Pseudogap and Local Pairs in High-Tc Superconductors

The temperature (T) dependence of pseudogap (PG) Δ*(T) is calculated for Bi2201 within the local pair (LP) model [1, 2]. The model is based on analysis of the excess conductivity derived from resistivity experiments in hightemperature superconductors (HTSs) and supposes the local pairs, which are fo...

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Datum:	2013
Hauptverfasser:	Solovjov, A.L., Tkachenko, M.A.
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Sprache:	English
Veröffentlicht:	Інститут металофізики ім. Г.В. Курдюмова НАН України 2013
Schriftenreihe:	Металлофизика и новейшие технологии
Schlagworte:	Электронные структура и свойства
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spelling	irk-123456789-1040602016-07-01T03:02:20Z Pseudogap and Local Pairs in High-Tc Superconductors Solovjov, A.L. Tkachenko, M.A. Электронные структура и свойства The temperature (T) dependence of pseudogap (PG) Δ(T) is calculated for Bi2201 within the local pair (LP) model [1, 2]. The model is based on analysis of the excess conductivity derived from resistivity experiments in hightemperature superconductors (HTSs) and supposes the local pairs, which are formed in HTSs at T well above Tc, to generate a pseudogap. To confirm the conclusion, Δ(T) is compared with the temperature dependence of the loss of the spectral weight W(EF)(T) measured by ARPES for the same Bi2201 sample [3]. A good agreement between Δ(T) and W(EF)(T) is found, confirming the local pairs to be one of the most likely cause for the PG formation. Температурну залежність псевдощілини Δ(T) розраховано для Bi2201 в межах моделю локальних пар [1, 2]. Цей модель засновано на аналізі надлишкової провідности, яка одержується з експериментів щодо питомого опору у високотемпературних надпровідниках (ВТНП), і припускає наявність локальних пар, що мають утворюватися у ВТНП за температур T, набагато більш високих, ніж Tc, формуючи псевдощілину. Для підтвердження цього висновку Δ(T) порівнюється з температурною залежністю втрати спектральної ваги W(EF)(T), що вимірюється ARPES в тому ж самому зразку Bi2201 [3]. Одержано хороший збіг Δ(T) і W(EF)(T), який підтверджує, що локальні пари є однією з найбільш ймовірних причин утворення псевдощілини. Температурная зависимость псевдощели Δ(T) рассчитана для Bi2201 в рамках модели локальных пар [1, 2]. Эта модель основана на анализе избыточной проводимости, которая получается из экспериментов по удельному сопротивлению в высокотемпературных сверхпроводниках (ВТСП), и подразумевает наличие локальных пар, которые должны образовываться в ВТСП при температурах T, намного более высоких, чем Tc, формируя псевдощель. Для подтверждения этого вывода Δ(T) сравнивается с температурной зависимостью потерь спектрального веса W(EF)(T), измеряемого ARPES в том же самом образце Bi2201 [3]. Получено хорошее совпадение Δ*(T) и W(EF)(T), подтверждающее, что локальные пары являются одной из наиболее вероятных причин образования псевдощели. 2013 Article Pseudogap and Local Pairs in High-Tc Superconductors / A.L. Solovjov, M.A. Tkachenko // Металлофизика и новейшие технологии. — 2013. — Т. 35, № 1. — С. 19-26. — Бібліогр.: 34 назв. — англ. 1024-1809 PACS numbers: 74.20.Fg, 74.25.Bt, 74.25.fc, 74.70.Xa, 74.72.-h, 74.72.Kf http://dspace.nbuv.gov.ua/handle/123456789/104060 en Металлофизика и новейшие технологии Інститут металофізики ім. Г.В. Курдюмова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Электронные структура и свойства Электронные структура и свойства
spellingShingle	Электронные структура и свойства Электронные структура и свойства Solovjov, A.L. Tkachenko, M.A. Pseudogap and Local Pairs in High-Tc Superconductors Металлофизика и новейшие технологии
description	The temperature (T) dependence of pseudogap (PG) Δ(T) is calculated for Bi2201 within the local pair (LP) model [1, 2]. The model is based on analysis of the excess conductivity derived from resistivity experiments in hightemperature superconductors (HTSs) and supposes the local pairs, which are formed in HTSs at T well above Tc, to generate a pseudogap. To confirm the conclusion, Δ(T) is compared with the temperature dependence of the loss of the spectral weight W(EF)(T) measured by ARPES for the same Bi2201 sample [3]. A good agreement between Δ*(T) and W(EF)(T) is found, confirming the local pairs to be one of the most likely cause for the PG formation.
