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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Search for Unconventional Superconductors at the Itinerant-to-Local Moment Crossover

Zhao, Liang 05 June 2013 (has links)
In searching for novel optimal superconductors, three strategic routes based on theoretical and experimental knowledge from the known high-Tc superconductors are followed. CaFe4As3 is a newly discovered 3D compound, with Fe2+ in tetrahedral coordination, similar to that in the parent compounds of the known superconductors. The thermodynamic and transport properties reveal a spin density wave (SDW) transition at TN = 88 K, and an incommensurate-to-commensurate SDW transition at T2=26.4 K. A large electronic specific heat coefficient γ=0.02 J/molK^2 and an unusually high Kadowaki-Woods (KW) ratio A/γ^2=55×10E−5 μΩcm mol^2K^2/mJ^2 point to strong electron correlations. While the commensurate SDW state below T2 is suppressed in Co-doped CaFe4As3, neither doping with P, Yb, Co and Cu, nor application of hydrostatic pressures up to 5 GPa, is able to fully suppress the robust incommensurate SDW order in this system. The new layered compound SrMnBi2 has been studied as a promising candidate for high Tc superconductivity as suggested by theoretical calculations. We found that SrMnBi2 is structurally similar to, but more two dimensional than the known Fe superconductors. Two phase transitions at T1=292 K and T2=252 K have been observed. A large electronic specific heat coefficient γ=36.5 mJ/molK^2 and a KW ratio of 9.38×10E−5 μΩcm mol^2K^2/mJ^2 indicate enhanced electron correlations. DFT calculations have revealed metallic Sr-Bi layers in SrMnBi2, as well as Dirac-cone like features in the band structure. Doping experiments on the Mott insulator Sr2F2Fe2OS2 have been carried out to search for superconductivity at the localized-to-itinerant moment crossover. Increasing amounts of T=Mn in Sr2F2(Fe1−xTx)2OS2 suppress the long range magnetic ordering at x≈0.2, and the subsequent increase in x results in a spin glass behavior for 0.2≤x≤0.5, and possibly a new magnetic order for x≥0.5. By contrast, Co-doping increases the AFM transition from TN=106 K for x=0 up to 124 K for x=0.3. The excitation gap determined from the electrical resistivity is minimized but remains finite around x=0.5 for T=Mn. In addition, a study has been done on a rare binary type I superconductor YbSb2. Besides the superconducting transition at Tc=1.30 K, a possible second superconducting phase is observed below Tc(2)=0.41 K. From thermodynamic and transport measurements, there is strong, unambiguous evidence for the type I nature of the superconductivity in YbSb2.
2

Search for Unconventional Superconductors at the Itinerant-to-Local Moment Crossover

Zhao, Liang 05 June 2013 (has links)
In searching for novel optimal superconductors, three strategic routes based on theoretical and experimental knowledge from the known high-Tc superconductors are followed. CaFe4As3 is a newly discovered 3D compound, with Fe2+ in tetrahedral coordination, similar to that in the parent compounds of the known superconductors. The thermodynamic and transport properties reveal a spin density wave (SDW) transition at TN = 88 K, and an incommensurate-to-commensurate SDW transition at T2=26.4 K. A large electronic specific heat coefficient γ=0.02 J/molK^2 and an unusually high Kadowaki-Woods (KW) ratio A/γ^2=55×10E−5 μΩcm mol^2K^2/mJ^2 point to strong electron correlations. While the commensurate SDW state below T2 is suppressed in Co-doped CaFe4As3, neither doping with P, Yb, Co and Cu, nor application of hydrostatic pressures up to 5 GPa, is able to fully suppress the robust incommensurate SDW order in this system. The new layered compound SrMnBi2 has been studied as a promising candidate for high Tc superconductivity as suggested by theoretical calculations. We found that SrMnBi2 is structurally similar to, but more two dimensional than the known Fe superconductors. Two phase transitions at T1=292 K and T2=252 K have been observed. A large electronic specific heat coefficient γ=36.5 mJ/molK^2 and a KW ratio of 9.38×10E−5 μΩcm mol^2K^2/mJ^2 indicate enhanced electron correlations. DFT calculations have revealed metallic Sr-Bi layers in SrMnBi2, as well as Dirac-cone like features in the band structure. Doping experiments on the Mott insulator Sr2F2Fe2OS2 have been carried out to search for superconductivity at the localized-to-itinerant moment crossover. Increasing amounts of T=Mn in Sr2F2(Fe1−xTx)2OS2 suppress the long range magnetic ordering at x≈0.2, and the subsequent increase in x results in a spin glass behavior for 0.2≤x≤0.5, and possibly a new magnetic order for x≥0.5. By contrast, Co-doping increases the AFM transition from TN=106 K for x=0 up to 124 K for x=0.3. The excitation gap determined from the electrical resistivity is minimized but remains finite around x=0.5 for T=Mn. In addition, a study has been done on a rare binary type I superconductor YbSb2. Besides the superconducting transition at Tc=1.30 K, a possible second superconducting phase is observed below Tc(2)=0.41 K. From thermodynamic and transport measurements, there is strong, unambiguous evidence for the type I nature of the superconductivity in YbSb2.
3

