Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors
In this paper, we evaluate the fitting parameters for the hopping model for the dxy and dxz bands within the Γ–M cut for different FeSe-based superconductors. Comparison of these parameters for DFT calculations and for experimentally obtained data reveals a dramatic change of hopping probability bet...
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Pustovit, Yu.V. Kordyuk, O.A. 2019-02-06T19:06:38Z 2019-02-06T19:06:38Z 2018 Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors / Yu.V. Pustovit, O.A. Kordyuk // Металлофизика и новейшие технологии. — 2018. — Т. 40, № 5. — С. 593-599. — Бібліогр.: 19 назв. — англ. 1024-1809 PACS: 74.20.Mn, 74.20.Pq, 74.25.Jb, 74.70.Xa, 74.78.-w, 75.25.Dk, 81.05.Zx DOI: https://doi.org/10.15407/mfint.40.05.0593 https://nasplib.isofts.kiev.ua/handle/123456789/146074 In this paper, we evaluate the fitting parameters for the hopping model for the dxy and dxz bands within the Γ–M cut for different FeSe-based superconductors. Comparison of these parameters for DFT calculations and for experimentally obtained data reveals a dramatic change of hopping probability between the nearest neighbours. This change is much bigger than the expected band renormalization and can be explained by the appearance of an antiferromagnetic-like ordering. В статье оценены параметры модели перескоков для аппроксимации dxy- и dxz-зон в Γ–M-сечении для разных сверхпроводников на основе FeSe. Сравнение значений параметров для экспериментально полученных электронных дисперсий и рассчитанных с помощью метода ТФП показало снижение вероятности перескоков между ближайшими соседями. Такие изменения можно объяснить возникновением некоторого упорядочения. У статті оцінено параметри моделю перескоків для апроксимації dxy- та dxz-зон у Γ–M-перерізі для різних надпровідників на основі FeSe. Порівняння значень цих параметрів для експериментально одержаних і розрахованих методою ТФГ електронних дисперсій показує зменшення ймовірности перескоку між найближчими сусідами. Такі зміни можуть бути пояснені появою певного виду впорядкування. en Інститут металофізики ім. Г.В. Курдюмова НАН України Металлофизика и новейшие технологии Электронные структура и свойства Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors Подавление перескоков электронов по ближайшим соседям в сверхпроводниках на основе FeSe Пригнічення перескоку електронів по найближчих сусідах у надпровідниках на основі FeSe Article published earlier |
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| title |
Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors |
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Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors Pustovit, Yu.V. Kordyuk, O.A. Электронные структура и свойства |
| title_short |
Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors |
| title_full |
Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors |
| title_fullStr |
Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors |
| title_full_unstemmed |
Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors |
| title_sort |
suppression of nearest neighbour electron hopping in fese-based superconductors |
| author |
Pustovit, Yu.V. Kordyuk, O.A. |
| author_facet |
Pustovit, Yu.V. Kordyuk, O.A. |
| topic |
Электронные структура и свойства |
| topic_facet |
Электронные структура и свойства |
| publishDate |
2018 |
| language |
English |
| container_title |
Металлофизика и новейшие технологии |
| publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
| format |
Article |
| title_alt |
Подавление перескоков электронов по ближайшим соседям в сверхпроводниках на основе FeSe Пригнічення перескоку електронів по найближчих сусідах у надпровідниках на основі FeSe |
| description |
In this paper, we evaluate the fitting parameters for the hopping model for the dxy and dxz bands within the Γ–M cut for different FeSe-based superconductors. Comparison of these parameters for DFT calculations and for experimentally obtained data reveals a dramatic change of hopping probability between the nearest neighbours. This change is much bigger than the expected band renormalization and can be explained by the appearance of an antiferromagnetic-like ordering.
В статье оценены параметры модели перескоков для аппроксимации dxy- и dxz-зон в Γ–M-сечении для разных сверхпроводников на основе FeSe. Сравнение значений параметров для экспериментально полученных электронных дисперсий и рассчитанных с помощью метода ТФП показало снижение вероятности перескоков между ближайшими соседями. Такие изменения можно объяснить возникновением некоторого упорядочения.