format	Article
author	Solovjov, A.L. Tkachenko, M.A.
author_facet	Solovjov, A.L. Tkachenko, M.A.
author_sort	Solovjov, A.L.
title	Pseudogap and Local Pairs in High-Tc Superconductors
title_short	Pseudogap and Local Pairs in High-Tc Superconductors
title_full	Pseudogap and Local Pairs in High-Tc Superconductors
title_fullStr	Pseudogap and Local Pairs in High-Tc Superconductors
title_full_unstemmed	Pseudogap and Local Pairs in High-Tc Superconductors
title_sort	pseudogap and local pairs in high-tc superconductors
publisher	Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate	2013
topic_facet	Электронные структура и свойства
url	http://dspace.nbuv.gov.ua/handle/123456789/104060
citation_txt	Pseudogap and Local Pairs in High-Tc Superconductors / A.L. Solovjov, M.A. Tkachenko // Металлофизика и новейшие технологии. — 2013. — Т. 35, № 1. — С. 19-26. — Бібліогр.: 34 назв. — англ.
series	Металлофизика и новейшие технологии
work_keys_str_mv	AT solovjoval pseudogapandlocalpairsinhightcsuperconductors AT tkachenkoma pseudogapandlocalpairsinhightcsuperconductors
first_indexed	2025-07-07T14:47:42Z
last_indexed	2025-07-07T14:47:42Z
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fulltext	19 PACS numbers: 74.20.Fg, 74.25.Bt, 74.25.fc, 74.70.Xa, 74.72.-h, 74.72.Kf Pseudogap and Local Pairs in High-Tc Superconductors A. L. Solovjov,* and M. A. Tkachenko* B. I. Verkin Institute for Low Temperature Physics and Engineering N.A.S.U., 47 Lenin Ave., 61103 Kharkiv, Ukraine International Laboratory of High Magnetic Fields and Low Temperatures, 95 Gajowicka Str., 53-421 Wroclaw, Poland The temperature (T) dependence of pseudogap (PG) Δ(T) is calculated for Bi2201 within the local pair (LP) model [1, 2]. The model is based on analysis of the excess conductivity derived from resistivity experiments in high- temperature superconductors (HTSs) and supposes the local pairs, which are formed in HTSs at T well above Tc, to generate a pseudogap. To confirm the conclusion, Δ(T) is compared with the temperature dependence of the loss of the spectral weight W(EF)(T) measured by ARPES for the same Bi2201 sam- ple [3]. A good agreement between Δ(T) and W(EF)(T) is found, confirming the local pairs to be one of the most likely cause for the PG formation. Температурну залежність псевдощілини Δ(T) розраховано для Bi2201 в межах моделю локальних пар [1, 2]. Цей модель засновано на аналізі над- лишкової провідности, яка одержується з експериментів щодо питомого опору у високотемпературних надпровідниках (ВТНП), і припускає наяв- ність локальних пар, що мають утворюватися у ВТНП за температур T, набагато більш високих, ніж Tc, формуючи псевдощілину. Для підтвер- дження цього висновку Δ(T) порівнюється з температурною залежністю втрати спектральної ваги W(EF)(T), що вимірюється ARPES в тому ж са- мому зразку Bi2201 [3]. Одержано хороший збіг Δ(T) і W(EF)(T), який пі- дтверджує, що локальні пари є однією з найбільш ймовірних причин утворення псевдощілини. Температурная зависимость псевдощели Δ(T) рассчитана для Bi2201 в рамках модели локальных пар [1, 2]. Эта модель основана на анализе из- быточной проводимости, которая получается из экспериментов по удель- ному сопротивлению в высокотемпературных сверхпроводниках (ВТСП), и подразумевает наличие локальных пар, которые должны образовывать- ся в ВТСП при температурах T, намного более высоких, чем Tc, формируя Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol. 2013, т. 35, № 1, сс. 19—26 Оттиски доступны непосредственно от издателя Фотокопирование разрешено только в соответствии с лицензией © 2013 ИМФ (Институт металлофизики им. Г. В. Курдюмова НАН Украины) Напечатано в Украине. 