Electronic structure of FeSe monolayer superconductors
We review a variety of theoretical and experimental results concerning electronic band structure of superconducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems AxFe₂Se₂–xSx and [Li₁–xFexOH]FeSe as well as the single FeSe layer films on SrTiO₃ sub...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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nasplib_isofts_kiev_ua-123456789-1293102025-02-23T18:02:41Z Electronic structure of FeSe monolayer superconductors Nekrasov, I.A. Pavlov, N.S. Sadovskii, M.V. Slobodchikov, A.A. К 30-летию открытия высокотемпературной сверхпроводимости We review a variety of theoretical and experimental results concerning electronic band structure of superconducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems AxFe₂Se₂–xSx and [Li₁–xFexOH]FeSe as well as the single FeSe layer films on SrTiO₃ substrate. We present the results of detailed first principle electronic band structure calculations for these systems together with comparison with some experimental ARPES data. The electronic structure of these systems is rather different from that of typical FeAs superconductors, which is quite significant for possible microscopic mechanism of superconductivity. This is reflected in the absence of hole pockets of the Fermi surface at T-point in Brillouin zone, so that there are no “nesting” properties of different Fermi surface pockets. LDA + DMFT calculations show that correlation effects on Fe-3d states in the single FeSe layer are not that strong as in most of FeAs systems. As a result, at present there is no theoretical understanding of the formation of rather “shallow” electronic bands at M-points. LDA calculations show that the main difference in electronic structure of FeSe monolayer on SrTiO ₃ substrate from isolated FeSe layer is the presence of the band of O-2p surface states of TiO₂ layer on the Fermi level together with Fe-3d states, which may be important for understanding the enhanced Tc values in this system. We briefly discuss the implications of our results for microscopic models of superconductivity. Calculations of electronic structure of FeSe systems were performed under the FASO state contract No. 0389-2014-0001 and partially supported by RFBR grant 14-02-00065. NSP and AAS work was also supported by the President of Russia grant for young scientists No. Mk-5957.2016.2. 2016 Article Electronic structure of FeSe monolayer superconductors / I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, A.A. Slobodchikov // Физика низких температур. — 2016. — Т. 42, № 10. — С. 1137-1147. — Бібліогр.: 53 назв. — англ. 0132-6414 PACS: 74.20.–z, 74.20.Rp, 74.25.Jb, 74.70.–b https://nasplib.isofts.kiev.ua/handle/123456789/129310 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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К 30-летию открытия высокотемпературной сверхпроводимости К 30-летию открытия высокотемпературной сверхпроводимости |
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К 30-летию открытия высокотемпературной сверхпроводимости К 30-летию открытия высокотемпературной сверхпроводимости Nekrasov, I.A. Pavlov, N.S. Sadovskii, M.V. Slobodchikov, A.A. Electronic structure of FeSe monolayer superconductors Физика низких температур |
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We review a variety of theoretical and experimental results concerning electronic band structure of superconducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems AxFe₂Se₂–xSx and [Li₁–xFexOH]FeSe as well as the single FeSe layer films on SrTiO₃ substrate. We present the results of detailed first principle electronic band structure calculations for these systems together with comparison with some experimental ARPES data. The electronic structure of these systems is rather different from that of typical FeAs superconductors, which is quite significant for possible microscopic mechanism of superconductivity. This is reflected in the absence of hole pockets of the Fermi surface at T-point in Brillouin zone, so that there are no “nesting” properties of different Fermi surface pockets. LDA + DMFT calculations show that correlation effects on Fe-3d states in the single FeSe layer are not that strong as in most of FeAs systems. As a result, at present there is no theoretical understanding of the formation of rather “shallow” electronic bands at M-points. LDA calculations show that the main difference in electronic structure of FeSe monolayer on SrTiO ₃ substrate from isolated FeSe layer is the presence of the band of O-2p surface states of TiO₂ layer on the Fermi level together with Fe-3d states, which may be important for understanding the enhanced Tc values in this system. We briefly discuss the implications of our results for microscopic models of superconductivity. |
| format |
Article |
| author |
Nekrasov, I.A. Pavlov, N.S. Sadovskii, M.V. Slobodchikov, A.A. |
| author_facet |
Nekrasov, I.A. Pavlov, N.S. Sadovskii, M.V. Slobodchikov, A.A. |