Search for Unconventional Superconductors at the Itinerant-to-Local Moment Crossover

Zhao, Liang 05 June 2013 (has links)
In searching for novel optimal superconductors, three strategic routes based on theoretical and experimental knowledge from the known high-Tc superconductors are followed. CaFe4As3 is a newly discovered 3D compound, with Fe2+ in tetrahedral coordination, similar to that in the parent compounds of the known superconductors. The thermodynamic and transport properties reveal a spin density wave (SDW) transition at TN = 88 K, and an incommensurate-to-commensurate SDW transition at T2=26.4 K. A large electronic specific heat coefficient γ=0.02 J/molK^2 and an unusually high Kadowaki-Woods (KW) ratio A/γ^2=55×10E−5 μΩcm mol^2K^2/mJ^2 point to strong electron correlations. While the commensurate SDW state below T2 is suppressed in Co-doped CaFe4As3, neither doping with P, Yb, Co and Cu, nor application of hydrostatic pressures up to 5 GPa, is able to fully suppress the robust incommensurate SDW order in this system. The new layered compound SrMnBi2 has been studied as a promising candidate for high Tc superconductivity as suggested by theoretical calculations. We found that SrMnBi2 is structurally similar to, but more two dimensional than the known Fe superconductors. Two phase transitions at T1=292 K and T2=252 K have been observed. A large electronic specific heat coefficient γ=36.5 mJ/molK^2 and a KW ratio of 9.38×10E−5 μΩcm mol^2K^2/mJ^2 indicate enhanced electron correlations. DFT calculations have revealed metallic Sr-Bi layers in SrMnBi2, as well as Dirac-cone like features in the band structure. Doping experiments on the Mott insulator Sr2F2Fe2OS2 have been carried out to search for superconductivity at the localized-to-itinerant moment crossover. Increasing amounts of T=Mn in Sr2F2(Fe1−xTx)2OS2 suppress the long range magnetic ordering at x≈0.2, and the subsequent increase in x results in a spin glass behavior for 0.2≤x≤0.5, and possibly a new magnetic order for x≥0.5. By contrast, Co-doping increases the AFM transition from TN=106 K for x=0 up to 124 K for x=0.3. The excitation gap determined from the electrical resistivity is minimized but remains finite around x=0.5 for T=Mn. In addition, a study has been done on a rare binary type I superconductor YbSb2. Besides the superconducting transition at Tc=1.30 K, a possible second superconducting phase is observed below Tc(2)=0.41 K. From thermodynamic and transport measurements, there is strong, unambiguous evidence for the type I nature of the superconductivity in YbSb2.
4

Search for Unconventional Superconductors at the Itinerant-to-Local Moment Crossover