20 A. L. SOLOVJOV and M. A. TKACHENKO псевдощель. Для подтверждения этого вывода Δ(T) сравнивается с тем- пературной зависимостью потерь спектрального веса W(EF)(T), измеряе- мого ARPES в том же самом образце Bi2201 [3]. Получено хорошее совпа- дение Δ(T) и W(EF)(T), подтверждающее, что локальные пары являются одной из наиболее вероятных причин образования псевдощели. Key words: high-temperature superconductors, conductivity, spectral gap, spectral weight. (Received September 19, 2012) 1. INTRODUCTION Up to now, the pseudogap (PG) observed mostly in underdoped (UD) cuprates remains the most intriguing and controversial property of high-temperature superconductors (HTSs). Below, any representative temperature T * >> Tc, for reasons, which have still not been finally es- tablished, the density of quasi-particle states at the Fermi level starts to decrease [4—6]. That is why the phenomenon has been named a ‘pseudogap’. Thus, below T , the HTSs goes into the PG regime, which is characterized by many unusual features [1, 7—10]. The paper addresses the problem of the PG, which is believed to ap- pear most likely due to the ability of a part of conduction electrons to form paired fermions (so called local pairs) in HTSs at T ≤ T [13, 15]. The possibility of the long-lived pair states formation in HTSs in the PG temperature range was justified theoretically in [2, 18—20]. In ac- cordance with proposed local pair (LP) model [1], at high temperatures (T ≤ T ), the local pairs are known to be in the form of strongly bound bosons (SBB), which satisfy the theory of Bose—Einstein condensation (BEC) [13, 15—20]. In accordance with this theory, the SBB are ex- tremely short but very tightly bound pairs. As a result, the SBB cannot be destroyed by thermal fluctuations. Besides, they have to be local (i.e. not interacting with one another) objects since the pair size is much less than the distance between the pairs. The important point here is that the SBB may be formed only in the systems with low and reduced density of charge carriers nf [15—19]. This condition is realized just in the UD cuprates [2, 7, 11, 13] and new FeAs-based superconductors [21, 22] resulting, in our opinion, in the PG formation. But, strictly speaking, the presence or absence of a PG in FeAs-based HTSs still re- main controversial [21, 23]. It is worth to emphasize that the coherence length ξab(T) = = ξab(0)(T/Tc − 1) −1/2, which actually determines the pair size, is ex- tremely short in HTSs [7, 8, 11—13, 15]. At the same time, the energy of a bound state of two fermions in the pair, εb ∝ ξ(T) −1, where ξ(T) is the coherence length of the superconductor, is very large. This is an PSEUDOGAP AND LOCAL PAIRS IN HIGH-Tc SUPERCONDUCTORS 21 additional requirement for the formation of the SBB [15—18, 24]. Eventually, just the value of ξab(T) will determine the system behav- iour [13, 15—17, 24]. On cooling, ξab(T) increases, whereas εb decreases. As a result, the local pairs have to change their state from the SBB into fluctuating Cooper pairs, which satisfy the BCS theory and behave in a good many ways like those of conventional superconductors [15, 18, 20, 24]. Thus, with decrease of temperature, there must be a transition from BEC to BCS state. Precisely how this happens is one of the chal- lenging questions in strongly correlated electron systems. Neverthe- less, the transition was predicted theoretically in [16, 17] and in more explicit form in Ref. [24], and approved in our experiments [13, 25]. This fact has to confirm our assumption as for existence of the local pairs in HTSs, which also has found a theoretical background in Ref. [2]. 