| author_sort |
Nekrasov, I.A. |
| title |
Electronic structure of FeSe monolayer superconductors |
| title_short |
Electronic structure of FeSe monolayer superconductors |
| title_full |
Electronic structure of FeSe monolayer superconductors |
| title_fullStr |
Electronic structure of FeSe monolayer superconductors |
| title_full_unstemmed |
Electronic structure of FeSe monolayer superconductors |
| title_sort |
electronic structure of fese monolayer superconductors |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2016 |
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К 30-летию открытия высокотемпературной сверхпроводимости |
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https://nasplib.isofts.kiev.ua/handle/123456789/129310 |
| citation_txt |
Electronic structure of FeSe monolayer superconductors / I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, A.A. Slobodchikov // Физика низких температур. — 2016. — Т. 42, № 10. — С. 1137-1147. — Бібліогр.: 53 назв. — англ. |
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Физика низких температур |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10, pp. 1137–1147
Electronic structure of FeSe monolayer superconductors
I.A. Nekrasov1, N.S. Pavlov1, M.V. Sadovskii1,2, and A.A. Slobodchikov1
1Institute for Electrophysics, Russian Academy of Sciences, Ural Branch
106 Amundsen str., Ekaterinburg 620016, Russia
E-mail: nekrasov@iep.uran.ru
2M.N. Mikheev Institute for Metal Physics, Russian Academy of Sciences, Ural Branch
18 S. Kovalevsky str., Ekaterinburg 620290, Russia
Received April 25, 2016, published online August 29, 2016
We review a variety of theoretical and experimental results concerning electronic band structure of supercon-
ducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems
AxFe2Se2–xSx and [Li1–xFexOH]FeSe as well as the single FeSe layer films on SrTiO3 substrate. We present the
results of detailed first principle electronic band structure calculations for these systems together with compari-
son with some experimental ARPES data. The electronic structure of these systems is rather different from that
of typical FeAs superconductors, which is quite significant for possible microscopic mechanism of superconduc-
tivity. This is reflected in the absence of hole pockets of the Fermi surface at Γ-point in Brillouin zone, so that
there are no “nesting” properties of different Fermi surface pockets. LDA+DMFT calculations show that correla-
tion effects on Fe-3d states in the single FeSe layer are not that strong as in most of FeAs systems. As a result, at
present there is no theoretical understanding of the formation of rather “shallow” electronic bands at M-points.
LDA calculations show that the main difference in electronic structure of FeSe monolayer on SrTiO3 substrate
from isolated FeSe layer is the presence of the band of O-2p surface states of TiO2 layer on the Fermi level to-
gether with Fe-3d states, which may be important for understanding the enhanced Tc values in this system. We
briefly discuss the implications of our results for microscopic models of superconductivity.
PACS: 74.20.–z Theories and models of superconducting state;
74.20.Rp Pairing symmetries (other than s-wave);
74.25.Jb Electronic structure (photoemission, etc.);
74.70.–b Superconducting materials other than cuprates.
Keywords: high-Tc superconductivity, FeSe-based superconductors, ARPES experiments.
1. Introduction
The discovery of a new class of superconductors based on
iron pnictides has opened up the new prospects for the study
of high-temperature superconductivity (cf. reviews [1–6]).
The nature of superconductivity in these novel materials and
other physical properties significantly differs from those of
high- cT cuprates, though they still have many common fea-
tures, which gives hope for a better understanding of the
problem of high-temperature superconductivity in general.
The discovery of superconductivity in iron pnictides was
soon followed by its discovery in iron chalcogenide FeSe.
A lot of attention was attracted to this system because of its
simplicity, though its superconducting characteristics (un-
der normal conditions) were quite modest ( 8 K)cT and
its electronic structure was quite similar to that of iron
pnictides (cf. review [7]).
The situation with iron chalcogenides fundamentally
changed with the appearance of intercalated FeSe-based
systems with the value of cT 30–40 K, which immedi-
ately attracted attention due to their unusual electronic
structure [8,9]. Currently quite the number of such com-
pounds is known. The first systems of this kind were
AxFe2–ySe2 (A = K, Rb, Cs) with the value of cT 30 K
[10,11]. It is generally believed that superconductivity in
this system appears in an ideal 122-type structure. Howev-
er samples studied so far always have been multiphase,
consisting of a mixture of mesoscopic superconducting and
insulating (antiferromagnetic) structures such as K2Fe4Se5,
which complicates the studies of this system.