Zhao, Liang 05 June 2013 (has links)
In searching for novel optimal superconductors, three strategic routes based on theoretical and experimental knowledge from the known high-Tc superconductors are followed. CaFe4As3 is a newly discovered 3D compound, with Fe2+ in tetrahedral coordination, similar to that in the parent compounds of the known superconductors. The thermodynamic and transport properties reveal a spin density wave (SDW) transition at TN = 88 K, and an incommensurate-to-commensurate SDW transition at T2=26.4 K. A large electronic specific heat coefficient γ=0.02 J/molK^2 and an unusually high Kadowaki-Woods (KW) ratio A/γ^2=55×10E−5 μΩcm mol^2K^2/mJ^2 point to strong electron correlations. While the commensurate SDW state below T2 is suppressed in Co-doped CaFe4As3, neither doping with P, Yb, Co and Cu, nor application of hydrostatic pressures up to 5 GPa, is able to fully suppress the robust incommensurate SDW order in this system. The new layered compound SrMnBi2 has been studied as a promising candidate for high Tc superconductivity as suggested by theoretical calculations. We found that SrMnBi2 is structurally similar to, but more two dimensional than the known Fe superconductors. Two phase transitions at T1=292 K and T2=252 K have been observed. A large electronic specific heat coefficient γ=36.5 mJ/molK^2 and a KW ratio of 9.38×10E−5 μΩcm mol^2K^2/mJ^2 indicate enhanced electron correlations. DFT calculations have revealed metallic Sr-Bi layers in SrMnBi2, as well as Dirac-cone like features in the band structure. Doping experiments on the Mott insulator Sr2F2Fe2OS2 have been carried out to search for superconductivity at the localized-to-itinerant moment crossover. Increasing amounts of T=Mn in Sr2F2(Fe1−xTx)2OS2 suppress the long range magnetic ordering at x≈0.2, and the subsequent increase in x results in a spin glass behavior for 0.2≤x≤0.5, and possibly a new magnetic order for x≥0.5. By contrast, Co-doping increases the AFM transition from TN=106 K for x=0 up to 124 K for x=0.3. The excitation gap determined from the electrical resistivity is minimized but remains finite around x=0.5 for T=Mn. In addition, a study has been done on a rare binary type I superconductor YbSb2. Besides the superconducting transition at Tc=1.30 K, a possible second superconducting phase is observed below Tc(2)=0.41 K. From thermodynamic and transport measurements, there is strong, unambiguous evidence for the type I nature of the superconductivity in YbSb2.
5

Transição metal-isolante com repulsão coulombiana de alcance infinito: estatística fracionária e estado fundamental. Mecânica estatística de polímeros magnéticos

Vitoriano dos Santos Júnior, Carlindo January 2000 (has links)
Made available in DSpace on 2014-06-12T18:03:00Z (GMT). No. of bitstreams: 2 arquivo7692_1.pdf: 156573 bytes, checksum: efbcda03282532417ac013b427e5ca96 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2000 / A versão de ALCANC infinito da hamiltoniana de Hubbard pode ser resolvida exatamente em qualquer dimensão. Em banda semi-cheia, o modelo apresenta uma transição metal-isolante (Mott) como função da interação quando seu valor é exatamente igual à largura da banda. Em nosso trabalho, estudamos este modelo em uma dimensão, onde o calculo exato da função de Green de 1- partícula permite obter a densidade de estudos modificada pela interação. Um diagrama de fase é então obtido. Obtemos também a função de correlação densidade-densidade e a susceptibilidade magnética do sistema. Em dimensão d>2, utilizamos uma densidade de estados parabólica e obtivemos numericamente várias das quantidades acima mencionadas. Nossos resultados evidenciaram diversas características microscópicas da transição Mott neste modelo
6

Spin-Orbital Order and Condensation in 4d and 5d Transition Metal Oxides

Svoboda, Christopher January 2017 (has links)
No description available.
7

Universalité du crossover de Mott à demi-remplissage et effets de la répulsion coulombienne aux premiers voisins sur la dynamique supraconductrice des isolants de Mott dopés aux trous