2. RESULTS AND DISCUSSION Within the proposed LP model, the PG in YPrBCO films [27], FeAs- based superconductor SmFeAsO0.85 with Tc = 55 K [22], and in slightly doped HoBCO single-crystals [28] is studied for the first time. But the basic results have been obtained from the analysis of the resistivity da- ta for a set of four YBCO films with different oxygen concentrations [13, 25]. The films were fabricated at Max Plank Institute (MPI) in Stuttgart by pulse laser deposition method [29]. All samples were the well-structured c-oriented epitaxial YBCO films, as it was confirmed by studying the corresponding X-ray and Raman spectra. Using the LP model, the temperature dependences of Δ for every film were ana- lysed. The main common feature of every found Δ(T) dependence is a maximum of Δ(T) observed at the same Tmax ≈ 130 K. The important point here is that ξab(Tmax) was found to be the same for every studied film, namely, ξab(Tmax) ≈ 18 Å [13, 25]. Above 130 K, ξab(T) is very small (ξab(T ) ≈ 13 Å), whereas the cou- pling energy εb is very strong. It is just the condition for the formation of the SBB [15—18]. It was found [25] that at Tmax < T < T every exper- imental Δ(T) curve can be fitted by the Babaev—Kleinert (BK) theory [19] in the BEC limit (low nf), in which the SBB have to form [15—20]. This finding has to confirm the presence of the local pairs in the films, which are supposed to exist at high temperatures just in the form of SBB. As SBB do not interact with one another, the local pairs demon- strate no superconducting (SC) (collective) behaviour in this tempera- ture interval. It has subsequently been shown to be consistent with the tunnelling experiments in Bi2223 [30], in which the SC tunnelling fea- tures are smeared out above Tmax. Thus, above Tmax, it is the so-called non-superconducting part of the PG. On cooling, ξab(T) continues to increase, but εb(T) becomes smaller. 22 A. L. SOLOVJOV and M. A. TKACHENKO Finally, at T ≤ Tmax ≈ 130 K, where ξab(T) > 18 Å, the local pairs begin to overlap and acquire the possibility to interact. Besides, they can be de- stroyed by the thermal fluctuations now, i.e., transform into fluctuat- ing Cooper pairs, as discussed above. The SC (collective) behaviour of the local pairs in this temperature region is distinctly seen in many ex- periments [27, 30—33]. Recently, the direct imaging of the local pair SC clusters persistence up to ≅ 140 K in Bi2212 is reported [9]. Thus, below Tmax, it is the SC part of the PG. Moreover, we consider ξab(Tmax) ≈ ≈ 18 Å to be the critical size of the local pair, at least in YBCO [13, 25]. Thus, the local pairs behave like SBB, when ξab(T) < 18 Å, and trans- form into fluctuating Cooper pairs, when ξab(T) > 18 Å below Tmax. The possibility of this BEC—BCS transition is the main assumption of the LP model. Consequently, it can be concluded that the PG description in terms of local pairs gives a set of reasonable and self-consistent results. How- ever, to justify the conclusion, it would be appropriate to have inde- pendent results of other research groups, who have measured straight- forwardly the PG or any other related effects. But, for a long time, there was a lack of indispensable data. Fortunately, analysis of the pseudogap in (Bi,Pb)2(Sr,La)2CuO6+δ (Bi2201) single-crystals with various Tc’s by means of ARPES spectra study was recently reported [3]. The study of Bi2201 allows avoid the complications resulting from the bilayer splitting and strong antinodal bosonic mode coupling inherent to Bi2212 and Bi2223 [32, 33]. Symme- trised energy distribution curves (EDCs) were found to demonstrate the