У статті оцінено параметри моделю перескоків для апроксимації dxy- та dxz-зон у Γ–M-перерізі для різних надпровідників на основі FeSe. Порівняння значень цих параметрів для експериментально одержаних і розрахованих методою ТФГ електронних дисперсій показує зменшення ймовірности перескоку між найближчими сусідами. Такі зміни можуть бути пояснені появою певного виду впорядкування.
|
| issn |
1024-1809 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146074 |
| citation_txt |
Suppression of Nearest Neighbour Electron Hopping in FeSe-Based Superconductors / Yu.V. Pustovit, O.A. Kordyuk // Металлофизика и новейшие технологии. — 2018. — Т. 40, № 5. — С. 593-599. — Бібліогр.: 19 назв. — англ. |
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| fulltext |
593
ЭЛЕКТРОННЫЕ СТРУКТУРА И СВОЙСТВА
PACS numbers: 74.20.Mn, 74.20.Pq, 74.25.Jb, 74.70.Xa, 74.78.-w, 75.25.Dk, 81.05.Zx
Suppression of Nearest Neighbour Electron Hopping
in FeSe-Based Superconductors
Yu. V. Pustovit*
and O. A. Kordyuk*,**
*G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03142 Kyiv, Ukraine
**Kyiv Academic University, N.A.S. and M.E.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03142 Kyiv, Ukraine
In this paper, we evaluate the fitting parameters for the hopping model for
the dxy and dxz bands within the cut for different FeSe-based supercon-
ductors. Comparison of these parameters for DFT calculations and for exper-
imentally obtained data reveals a dramatic change of hopping probability be-
tween the nearest neighbours. This change is much bigger than the expected
band renormalization and can be explained by the appearance of an antifer-
romagnetic-like ordering.
Key words: FeSe, electronic structure, iron-based superconductors, interca-
lated systems, FeSe films.
У статті оцінено параметри моделю перескоків для апроксимації dxy- та
dxz-зон у – -перерізі для різних надпровідників на основі FeSe. Порів-
няння значень цих параметрів для експериментально одержаних і розра-
хованих методою ТФГ електронних дисперсій показує зменшення ймові-
рности перескоку між найближчими сусідами. Такі зміни можуть бути
пояснені появою певного виду впорядкування.
Ключові слова: FeSe, електронна структура, залізні надпровідники, інте-
ркальовані системи, плівки FeSe.
В статье оценены параметры модели перескоков для аппроксимации dxy- и
Corresponding author: Yuriy Valeriyovych Pustovit
E-mail: jura.pustvit@gmail.com
Citation: Yu. V. Pustovit and O. A. Kordyuk, Suppression of Nearest Neighbour
Electron Hopping in FeSe-Based Superconductors, Metallofiz. Noveishie Tekhnol., 40,
No. 5: 593–599 (2018), DOI: 10.15407/mfint.40.05.0593.
Ìåòàëëîôèç. íîâåéøèå òåõíîë. / Metallofiz. Noveishie Tekhnol.
2018, т. 40, № 5, сс. 593–599 / DOI: 10.15407/mfint.40.05.0593
Îòòèñêè äîñòóïíû íåïîñðåäñòâåííî îò èçäàòåëÿ
Ôîòîêîïèðîâàíèå ðàçðåøåíî òîëüêî
â ñîîòâåòñòâèè ñ ëèöåíçèåé
2018 ÈÌÔ (Èíñòèòóò ìåòàëëîôèçèêè
èì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàèíû)
Íàïå÷àòàíî â Óêðàèíå.
mailto:jura.pustvit@gmail.com
https://doi.org/10.15407/mfint.40.05.0593
https://doi.org/10.15407/mfint.40.05.0593
594 Yu. V. PUSTOVIT and O. A. KORDYUK
dxz-зон в – -сечении для разных сверхпроводников на основе FeSe. Срав-
нение значений параметров для экспериментально полученных электрон-
ных дисперсий и рассчитанных с помощью метода ТФП показало сниже-
ние вероятности перескоков между ближайшими соседями. Такие изме-
нения можно объяснить возникновением некоторого упорядочения.