A substantial further increase of cT up to 45 K has been
achieved by intercalation of FeSe layers with rather large
molecules in compounds such as Lix(C2H8N2)Fe2–ySe2
[12] and Lix(NH2)y(NH3)1–yFe2Se2 [13]. The growth of cT
© I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, and A.A. Slobodchikov, 2016
I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, and A.A. Slobodchikov
in these systems might be associated with increase of the
distance between the FeSe layers from 5.5 Å to 7 Å in
AxFe2–ySe2 and 8–11 Å in the large molecules intercalated
systems, i.e., with the growth of the two-dimensional char-
acter of the materials. Most recently the active studies has
started of [Li1–xFexOH]FeSe system with the value of
43 KcT [38,39], where a good enough single-phase
samples and single crystals were obtained.
A significant breakthrough in the study of iron-based
superconductors happened with the observation of a record
high cT in epitaxial films of single FeSe monolayer on a
substrate of SrTiO3 (STO) [14]. These films were grown as
described in Ref. 14 and most of the works to follow on the
001 plane of the STO. The tunnel experiments reported in
Ref. 14 produced the record values of the energy gap,
while the resistivity measurements gave the temperature of
the beginning of superconducting transition substantially
higher than 50 K. It should be noted that the films under
study are very unstable on the air. Thus in most works the
resistive transitions were mainly studied on films covered
with amorphous Si or several FeTe layers. It significantly
reduces the observed values of cT . Unique measurements
of FeSe films on STO, done in Ref. 15 in situ, gave the
record value of cT > 100 K. So far, these results have not
been confirmed by the other authors. However ARPES
measurements of the temperature dependence of the super-
conducting gap in such films, now confidently demonstrate
value of cT in the range of 65–75 K.
Films consisting of several FeSe layers produce the
values of cT significantly lower than those for the single-
layer films [16]. Recently monolayer FeSe film on 110 STO
plane [17] covered with several FeTe layers was grown.
Resistivity measurements on these films (including meas-
urements of the upper critical magnetic field 2cH ) gave
value of cT 30 K. At the same time, the FeSe film,
grown on BaTiO3 (BTO) substrate, doped with Nb (with
even larger than in STO values of the lattice constant
3.99 Å ), showed in the ARPES measurements the value
of cT 70 K [18]. In a recent paper [19] it was reported
the observation of quite high values of the superconducting
gap in FeSe (from tunnelling spectroscopy) for FeSe mo-
nolayers grown on 001 plane of TiO2 (anatase), which in
its turn was grown on the 001 plane of SrTiO3. The lattice
constant of anatase is very close to the lattice constant of
bulk FeSe, so FeSe film remains essentially unstretched.
Single-layer FeSe films were also grown on the graphe-
ne substrate, but the value of cT was of the order of 8–10 K
similar to bulk FeSe [20]. That emphasizes the role of the
unique properties of substrates such as Sr(Ba)TiO3, which
can play determining role in the significant increase of cT .
More information about the experiments on single-layer
FeSe films can be found in the recently published review
of Ref. 21. Below we shall concentrate on the present day
understanding of the electronic structure of FeSe monolay-
er systems.
2. Crystal structures of iron-based superconductors
Bulk FeSe system has the simplest crystal structure
among other iron high- cT superconductors. A unit cell is a
tetrahedron with Fe ion in the center and Se in its vertices.
The symmetry group is P4/nmm with lattice constants
= 3.765a Å (Fe–Fe distance) and = 5.518c Å (interlayer
distance), with the height of the Se ions over the Fe planes
Se = 0.2343z Å [22].
Figure 1 schematically shows a simple crystal structure
of iron-based superconductors [1–7]. The common element
for all of them is the presence of the FeAs or FeSe plane
(layer), where Fe ions form a simple square lattice. The
pnictogen (Pn–As) or chalcogen (Ch–Se) ions are located
at the centers of the squares above and below Fe plane in a
staggered order. The 3d states of Fe in FePn plane (Ch)
play a decisive role in the formation of the electronic prop-
erties of these systems, including superconductivity. In this
sense, these layers are quite similar to the CuO2 planes in
cuprates (copper oxides). Also these systems can be con-
sidered, to a first approximation, as a quasi-two dimen-
sional.
Note that all of the FeAs crystal structures shown in
Fig. 1 are ion-covalent crystals. Chemical formula, say for
a typical system 122, can be written for example as
Ba+2(Fe+2)2(As–3)2. Charged FeAs layers are held by Cou-
lomb forces from the surrounding ions. In the bulk FeSe
electrically neutral FeSe layers are held by much weaker
van der Waals interactions. This makes the system suitable
for intercalation of various atoms and molecules that can
be fairly easy introduced between the layers of FeSe. Che-
mistry of intercalation processes for iron chalcogenide super-
conductors is discussed in detail in a recent review [23]. The
crystal structure of KxFe2Se2 and [Li1–xFexOH]FeSe sys-
tems are shown in Fig. 2(b).