opening of the pseudogap on cooling below T . It was shown that T * ob- tained from the resistivity measurements agrees well with one deter- mined from the ARPES data using a single spectral peak criterion [3]. Finally, from the ARPES experiments, information about tempera- ture dependence of the loss of the spectral weight close to the Fermi level, W(EF), was derived [3]. The W(EF) versus T measured for opti- mally doped OP35K Bi2201 (Tc = 35 K, T * = 160 K) turned out to be ra- ther unexpected, as shown in Fig. 1, a taken from Ref. [3]. Above T , the W(EF) is nonlinear function of T. But, below T , over the tempera- ture range from T * to Tpair = 110±5 K (Fig. 1, a), the W(EF)(T) decreases linearly that is considered as a characteristic behaviour of the ‘proper’ PG state [3]. However, no assumption as for physical nature of this lin- earity as well as for existence of the paired fermions in the PG region is proposed. Below Tpair, the W(EF) vs T noticeably deviates down from the linearity (Fig. 1, a). The deviation suggests the onset of another state of the system, which likely arises from the pairing of electrons, since the W(EF)(T) associated with this state smoothly evolves through Tc (Fig. 1, a). To compare results and justify our LP model, the ρab vs T of the OP35K Bi2201 reported in the Supplementary to Ref. [3] was studied PSEUDOGAP AND LOCAL PAIRS IN HIGH-Tc SUPERCONDUCTORS 23 within the model. Resulting Δ(T) = Δ max is plotted in Fig. 1, b (circles). The Δ(T) was calculated, using equation   −    Δ =  ′σ ξ ε ε ε     2 4 * * * 0 0 1 ln 16 ( ) (0) 2 sinh(2 )c c c T e A T T T (1) proposed in Ref. [25] with respect to the LP model. Here, A4 is a numer- ical factor, which has the meaning of the C-factor in the fluctuation conductivity theory [13]. All other parameters, including the coher- ence length along c-axis ξc(0) and the theoretical parameter εc0 , direct- ly come from the experiment. To find A4, we calculate σ′(ε) and fit it to the experiment in the range of 3D Aslamazov—Larkin (AL) fluctua- tions near Tc [13, 25] where lnσ′(lnε) is a linear function of the reduced temperature, ε = (T − Tc mf)/Tc mf, with a slope λ = −1/2. Tc mf is a mean- field critical temperature [26]. Equation (1) was solved with the follow- Fig. 1. Spectral weight W(EF) vs T (dots) for OP35K Bi2201 (a). Pseudogap Δ(T)/Δ* max (circles) and spectral gap SG(T)/SGmax (dots) for the same sample (b). 24 A. L. SOLOVJOV and M. A. TKACHENKO ing reasonable set of parameters: Tc = 35 K, Tc mf = 36.9 K, T * = 160 K, ξc(0) ≈ 2.0 Å, εc0 * = 0.89, and A4 = 59. The σ′(T) is the experimentally measured excess conductivity derived from the resistivity data [13]. As expected, the shape of the Δ(T) curve, with a maximum at Tmax ≈ ≈ 100 K (Fig. 1, b), is similar to that found for YBCO films [13, 25]. Moreover, the maximum of Δ(T) = Δ* max at Tmax (Fig. 1, b) coincides with Tpair (Fig. 1, a) that seems to be reasonable. In fact, in accordance with our logic, Tmax is just the temperature, which divides the PG re- gion on SC and non-SC parts depending on the local pair state, as dis- cussed above. Let us remind that above Tmax the local pairs are expected to be in the form of SBB. Most likely just the specific properties of the SBB cause the linear W(EF)(T) in this temperature range (Fig. 1, a). The two facts are believed to confirm the conclusion. First, when SBB disappear above T , the linearity disappears too. Second, below Tmax, or below Tpair in terms of Ref. [3], the SBB have to transform into fluctu- ating Cooper pairs giving rise to the SC (collective) properties of the system. This argumentation coincides with the conclusion