Two-Dimensional Hubbard Modelat Low Electron Density

Fukuyama, Hidetoshi; Hasegawa, Yūko; Narikiyo, Osamu

doi:10.1143/jpsj.60.2013

Cited by 69 publications

(34 citation statements)

References 20 publications

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“…The authors considered 3D and 2D Hubbard model at low electron densities. In agreement with T-matrix Kanamori ideas [82] they came to the conclusion that Hubbard model at low density is equivalent to the Fermi-gas model with the effective gas parameters given by 0 [83]. As a result they got the same T C 's of triplet p-wave pairing as in the case of Fermi-gas under the substitution of r 0 on d [82] in gas parameters in the Eqs.…”

Section: I) Introductionsupporting

confidence: 66%

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

Kagan

2016

Jetp Lett.

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In a short review-article we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn-Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin-Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T C of the order of 100 K) we should proceed to the t-J model with the Van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we stress that to describe superconductivity in metallic hydrogen alloys under pressure (with T C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron-phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal-Eliashberg strong coupling theory or even Fermi-Bose mixture theory of Alexandrov, Ranninger and its generalizations. I) IntroductionRecent discovery of Cooper pairing at 190 K in metallic hydrogen sulfide H 2 S under high pressure revives our hopes to move forward from high-temperature to room-temperature superconductivity [1][2][3][4][5]. In the same time there are many interesting low-temperature superconducting systems with anomalous types of pairing and a nontrivial structure of the order parameter.In the beginning of the review-article we discuss the mechanisms of unconventional superconductivity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We briefly discuss the phase-diagrams of these systems in free space and on the lattice and find the areas of the superconductive state in the framework of the Fermi-gas model with hard core repulsion, the Hubbard model [6] and the Shubin-Vonsovsky model [7,8]. We demonstrate that the critical superconductive temperature can be greatly increased in the spinpolarized case or in a two-band situation already at low densities.The proposed theory is based on the Kohn-Luttinger mechanism of superconductivity [9] and its generalizations and explains or predicts p-, d-, f-and anomalous s-wave pairing in various materials such as the idealized monolayer and bilayer graphene, heavy-fermion systems, layered

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Section: I) Introductionsupporting

confidence: 66%

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

Kagan

2016

Jetp Lett.

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“…At T = 0, a static particle-hole polarization bubble Π(q, ω = 0, T = 0) in D = 2 has an asymmetric square root singularity at q → 2k F + 0 [39,40,44,45]. A finite T or finite ω soften the singularity and yield Π(q, ω, T ) − Π(q, 0, 0) ∝ max{T, ω} in the momentum range |q − 2k F | ∼ T /v F [31,40,46]. A simple calculation shows that fermions which contribute to δχ s (0, T ) have energies of order ∼ T and are located in a narrow angular range where the angle θ between vectors k and q is almost π :…”

Section: Introductionmentioning

confidence: 99%

Nonanalytic corrections to the Fermi-liquid behavior

2003

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The issue of non-analytic corrections to the Fermi-liquid behavior is revisited. Previous studies have indicated that the corrections to the Fermi-liquid forms of the specific heat and the static spin susceptibility scale as T D and T D−1 , respectively (with extra logarithms for D = 1, 3). In addition, the non-uniform spin susceptibility is expected to depend on the bosonic momentum Q in a non-analytic way, i.e., as Q D−1 (again with extra logarithms for D = 1, 3). It is shown that these non-analytic corrections originate from the universal singularities in the dynamical bosonic response functions of a generic Fermi liquid. In contrast to the leading, Fermi-liquid forms which depend on the interaction averaged over the Fermi surface, the non-analytic corrections are parameterized by only two coupling constants, which are the components of the interaction potential at momentum transfers q = 0 and q = 2kF . For 3D systems, a recent result of Belitz, Kirkpatrick and Vojta for the spin susceptibility is reproduced and the issue why a non-analytic momentum dependence of the non-uniform spin susceptibility (Q 2 ln |Q|) is not paralleled by a non-analyticity in the T − dependence (T 2 ) is clarified. For the case of a 2D system with a finite-range interaction, explicit forms of the corrections to the specific heat (∝ T 2 ), uniform (∝ T ) and non-uniform (∝ |Q|) spin susceptibilities are obtained. It is shown that previous calculations of the temperature dependences of these quantities in 2D were incomplete. Some of the results and conclusions of this paper have recently been announced in a short communication [A. V. Chubukov and D. L. Maslov, cond-mat/0304381].

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“…В развернувшейся после работ Андерсона дискуссии приняло участие большое число теоретиков. Большинство из них (Энгельбрехт и Рандей ра [55], Фукуяма [56], Фабрицио -Тоссати -Парола [57], Прокофьев -Стамп [58], Баранов -Каган -Марьенко [59]) придерживаются ферми газовой идеоло гии и доказывают ее внутреннюю непротиворечивость в двумерьи с помощью лестничных и паркетных прибли жений в рамках диаграммной техники. Андерсон про должает настаивать на своей точке зрения, считая, что в двумерьи такая диаграммная техника (даже на уровне суммирования бесконечного ряда паркетных диаграмм) не работает.…”

Section: двумерные монослои как мостик между сверхтекучестью и сверхпunclassified

Fermi-gas approach to the problem of superfluidity in three- and two- dimensional solutions of <sup>3</sup>He in <sup>4</sup>He

Kagan¹

1994

Uspekhi Fizicheskikh Nauk

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Two-Dimensional Hubbard Modelat Low Electron Density

Cited by 69 publications

References 20 publications

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

Nonanalytic corrections to the Fermi-liquid behavior

Fermi-gas approach to the problem of superfluidity in three- and two- dimensional solutions of <sup>3</sup>He in <sup>4</sup>He

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