Reymbaut, Alexis January 2016 (has links)
Le mécanisme d'appariement donnant naissance à la supraconductivité non conventionnelle reste disputé à ce jour. Une des principales difficultés sous-jacentes nous vient du lien entre cette supraconductivité et la physique de Mott. Dans le but d'éclaircir cela, cette thèse propose de traiter trois points. Tout d'abord, nous nous intéressons aux crossovers caractérisant le régime à haute température du modèle de Hubbard demi-rempli, soit dans une situation où les fluctuations à grande longueur d'onde et même l'ordre à longue portée suggèrent que la transition de Mott n'est pas pertinente. En comparant les résultats issus de la théorie de champ moyen dynamique (DMFT), de la théorie de champ moyen dynamique cellulaire (CDMFT), et de l'approximation d'amas dynamique (DCA), nous montrons que, bien que la plupart des crossovers soient masqués par la température de Néel, le crossover de Mott (séparant le mauvais isolant de l'isolant de Mott et caractérisé par l'ouverture prononcée du gap de Mott) survit à toute température. De plus, les différentes techniques numériques voient leurs crossovers de Mott se rejoindre à une température de l'ordre de $0.45\, t$, démontrant qu'à ces températures, l'effet est dominé par la physique à très courte portée. La deuxième partie de cette thèse cherche à rendre possible l'extraction de quantités donnant accès à la dynamique supraconductrice à température finie, telle que la fonction spectrale anormale, \textit{via} la méthode d'entropie maximale. Nous avons ainsi développé la méthode MaxEntAux qui permet de calculer la fonction spectrale anormale à partir d'une fonction spectrale auxiliaire et de fonctions spectrales normales, toutes de signe constant positif et donc toutes calculables à travers la méthode d'entropie maximale. La dernière partie de cette thèse applique la méthode MaxEntAux à l'étude de la dynamique supraconductrice d'un isolant de Mott dopé aux trous et décrit par le modèle de Hubbard étendu, incorporant l'effet de la répulsion aux premiers voisins $V$. Nous montrons que $V$ joue deux rôles antagonistes dans la dynamique supraconductrice: cette répulsion renforce l'appariement à basse fréquence à travers la constante d'échange antiferromagnétique $J = 4t^2/(U-V)$ tout en accroissant la répulsion coulombienne à haute fréquence. La compétition non triviale qui en résulte tend à augmenter la température critique à faible dopage et à la diminuer à fort dopage. En parallèle, les valeurs du célèbre rapport $\Delta_{SC}/T_c$ que nous obtenons sont significativement plus grandes que les valeurs prédites par la théorie BCS, mais sont en très bel accord avec l'expérience et présentent une certaine universalité, notamment dans le régime de dopages intermédiaires. Enfin, $V$ semble également pousser le système étudié vers un ordre de charge commensurable en y favorisant la double occupation.
8

Études spectroscopiques des nouveaux états électroniques induits par fort couplage spin-orbite dans les iridates / Spectroscopic studies of novel electronic states induced by strong spin-orbit coupling in iridates