of Ref. [3] as for SC part of the pseudogap below Tpair. As SBB are now also absent, the linearity of W(EF)(T) disappears too. Thus, we consider the Δ(T) calculated within the LP model (Fig. 1, b) to be in a good agreement with the temperature dependence of the loss of the spectral weight W(EF) (Fig. 1, a) obtained from the ARPES experiments performed on the same sample. In this way, the results of ARPES experiments re- ported in Ref. [3] are believed to confirm our conclusion as for exist- ence of the local pairs in HTSs, at least in Bi2201 compounds. The normalized spectral gap (SG(T)) (dots), which is equal to the en- ergy of the spectral peaks of EDCs measured by ARPES, is also plotted in Fig. 1, b [3]. In this case, it is important that SG(T) smoothly evolves through both Tpair and Tc. This fact is believed to confirm the local pair presence above Tpair assumed in the LP model. But, there are at least two differences between the curves shown in Fig. 1, b. First, there is no direct correlation between the SG(T) and the W(EF)(T) (Fig. 1, a and b). Why the maximum of SG(T) is shifted toward low temperatures com- pared to Tpair is not known now. The second difference is the absolute value of the SG compared to the PG. The spectral gap has SGmax ≈ 40 meV and SG(Tc) ≈ 38 meV [3]. It gives 2SG(Tc)/(kBTc) ≈ 26, which is ap- parently too high. The PG values are Δ* max ≈ 16.5 meV and Δ(Tc) ≈ 6.96 meV, respectively. It gives 2Δ(Tc)/(kBTc) ≈ 6.4, which is a common value for the Bi compounds [34] with respect to relatively low Tc in considered case. Thus, no direct coincidence between the SG and PG is found. 3. CONCLUSION We present a detailed consideration of the LP model developed to study PSEUDOGAP AND LOCAL PAIRS IN HIGH-Tc SUPERCONDUCTORS 25 the PG in HTSs. In accordance with the model, the local pairs have to be the most likely candidate for the PG formation. At high tempera- tures (Tpair < T ≤ T ), we believe that the local pairs should have the form of SBB, which satisfy the BEC theory (non-SC part of a PG). Be- low Tpair, the local pairs have to change their state from the SBB into fluctuating Cooper pairs, which satisfy the BCS theory (SC part of a PG). Thus, with decrease of temperature, there must be a transition from BEC to BCS state [13, 15—18, 25]. The possibility of such a transi- tion is considered to be one of the basic physical principles of the high- Tc superconductivity. The transition was predicted theoretically in Refs [16, 17, 24] and corroborated by our experiments. A key test for our consideration is the comparison of Δ(T) calculated within the LP model with the temperature dependence of the loss of the spectral weight close to the Fermi level W(EF)(T) measured by ARPES for the same sample [3]. Resulting Δ(T) is found to be in a good agree- ment with the W(EF)(T) obtained for OP35K Bi2201 (Fig. 1). It enables us to explain reasonably the W(EF)(T) both above and below Tpair in terms of local pairs. The obtained results are also in agreement with the conclusions of Refs [9, 32, 33] as for SC and non-SC parts of the PG in Bi systems. Besides, formation of local pairs is also believed to ex- plain the rise of the polar Kerr effect and response of the time-resolved reflectivity both observed for Bi systems just below T [32]. While, the Nernst effect [9], which is likely caused by the SC properties of the lo- cal pairs, is observed only below Tpair, or below Tmax in terms of our model. The authors are grateful to V. M. 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Pseudogap and Local Pairs in High-Tc Superconductors

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