
3 T
7 T
H||c
K0.8Fe1.7Se2
FIG. 4: (color online). Temperature dependence of the re-
sistance of a K0.8Fe1.7Se2 single crystal with magnetic fields
applied along the c axis of 0, 3, and 7 T, respectively. The
inset is an extended view with normalized resistance at 35 K
around the superconducting transition.
transfer between the two different Fe sites with differ-
ent occupancies. It has been established [17] that the
major difference between superconductor and insulator
is that of the Fe occupancies. The Fe(1) site of the su-
perconducting sample is almost fully occupied, while it
is partially occupied in an insulating sample. However,
vacant Fe(2) site of the insulator has more occupancies
than those of the superconducting sample. The reduction
of Tcand enhancement of TH with the applied pressure
are thus suggested to originate from the same mechanism
- pressure-induced charge transfer from Fe(1) to Fe(2).
Figure 5(a) shows the pressure dependence of THand
a kink (TK) on the high-temperature side in the metal-
lic state. The metallic characteristic of the resistance at
10.2 GPa can be observed in the inset of Fig. 5. The
phase transformation from the low-pressure semiconduc-
tor to the high-pressure metal occurs at around 9 GPa.
This is the pressure at which superconductivity tends to
zero as shown in Fig. 2. The exact transition pressure is
estimated from the pressure dependence of the activation
energy for the electric transport in the high-temperature
semiconducting state (Fig. 5(b)). The extension of the
fitting curve yields a critical pressure of 8.7 GPa. Here
the activation energy is obtained by fitting the temper-
ature dependence of resistance in terms of an Arrhenius
equation.
The observations of the disappearance of superconduc-
tivity and the absence of the transition from the high-
temperature semiconductor to low-temperature metal
together with the phase transformation from the low-
pressure semiconductor to high-pressure metal indicate
that the critical pressure of 8.7 GPa is in fact a quantum
critical point.Amongst strongly correlated electronic
materials, the magnetic order coexisting with supercon-

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4
100
30
150
200
250
TH,K (K)
024
6
8 10
Pressure (GPa)
0
10
20
EA (meV)
0100200300
T (K)
0.3
0.6
0.9
R (Ω)
10.2 GPa
(a)
(b)
M
S
M
M
TK
FIG. 5: (color online). Pressure dependence of (a) TH,K in the
hump shape or kink of resistance and (b) the activation energy
of the electric transport of the high-temperature resistivity of
a K0.8Fe1.7Se2 single crystal. The line in (b) is the linear
fitting to the data points. Inset: temperature dependence of
the resistance at 10.2 GPa. The vertical dashed line denotes
the phase boundary.
ductivity has either a small magnetic moment or low or-
dering temperature [26, 27]. The very large antiferro-
magnetic orders and high ordering temperatures [13, 16]
indicate that the quantum criticality in this iron-selenide-
based superconductor is unique. The coexistence of the
superconductivity and antiferromagnetic ordering in iron
selenides [13–17] are different to those in ReOFeAs and
MFe2As2[10, 28], whose superconductivity emerges when
the antiferromagnetic ordering is suppressed. However,
superconducting state coexisting with a phase-separated
static magnetic order was also observed in MFe2As2sys-
tems [29]. The issue regarding whether the antiferromag-
netism and superconductivity in K1−xFe2−ySe2 could
also come from two different phases remains unsettled.
This calls for further investigations of high-pressure mag-
netic properties.
In summary, we have reported a finding of pressure-
driven quantum criticality in a newly discovered super-
conductor K0.8Fe1.7Se2through a thorough and detailed
investigation of electric transport and structural prop-
erties. Approaching the quantum critical point around
8.7 GPa, superconductivity tends to disappear and ac-
tivation energy for the electric transport of the high-
temperature resistance goes to zero. Beyond the point,
the resistance shows a metallic behavior over the whole
temperature range studied. The observed reduction of
the superconducting transition temperature and the en-
hancement of the resistance hump temperature are sug-
gested to result from pressure-induced charge transfer be-
tween two iron sites with different occupancies.
We thank the T. Xiang, Z. Fang and G. M. Zhang
for valuable discussions. This work was supported by
the NSCF (10874230, 10874046, and 11074294), 973
projects (2010CB923000 and 2011CBA00109), and Chi-
nese Academy of Sciences. Work done in the U.S. was
supported by the DOE under Grant No. de-sc0001057.
∗Both the first authors contributed equally to this work.
†Electronic address: llsun@aphy.iphy.ac.cn
‡Electronic address: zhxzhao@aphy.iphy.ac.cn
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