Louat, Alex 04 December 2018 (has links)
L'étude de l'état isolant de Mott est un des domaines très actif de la recherche en matière condensée car les fortes corrélations qui en sont à l'origine donnent naissance à des états de la matière très variés et avec des applications potentielles. Sr₂IrO₄ est un isolant de Mott exotique car induit par un fort couplage spin-orbite. Il permet d'étudier l'impact des corrélations électroniques sur les propriétés de basses énergies sous un angle nouveau. L'objet de cette thèse est l'étude expérimentale des propriétés électroniques de ces composés iridates par des mesures d'ARPES permettant des observations directes de la structure électronique dans l'espace réciproque et de RMN et μSR, qui donnent une vision locale dans l'espace réel. Nous nous sommes en particulier intéressés à la transition isolant métal pouvant survenir en dopant ce composé. Une façon originale de doper Sr₂IrO₄ que nous avons étudiée en détails est de substituer l'iridium par du rhodium. Les deux sont isovalents, mais le rhodium capture un électron conduisant à un dopage effectif en trous. Grâce à l’ARPES, nous avons mis en évidence les différentes bandes de la structure électronique. Nous avons étudié attentivement le caractère orbital de ces bandes et mis en évidence des anisotropies résiduelles en certains points de l’espace réciproque, survivant malgré la présence du fort couplage spin-orbite. Ceci, ainsi que des effets de repliement de la structure électronique, donnent lieu à des variations brutales d'intensité, qui doivent être prises en compte pour analyser correctement les spectres. Lors du dopage avec le Rh, la phase métallique obtenue reste très incohérente, avec une absence de pic de quasiparticule et un pseudogap uniforme sur l'ensemble de la surface de Fermi. Le gap de Mott ne semble pas se fermer. Le pseudogap peut révéler une brisure de symétrie mais aussi l’effet du désordre introduit par le Rh et nous discuterons son origine, en lien avec la physique d’autres systèmes corrélés. Nous montrons que pour de faibles taux de substitution Ir/Rh, l’ajout de porteurs trous contrôle le comportement du système alors qu’à des taux de substitutions plus élevés, le nombre de porteurs est stable mais le désordre augmente et contrôle à son tour la physique. Nous nous sommes aussi intéressés aux propriétés électroniques et magnétiques sondées par la RMN de l'oxygène 17 sur poudre et poudre orientée et par μSR. La RMN permet de différencier les deux sites d'oxygène de Sr₂IrO₄ nous permettant de déterminer certains paramètres nucléaires préalables à l'étude fine des propriétés électroniques. Dans le composé pur, nous avons étudié la transition magnétique et observé ce qui semble être le développement d'un moment sur l'oxygène apical. Dans les composés dopés, nous ne voyons pas de désordre structural important malgré des taux de dopage allant jusqu'à 15% de rhodium. Les propriétés magnétiques présentent néanmoins des signes d’inhomogénéité, plus marqués dans le cas du dopage lanthane. Les fluctuations dans le composé métallique montrant une prédominance des corrélations antiferromagnétiques. De son côté, la μSR a permis de construire le diagramme de phases de la transition antiferromagnétique et de mettre en évidence l'inhomogénéité de la transition magnétique dans les échantillons faiblement dopés. À basse température, nous confirmons que la phase magnétique évolue, peut-être avec l’apparition d’un moment sur l’oxygène, et cet effet est même renforcé dans les composés faiblement dopés. Au-dessus de la température de transition antiferromagnétique, nous n'avons pas trouvé de signature d'une transition vers une phase de boucles de courant observée par d'autres techniques. Cette étude permet d’attribuer à Sr₂IrO₄ dopé rhodium le caractère assez rare de matériau 2D fortement corrélé à désordre contrôlé. De manière plus générale, cet exemple devrait permettre de mieux comprendre les effets éventuels de désordre associés à d’autre façons de doper les iridates. / The study of the insulating Mott state is a very active field of research in condensed matter because of the strong correlations usually at play which can lead to a large variety of states of matter, with potential applications. Sr₂IrO₄ is an exotic Mott insulator because it is induced by a strong spin-orbit coupling. It allows studying the impact of electronic correlations on the low energy properties from a new viewpoint. The subject of this thesis is the experimental study of the electronic properties of these iridate compounds by ARPES measurements allowing direct observations of the electronic structure in reciprocal space and NMR and μSR, which give a local view in real space. We have in particular studied the metal to insulator transition which can occur in this compound upon doping. An original way to dope Sr₂IrO₄ that we have investigated in details is to substitute iridium by rhodium. Both are isovalent but the rhodium captures an electron leading to an effective hole doping. Thanks to ARPES we have identified the different bands in the electronic structure. We have studied in details the orbital character of these bands and pointed out residual anisotropies at some points in the reciprocal space, which survive despite the strong spin-orbit coupling. This, as well as the folding effects of the electronic structure, give rise to sudden variations in intensity, which must be taken into account in order to correctly analyze the spectra. Upon doping with Rh, the obtained metallic phase remains very incoherent, with no quasiparticle peak and a uniform pseudogap over the full Fermi surface. The Mott gap does not seem to be closing. The pseudogap can reveal symmetry breaking but also the effect of the disorder introduced by the Rh and we will discuss its origin, in relation to the physics of other correlated systems. We show that for low Ir/Rh substitution rates, the addition of hole carriers controls the behavior of the system while at higher substitution rates, the number of carriers is stable but the disorder increases and in turn controls physics.We were also interested in the electronic and magnetic properties probed by 17 oxygen NMR on powder and oriented powder samples and by μSR. NMR makes it possible to differentiate the two oxygen sites in Sr₂IrO₄ allowing determining some nuclear parameters necessary to the fine study of the electronic properties. In the pure compound, we have studied the magnetic transition and observed what appears to be the development of a moment on the apical oxygen. In the doped compounds, we do not see any significant structural disorder despite doping levels up to 15% rhodium. However, the magnetic properties nevertheless show signs of inhomogeneity, which are more pronounced in the case of lanthanum doping. The fluctuations in the correlated metal compound show a predominance of antiferromagnetic correlations. From our μSR investigation, we could construct the magnetic phase diagram which highlights the inhomogeneity of the magnetic transition in the low-doped samples. At low temperature, we confirm that the magnetic phase evolves, perhaps with the appearance of a moment on the oxygen, and this effect is even enhanced in the lightly doped compounds. Above the antiferromagnetic transition temperature, we did not find signatures of the current loop phase observed by other techniques. This study makes it possible to attribute to Sr₂IrO₄ doped with rhodium the rather rare character of strongly correlated 2D material with controlled disorder. More generally, this example should provide a better understanding of the potential effects of disorder associated with other ways to dope iridates.
9