Fig. 1. (Color online) Typical crystal structures of iron-based su-
perconductors.
1138 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10
Electronic structure of FeSe monolayer superconductors
The structure of the FeSe monolayer film on STO is
shown in Fig. 3. It can be seen that the FeSe layer is direct-
ly adjacent to the surface TiO2 layer of STO. Note that the
lattice constant within FeSe layer in a bulk samples is
equal to 3.77 Å, while STO has substantially greater lattice
constant equal to 3.905 Å. Thus the single-layer FeSe film
should be noticeably stretched, compared with the bulk
FeSe. However this tension quickly disappears as the num-
ber of subsequent layers grows.
3. Electronic structure of iron–selenium systems
Electronic spectrum of iron pnictides now is well un-
derstood, both by theoretical calculations based on the mo-
dern band structure theory and ARPES experiments [1–6].
Almost all physical effects of interest to superconductivity
are determined by electronic states of FeAs plane (layer),
shown in Fig. 1(b). The spectrum of carriers in the vicinity
of the Fermi level ± 0.5 eV, where superconductivity is
formed, practically have only Fe-3d character. Thus the
Fermi level is crossed by four or five bands (two or three
hole and two electronic ones), forming a typical semime-
tallic dispersions.
In this rather narrow energy interval around the Fermi
level the dispersions can be considered as parabolic [4,24].
LDA+DMFT calculations [25,26] show that the role of
electronic correlations in iron pnictides, unlike the cup-
rates, is relatively insignificant. It is reduced to a noticea-
ble renormalization of the effective masses of the electron
and hole dispersions, as well as to general “compression”
(reduction) of the bandwidth.
The presence of the electron and hole Fermi surfaces of
similar size, satisfying (approximately!) the “nesting” con-
dition plays a very important role in the theories of super-
conducting pairing in iron arsenides based on (antiferro-
magnetic) spin fluctuations [4]. We shall see below that the
electronic spectrum and Fermi surfaces in the Fe chalcoge-
nides are very different from this qualitative picture of Fe
Fig. 2. (Color online) (a) Ideal (x = 1) crystal structure of 122-type
of KxFe2Se2, (b) Ideal (x = 0) crystal structure of [Li1–xFexOH]FeSe
compound.
Fig. 4. (Color online) (a) LDA bands of Ba122 near the Fermi level (E = 0) [29], (b) LDA bands of KxFe2Se2 (black lines) and
CsxFe2Se2 (blue lines). Additional horizontal lines correspond to Fermi levels of 20% and 60% hole doping [27].
Fig. 3. (Color online) Crystal structure of FeSe monolayer on
(001) surface of SrTiO3.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10 1139
I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, and A.A. Slobodchikov
pnictides. It raises the new problems for the explanations
of microscopic mechanism of superconductivity in FeSe
systems.
3.1. AxFe2Se2 system
LDA calculations of electronic structure of the AxFe2–ySe2
(A = K, Cs) system were performed immediately after its
experimental discovery [27,28]. Surprisingly enough, this
spectrum has appeared to be qualitatively different from
that of the bulk FeSe and spectra of all known systems
based on FeAs. In Fig. 4 we compare energy bands of
BaFe2As2 (Ba122) [29] (the typical prototype of FeAs sys-
tems) and AxFe2–ySe2 (A = K, Cs) [27]. One can see a sig-
nificant difference in the spectra near the Fermi level.
In Fig. 5 we show the calculated Fermi surfaces for two
systems AxFe2–ySe2 (A = K, Cs) at various doping levels [27].
We see that they differ significantly from the Fermi surfac-
es of FeAs systems Fermi surfaces — in the center of the
Brillouin zone, there are only small (mainly electronic!)
Fermi sheets, while the electronic cylinders in the Brillouin
zone corners are substantially larger. The shape of the
Fermi surface, typical for bulk FeSe and FeAs systems, can
be reproduced only at a much larger (experimentally inac-
cessible) levels of the hole doping [27].
This shape of the Fermi surfaces in AxFe2–ySe2 systems
was rather soon supported by ARPES experiments. For
example, in Fig. 6 we show ARPES data of Ref. 30, which
obviously is in agreement with LDA data of Refs. 27, 28.