Ключевые слова: FeSe, электронная структура, железные сверхпровод-
ники, интеркалированные системы, плёнки FeSe.
(Received February 22, 2018)
1. INTRODUCTION
Iron-based superconductors is a new class of high-temperature super-
conductors, which was discovered in 2008 [1 3]. Fermi surface topolo-
gy of iron-based superconductors have been predicted by numerous
density functional theory (DFT) calculations and confirmed by many
experiments [1 5]. However, there are some differences between the
results of calculations and experimentally obtained data.
First of all, it is strong renormalization of bands, which differs for
distinct bands and different compounds. However, these differences
can be explained by dynamical mean-field theory (DMFT) calculations
[6, 7].
Another difference is a shrinking of experimentally obtained Fermi
surfaces in comparison to DFT calculated ones. Such a shrinking is
supposed to be a result of the shifts of bunches of the hole and electron
bands in the opposite directions in the centre and at the corner of the
Brillouin zone [8 10].
There are several explanations for such shifts in opposite directions.
In Ref. [11], it is supposed that such shifts are fully consistent with the
enhancement of the Pomeranchuk s -susceptibility predicted by the
analytical renormalization group technique. Another mechanism con-
siders these differences as a result of self-energy corrections due to ex-
change of the spin fluctuations between the hole and electron pockets.
In this case, the band shifts are supposed to be orbital-dependent ones
[12 14].
In this paper, we analyse experimentally obtained ARPES data and
DFT calculations of different FeSe-based superconductors in terms of
hopping parameters [15, 16]. It is shown that characteristic shifts of
the experimentally obtained bands can be naturally explained by block-
ing of hopping between the nearest neighbours.
2. EVALUATION OF HOPPING PARAMETERS
Taking into account the hopping between up to three nearest neigh-
SUPPRESSION OF NEAREST NEIGHBOUR ELECTRON HOPPING IN FeSe 595
bours, the dispersion in the direction for the 2-Fe unit cell is given
by formula:
(k) 0 t1cos(kxa) t2cos(2kxa) t3cos(3kxa),
where t1, t2, and t3 are the hopping integrals, which are proportional to
probabilities of hopping between the nearest neighbours, next nearest,
and next-next nearest neighbours, respectively. The hopping integrals
obtained by fitting the experimental and DFT dispersions to this for-
mula for different FeSe-based (Figs. 1–3) compounds are presented in
Tables 1–3. In this case, we pay attention only on two bands, whose po-
sitions have been obtained experimentally.
It is supposed that the band structure in the range 0 1 eV is renormal-
ized with some factor of renormalization. The value of the renormaliza-
tion factor differs for distinct compounds and bands. Different papers
give different renormalization factor values ranging from 2 to almost
17 [9, 17 19], but it is more probable that for FeSe-based superconduc-
tors these factors are near 3 [4]. Such variety may be explained by the
various methods for determination of the renormalization parameters.
The value of these parameters can be obtained by comparing the veloci-
ties (first derivatives with respect to k of the electronic dispersions) or
masses (second derivatives) in different points of the Brillouin zone.
These methods work properly within the ‘rigid’ band, but the band
shifts in opposite directions make determination of these parameters
ambiguous.
In terms of the hopping model, the renormalization factors can be
Fig. 1. Fit of calculated (dashed lines) and experimentally obtained (solid
lines) dxz (in -point upper band) and dxy (in -point lower band) for FeSe.
596 Yu. V. PUSTOVIT and O. A. KORDYUK
determined by various ways. For example, d dk ka2(t1 2t2 3t3) in
the vicinity of -point, and d dk a(t1 3t3) for k /(3a).
If the renormalization is related with the enhancement of quasi-
Fig. 2. Fit of calculated (dashed lines) and experimentally obtained (solid
lines) dxy (in -point upper band) and dxy (in -point lower band) for KFeSe.