TUNNELING SPECTROSCOPY STUDY OF CALCIUM RUTHENATE

Bautista, Anthony 01 January 2010 (has links)
The ruthenates are perhaps one of the most diverse group of materials known up to date. These compounds exhibit a wide array of behaviors ranging from the exotic pwave superconductivity in Sr2RuO4, to the itinerant ferromagnetism in SrRuO3, and the Mott-insulating behavior in Ca2RuO4. One of the most intriguing compounds belonging to this group is Ca3Ru2O7 which is known to undergo an antiferromagnetic ordering at 56K and an insulating transition at 48K. Most intriguing, however, is the behavior displayed by this compound in the presence of an external magnetic field. For fields parallel to the a-axis, the compound undergoes a metamagnetic transition into the ferromagnetic region at 6 T. If the external field direction is changed to the b-axis then the result will be different. colossal magnetoresistance occurs and a fall in reistivity of up to three orders of magnitude is recorded at fields of 15T. Most interesting, however, is the energy gap observed for this material. A number of groups have measured such gap with different methods and found conflicting results. For this reason it was of vital importance to perform measurements on this compound and try to resolve this issue. Tunneling spectroscopy is one of the most powerful techniques which can be used to probe the electronic properties of a material. The method is best suited to measure the density of states of a material and hence the nature of the strong correlations which dictate the properties of the compound. We performed a series of tunneling spectroscopy measurements by means of planar tunnel junctions. These types of junctions were chosen because of their stability over a large temperature range and their stability in the presence of an external field. The anisotropies which showed up in the resistivity and magnetization measurements manifested also in our data. For tunneling parallel to the a-axis, we observed a gap opening at 48K with a width a peak to peak width of 2Δa ~258±15meV. As the temperature was lowered, the gap size increased reaching a maximum width of 2Δa ~ 845±38meVat 4.2K. Tunneling parallel to the b-axis, the gap has a much smaller size than the a-axis gap. At 48K the gap width is about 2Δb ~ 201±13 meV and reaches a maximum width of 2Δb ~ 366±33 meV at 4.2K. For the c-axis, the situation is different since the gap opens at 56K instead of 48K. The gap width at 56K is about 2Δc ~ 102±6meV and reaches a maximum width of 2Δc ~ 179±14 meV at 4.2K. In the presence of an external field, we noticed that the overall behavior was always the same in the ab-plane but differed in c-axis direction. In our experiment, an external field was applied along the a-axis and measurements were made at 4.2K. For aaxis tunneling, the gap width decreased to a value of 2Δa ~ 587±27 meV at 4.2 K at 7T. On the other hand, the gap width in the b-axis direction decreased to a value of 2Δb ~ 308±25 meV for the same field. For the c-axis direction, the gap decreased to a value of 2Δc ~ 112±8 meV at 7T. The DOS of the c-axis differs for fields of 6T and above. A third peak emerges inside the gap on the valence side of the DOS. This third peak seems to be a direct consequence of the metamagnetic transition at 6T observed by other groups and may be attributable to a spin-filtering effect.
10

Transition de Mott et supraconductivité dans les matériaux organiques

Bourassa, Louis January 2017 (has links)
Dans ces travaux, nous avons étudié la rigidité superfluide en CDMFT (théorie du champ moyen dynamique sur amas) dans les matériaux organiques supraconducteurs. Ceux-ci appartiennent à la catégorie des supraconducteurs à haute température. Nous obtenons des résultats, en accord qualitatif avec l'expérience, qui suivent la tendance suggérée par la loi dite de Homes. La température critique et la masse effective ont donc également été calculées à des fins d'analyses. Ces dernières quantités sont également en accord avec l'expérience et les travaux antérieurs.

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