One can clearly see that in this system it is impossible
to speak of any, even approximate, “nesting” properties of
electron and hole Fermi surfaces.
LDA+DMFT calculations for system for various doping
levels were done in Refs. 31, 32. There, along with the stan-
dard LDA+DMFT approach, we also used our LDA +DMFT′
[33,34] approach, which allows, in our opinion, to solve
the problem of “double counting” of Coulomb interaction
in the LDA+DMFT in a more consistent way. For DMFT
calculations Coulomb and exchange interactions of the
electrons in the Fe-3d shell we have chosen = 3.75U eV
and = 0.56J eV and as an impurity solver Hirsh–Fye
Quantum Monte-Carlo algorithm (QMC) was used. The
results of the LDA calculations are useful to compare with
the ARPES data obtained in Refs. 35, 36.
It is turned out that for K1–xFe2–ySe2 correlation effects
play quite an important role. They lead to a noticeable
change in LDA energy dispersions. In contrast to iron
arsenides, where the quasiparticle bands near the Fermi
level are well defined, in the K1–xFe2–ySe2 compounds in
the vicinity of the Fermi level there is a strong suppression
of quasiparticle bands. This reflects the fact that the corre-
lation effects in this system are stronger than in iron
arsenides. The value of the quasiparticle renormalization
(correlation narrowing) of the bands at the Fermi level is
4–5, whereas in iron arsenides this factor is only 2–3 for
the same values of the interaction parameters.
Fig. 5. (Color online) LDA Fermi surfaces AxFe2Se2 (A = K, Cs)
for the stoichiometric (left) and 20% (right) hole doping [27].
Fig. 6. (Color online) ARPES Fermi surfaces of K0.68Fe1.79Se2 ( cT = 32 K) and Tl0.45 K0.34Fe1.84Se2 ( cT = 28 K) [30].
1140 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10
Electronic structure of FeSe monolayer superconductors
The results of these calculations, in general, are in good
qualitative agreement with the ARPES data [35,36]. Both
demonstrate strong damping of quasiparticles in the imme-
diate vicinity of the Fermi level and a strong renormaliza-
tion of the effective mass as compared to systems based
on FeAs. However, in our calculations formation of unusu-
ally “shallow” (depth 0.05 eV) electron bands near
the X -point in the Brillouin zone, observed in ARPES
experiments, is not visible.
In Ref. 36 the authors reported systematic ARPES study
of the KxFe2–ySe2–zSz system at different doping levels. It
was shown that the sulfur doping level z can control the
depth of the “shallow” electron band near the X -point
(Fig. 7, δ band). We tried to model this situation for differ-
ent compositions of KxFe2–ySe2–zSz, taking into account
the changes of lattice constant. We considered three cases
of KxFe2–ySe2–zS2, KxFe2–ySe1S1 and KxFe2–ySe0.4S1.6.
The appropriate values of lattice constants used in our cal-
culations are listed in Table 1.
The LDA calculated density of states and band disper-
sions are presented in Figs. 8 and 9, correspondingly. Upon
sulfur doping the bandwidth of Fe-3d states increases,
while the bottom of the δ band slightly goes down. Corre-
sponding δ band bottom positions are 0.37, 0.38, 0.40 eV.
The Se-4p states also go down in energy (see Table 1).
These results are in qualitative agreement with ARPES
experiments, though the unusually low values of band bot-
tom energies (“shallow” band formation) of δ band remain
a mystery. We can also note, that according to Table 1
K2Fe2Se2 has the smallest (LDA) bandwidth of 3d states
and it grows with sulfur doping. Thus one can expect, that
K2Fe2Se2 is the most correlated system in this series.
3.2. [Li1–xFexOH]FeSe system
In Ref. 42 we presented the results of LDA calculations
for stoichiometric LiOHFeSe. Corresponding energy band
dispersions are shown in Fig. 10(a). At first glance, the
energy spectrum of this system is quite similar to the spec-
tra of the most of FeAs-based systems and bulk FeSe. In
particular, the main contribution to the density of states in
the wide energy range around the Fermi level is deter-
mined solely by Fe-3d. The Fermi surfaces are qualitative-
ly similar to that of majority of Fe-based superconductors.