Fig. 3. Fit of calculated (dashed lines) and experimentally obtained (solid
lines) dxz (in -point upper band) and dxy (in -point lower band) for monolayer
FeSe film on STO substrate.
SUPPRESSION OF NEAREST NEIGHBOUR ELECTRON HOPPING IN FeSe 597
particle mass, d
2 dk2
a(0.5t1 2t2 3t3) for k /(3a) and d
2 dk2
a(t1 4t2 9t3) for -point.
So, direct comparison of the experimental and the calculated disper-
sions cannot be made due to changes of renormalization factor with re-
spect to ways of its definition and due to the shift of the bands in oppo-
site directions. Thus, the most reliable way to compare the experi-
mental and calculated dispersions is to evaluate the ratio between hop-
ping integrals of each.
Since the DFT calculations do not take into account the band renor-
malization due to electronic correlations, the obtained values of hop-
ping parameters for the calculated and experimentally obtained bands
differ essentially but related by a ‘renormalization coefficient’. For t2
and t3, the ratio between coefficients of fitting for the calculated and
TABLE 1. Fitting parameters for FeSe.
FeSe 0 t1 t2 t3
dxz(calc/exp)
dxy(calc/exp)
0.209
0.302
0.063
0.067
0.233
0.322
0
0.005
0.149
0.102
0.053
0.019
0.037
0.034
0.019
0.008
TABLE 2. Fitting parameters for KFeSe.
KFeSe 0 t1 t2 t3
dxz(calc/exp)
dxy(calc/exp)
0.209
0.385
0.15
0.07
0.123
0.299
0.007
0.006
0.126
0.072
0.058
0.016
0.024
0.002
0.01
0.0075
TABLE 3. Fitting parameters for monolayer FeSe film on STO substrate.
FeSe(Monolayer) 0 t1 t2 t3
dxz(calc/exp)
dxy(calc/exp)
0.195
0.406
0.141
0.076
0.221
0.276
0
0
0.179
0.146
0.053
0.016
0.065
0.029
0.019
0.003
TABLE 4. Ratio between hopping integrals for calculated and experimentally
obtained electronic dispersions for FeSe, KFeSe, and single layer FeSe film on
STO substrate.
t1(calc)/t1(exp) t2(calc)/t2(exp) t3(calc)/t3(exp)
dxz dxy dxz dxy dxz dxy
FeSe
KFeSe
FeSe (single layer)
17
64
50
2.8
2.2
3.4
5.4
4.5
9.125
2.05
2.4
3.4
4.25
0.26
9.6
598 Yu. V. PUSTOVIT and O. A. KORDYUK
experimental obtained bands is close to the renormalization factor of
the band (e.g., for FeSe, it is 2 3 for dxz band and 4 5 for dxy band; Ta-
ble 4). An important difference is that t1 for experimentally obtained
bands for all compounds is much smaller than for results of DFT calcu-
lations. For all compounds and all bands, t1 becomes zero or its value is
near zero. As have been proposed in this article, changes of t1 are equiva-
lent to decreasing of probability or complete blocking of the nearest
neighbour hopping that can be result of appearance of some kind of or-
dering.
3. CONCLUSIONS
In this paper, the hopping parameters for the dxy and dxz bands for the
cut of different FeSe-based superconductors have been obtained.
As shown, the hopping integral for the nearest neighbours based on
experimentally obtained data undergoes significant depletion compar-
ing to the DFT calculated data. This depletion cannot be explained by
simple band renormalization, but rather by decreasing of probability
of nearest neighbour hopping, that can be a consequence of an antifer-
romagnetic-like ordering.
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https://doi.org/10.1103/PhysRevB.83.104516
https://doi.org/10.1016/0022-3697(95)00269-3
https://doi.org/10.1016/0022-3697(95)00269-3
https://doi.org/10.1103/PhysRevB.67.064504
https://doi.org/10.1103/PhysRevB.67.064504
https://doi.org/10.1103/PhysRevB.81.014526
https://doi.org/10.1103/PhysRevLett.104.097002
https://doi.org/10.1103/PhysRevLett.103.037002
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