However, this is somewhat misleading impression. Real
[Li0.8Fe0.2OH]FeSe system, where superconductivity was
Fig. 7. (Color online) (a) Doping dependence of the ARPES along the Γ– X direction in KxFe2–ySe2–zSz. (b) The bandwidth of δ and β
bands as a function of doping. (c) Doping dependence of the effective mass ( *m ) and Fermi velocity ( Fv ) of the δ band [36].
Table 1. Lattice constants for KxFe2–ySe2–zSz [27,37], LDA bandwidth of Fe-3d bands (eV) and energy interval of Se-4p states
KxFe2–ySe2–zSz a, Å c, Å Bandwidth of Fe-3d states, eV Selenium states energies, eV
KFe2Se2 3.9136 14.0367 3.5 (–5.8; –3.45)
K0.70Fe1.55Se1.01S0.99 3.805 13.903 3.9 (–6.1;–3.55)
K0.80Fe1.64Se0.42S1.58 3.781 13.707 4.0 (–6.2;–3.6)
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10 1141
I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, and A.A. Slobodchikov
discovered, the partial replacement of Li by Fe in LiOH
intercalation layers leads to noticeable LiOH electron dop-
ing, so that the Fermi energy moves upwards (relative
to the stoichiometric case) by about 0.15–0.2 eV. Then,
as can be seen from Fig. 10(a), the hole bands close to the Fig. 9. LDA band dispersions of KxFe2–ySe2–zSz compounds.
Fig. 8. LDA density of states of KxFe2–ySe2–zSz compounds.
Fig. 10. (Color online) (a) LDA bands for LiOHFeSe (Fermi level is at E = 0) [42], (b) LDA Fermi surface LiOHFeSe, corresponding
to electron doping of 0.3 electrons per unit cell, (c) experimental ARPES Fermi surfaces for [Li0.8Fe0.2OH]FeSe [43], (d) experimental
ARPES bands near the Fermi level of [Li0.8Fe0.2OH]FeSe [43].
1142 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10
Electronic structure of FeSe monolayer superconductors
Γ-point shifts below the Fermi level and the hole cylinders
of Fermi surface almost disappear. The general view of the
LDA calculated Fermi surface for this level of electron
doping is shown in Fig. 10(b). It has an obvious similarity
with the results for the AxFe2–ySe2 system (see Fig. 5).
These conclusions are directly confirmed by ARPES ex-
periments [43], with the results shown in Fig. 10 (c).
From Fig. 10 one can see that the Fermi surface consists
mostly of electronic cylinders surrounding the M -points,
while around the Γ-point the Fermi surface is either absent
or very small. In any case, for this system we can not speak
of any “nesting” of electron and hole Fermi surfaces in any
sense. Electronic dispersions found in the ARPES experi-
ments are very similar to corresponding ARPES disper-
sions reported in Refs. 35, 36 for KxFe2–ySe2–zS2 system.
These are qualitatively similar to dispersions obtained in
LDA and LDA+DMFT calculations, including rather
strong correlation bands narrowing (by about several times
with different compression factor for different bands)
[31,32]. However, the explanation of the formation of ex-
tremely “shallow” electron δ band with depth 0.05 eV
near the M-point remains unclear. This requires an unusu-
ally strong correlation compression which hardly can be
obtained from the LDA+DMFT calculations, while the
diameter of electronic cylinders around M -points is nearly
unchanged by correlations and almost coincides with the
results of LDA calculations.
An interesting debate flared up around the possible na-
ture of magnetic ordering of Fe ions, which replaces Li
ions within intercalation LiOH layers. In Ref. 38 it was
stated that this ordering is just a canted antiferromagnet.
However, in Ref. 39, on the basis of magnetic measure-
ments, it was claimed that it is ferromagnetic, with Curie
temperature CT 10 K, i.e., substantially below the super-
conducting transition temperature. This conclusion was
confirmed indirectly in Ref. 40 by observing the scattering
of neutrons on the lattice of Abrikosov vortices, which
might be induced in the FeSe layers by ferromagnetic or-
dering of Fe spins in the Li1–xFexOH layers. At the same
time, in Ref. 41 it was argued that Mössbauer measure-
ments indicate the absence of any kind of magnetic order-
ing on Fe ions in intercalation layers.
In Ref. 42 LSDA calculations of the exchange integrals
were performed for some typical magnetic configurations
of Fe ions, replacing Li in LiOH layers. For the most likely
magnetic configuration, leading to magnetic ordering, we
have obtained the positive (ferromagnetic) sign of the ex-
change interaction, and simple estimate of the Curie tem-
perature produced the value of Curie temperature 10 K,CT ≈
which is in excellent agreement with the results of experi-
ment of Refs. 39, 40.
3.3. FeSe monolayer films
LDA calculations of the spectrum of the isolated FeSe
monolayer can be performed in a standard slab approach.
To calculate electronic properties we used the Quantum-
Espresso [44] package. The results of these calculations
are shown in Fig. 11(a). It can be seen that the spectrum
has the form typical for FeAs-based systems and bulk FeSe
discussed in detail above. However ARPES experiments
[45–47] convincingly show that this is not so. For FeSe
monolayers on STO only electronic Fermi surface sheets
are observed around the M -points of the Brillouin zone,
while hole sheets, centered around the Γ-point (in the cen-
ter of the zone), are simply absent. An example of such
data is shown in Fig. 12(a) [45]. Similarly to intercalated
FeSe systems there are no signs of “nesting” of Fermi sur-
face — there are just no surfaces to “nest”!
In an attempt to explain the contradiction between
ARPES experiments [45] and band structure calculations
reflected in the absence of hole cylinder in the Γ-point,
one can suppose that this may be the consequence of
FeSe/STO monolayer stretching due to mismatch of lattice
constants of the bulk FeSe and STO. We have studied this
problem by varying the lattice parameter a and Se height
Sez in the range 5%± around the bulk FeSe parameters.
Fig. 11. (Color online) (a) LDA bands of an isolated FeSe monolayer near the Fermi level (E = 0). Red line shows approximate Fermi
level position to agree with ARPES experimental data. (b) LDA+DMFT bands of isolated electronically doped FeSe monolayer near the
doping-shifted Fermi level.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10 1143
I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, and A.A. Slobodchikov
Before the electronic structure was calculated crystal struc-
ture was relaxed. Unfortunately, the conclusion was that
the changes of lattice parameters do not lead to qualitative
changes of FeSe Fermi surfaces and the hole cylinders in
the Γ-point always remain.
However, there is another rather simple qualitative ex-
planation for the absence of hole cylinders and the ob-
served Fermi surfaces can be obtained by assuming that the
system is just electronically doped. The Fermi level has to
be moved upwards in energy by the value of 0.2–0.25 eV,
as shown by the solid (red) horizontal line in Fig. 11(a),
which corresponds to the doping level of 0.15–0.2 electron
per Fe ion.
Strictly speaking, the nature of this doping is not fully
identified. But there is a common belief that it is associated
with the formation of oxygen vacancies in the SrTiO3 sub-
strate (within the topmost layer of TiO2), occurring during
the various technological steps used during the film prepa-
ration, such as annealing, etching, etc. It should be noted
that the formation of the electron gas at the interface with
the SrTiO3 is a widely known phenomenon, which was
studied for a long time [48]. At the same time, for
FeSe/STO system this issue remains poorly understood
(see, however, Refs. 49, 50).
Electron correlations have relatively little influence on
the spectrum of the FeSe monolayer. Figure 11(b) shows
the results of LDA+DMFT calculations for estimated ex-
perimental value of electron doping. DMFT calculations
were done for the values of the Coulomb and exchange
(Hund) electron interactions in the Fe-3d shell equal to
= 3.5U eV and = 0.85J eV. As impurity solver we used
the continuous time quantum Monte-Carlo (CT-QMC)
algorithm. The inverse dimensionless temperature was
taken to be β = 40. It can be seen that the spectrum is very
weakly renormalized by correlations and preserves the
general LDA-like shape, with a slight band compression
factor of about 1.3.
Electronic dispersion in monolayer FeSe films was
measured by ARPES and reported in a number of papers
[18,46]. The results of Ref. 46 are shown in Fig. 12(b).
They are consistent with those of other studies and, in gen-
eral, are similar to those obtained for the intercalated FeSe
systems (see, e.g., Fig. 10(c)). Overall, they are qualitative-
ly similar to the results of LDA+DMFT but there is no
quantitative agreement. In particular, in the ARPES exper-
iments the presence of the unusual “shallow” electron band
at M -point, with the band bottom at 0.05 eV is clearly
observed. However, our calculated dispersions show a
“depth” of almost an order of magnitude larger.
It should also be noted that an additional “shadow” or
“replica” electronic band near the M -point was observed
in Ref. 46, which is 100 meV below the parent band
“shallow” band, and is clearly visible in Fig. 12(b). This
“shadow” band is completely missed in the band structure
calculations. The possible nature of this band (due to inter-
action with 100 meV STO optical phonons) and its im-
portance for mechanisms of cT enhancement in FeSe/STO
films was discussed in Ref. 46.
Now let us discuss the results of our LDA calculations
of electronic structure of the FeSe monolayer film on
SrTiO3 substrate as shown in Fig. 3. These calculations
were again performed with Quantum Espresso [44]. By
looking on left panel of Fig. 13 one can immediately rec-
ognize that there appears an additional hole band near the
M -point. To understand its origin we plotted on right pan-
el of Fig. 13 O-2p states of topmost surface TiO2 layer of
STO substrate. We can conclude, that the presence of STO
interface leads to the appearance of this additional band of
O-2p surface states near the Fermi level with probable
“nesting” with hole Fe-3d band with nesting vector Q = 0.
Fig. 12. (Color online) (a) Experimental ARPES Fermi surface of FeSe monolayer [45], (b) experimental ARPES bands of FeSe mono-
layer near the Fermi level [46].
1144 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 10
Electronic structure of FeSe monolayer superconductors
Also we observe rather small splitting of electron bands at
M -point. The relevance of these results to ARPES exper-
iments and their significance for enhanced superconductiv-
ity in FeSe/STO system are at present unclear. However,
the additional electron band splitting may have the relation
to the observation of the “replica” band at M -point [46],
providing the explanation of its appearance not related to
interaction with optical phonons in STO.
4. Conclusion
We have presented a short review of calculations of
electronic band structure of high- cT systems based on FeSe
monolayers, from intercalated compounds like AxFe2Se2–zSz
(A = K, Cs,...) and [Li1–xFexOH]FeSe to single FeSe layer
films of SrTiO3 substrate.
Our calculations show, that in all these systems the
general structure of electronic spectrum is significantly
different from the “standard model” typical for almost all
FeAs-based superconductors and bulk FeSe. This structure
is characterized by the practical absence of hole-like Fermi
surface cylinders around the Γ-point at the center of the
Brillouin zone with only electron-like cylinders present
around the M -points in the corners of the Brillouin zone.
These results are essentially confirmed by the available
ARPES experiments. An apparent absence of obvious
“nesting” properties between electron and hole Fermi sur-
face pockets cast serious doubts upon the most popular
picture of Cooper pairing, assumed to realize in FeAs sys-
tems, based on the exchange of antiferromagnetic fluctua-
tions and leading to the picture of s± pairing [4].
The role of electronic correlations in FeSe monolayers
remain rather controversial. LDA+DMFT calculations for
KxFe2Se2S system show that here these correlations are
more important than in typical FeAs systems, leading to
stronger bandwidth compression (different for different Fe-
3d bands) and rather poorly defined quasiparticles close to
the Fermi level. In contrast to this, in isolated FeSe single-
layer system the same calculations demonstrate rather
weak influence of correlations with small bandwidth com-
pression (effective mass renormalization). The role of
SrTiO3 substrate may also be important leading to the ap-
pearance of O-2p hole band of TiO2 layer in the vicinity of
the Fermi level.
The serious problems for understanding of the observa-
ble electronic structure of FeSe monolayer systems remain
to be solved. In particular, at present there are no accepta-
ble explanation of formation of unusually “shallow” elec-
tronic bands around the ( )M X -points, with Fermi energies
0.05 eV, observed in ARPES experiments on all of these
systems. It can be guessed that this fact reflects our poor
understanding of electron correlations and the question
remains open. Note that the existence of such small Fermi
energies in conduction bands of the system under discus-
sion signifies the serious problems related to the
antiadiabatic regime of Cooper pairing [51]. Taking into
account the typical values of the energy gap in FeSe mono-
layer superconductors ∆ 0.015–0.020 eV [18,47] we
also obtain the anomalously low gap to the Fermi energy
ratios: / FE∆ 0.25–0.5, which indicate, that these super-
conductors belong to BCS–BEC crossover region [52,53].
Acknowledgments
Calculations of electronic structure of FeSe systems
were performed under the FASO state contract
No. 0389-2014-0001 and partially supported by RFBR
grant 14-02-00065. NSP and AAS work was also support-
ed by the President of Russia grant for young scientists
No. Mk-5957.2016.2.
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http://dx.doi.org/10.1007/BF00683774
1. Introduction
2. Crystal structures of iron-based superconductors
3. Electronic structure of iron–selenium systems
3.1. AxFe2Se2 system
3.2. [Li1–xFexOH]FeSe system
3.3. FeSe monolayer films
4. Conclusion
Acknowledgments
|