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Optimal interlayer hopping and high temperature Bose–Einstein condensation of local pairs in quasi 2D superconductors

Kornilovitch, P. E., Hague, J. P.

Published Jan 28, 2015• 6 citations
OpenAlex

Abstract

Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from Bose–Einstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the Bose–Einstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures.

Related papers

Optimal interlayer hopping and high temperature Bose–Einstein condensation of local pairs in quasi 2D superconductors

P E Kornilovitch, J. P. Hague

Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from Bose-Einstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the Bose-Einstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures.

arXiv:1407.3040•Journal of Physics Condensed Matter•Jan 28, 2015•7 citations

BOSE-EINSTEIN CONDENSATION IN QUASI-2D SYSTEMS: APPLICATIONS TO HIGH- T c SUPERCONDUCTIVITY

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We describe high-Tc superconductivity in layered materials within a BCS theory as a BEC of massless-like Cooper pairons satisfying a linear dispersion relation, and propagating within quasi-2D layers of finite width defined by the charge distribution about the CuO_2 planes. We obtain a closed formula for the critical temperature, Tc, that depends on the layer width, the binding energy of Cooper's pairs, and the average in-plane penetration depth. This formula reasonably reproduces empirical values of superconducting transition temperatures for several different cuprate materials near the optimal doping regime, as well as for YBCO films with different doping degrees.

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Physical properties of two-dimensional (2D) superconductors is an active area of long time researches in which many, even principle, questions are still open. One of them is a possibility of a smooth crossover of the system from the standard Bardeen–Cooper–Schrieffer (BCS) regime of strongly overlapping Cooper pairs to the regime of Bose–Einstein condensation (BEC) of almost non-overlapping local pairs. The adequate to the real process description of this transition which can happen either by changing the doping or temperature would lead to a better understanding of the superconducting properties of materials. Though the crossover is not observed in one of the most important layered systems—namely, cuprate superconductors—we demonstrate that in systems with stronger electron-electron attraction it is possible. In particular, in the d-wave channel at sufficiently high doping the crossover can take place with growth of temperature two times, i.e., as BEC→BCS, and followed by reverse BCS→BEC condensation. The physical mechanisms of such transitions and possibility to detect them experimentally in real systems are discussed.

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Trion formation and unconventional superconductivity in a three-dimensional model with short-range attraction

P. E. Kornilovitch

A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schrödinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. By comparing the energy of three-fermion bound clusters (trions) with the energy of one pair plus one free particle, a trion formation threshold is accurately determined, and the region of pair stability is mapped out. It is found that the “close-packed” density of fermion pairs, which is associated with a maximum pair condensation temperature in this model, is the highest in a strongly anisotropic case. It is also argued that pair superconductivity with the highest critical temperature is always close to trion formation, which makes the system prone to phase separation and local charge ordering.

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On Bose-Einstein condensation in quasi-2D systems with applications to high Tc superconductivity II

Carlos Villarreal, MANUEL DE LLANO

We calculate the number and energy densities of a quasi-2D Bose-Einstein gas constrained within a thin region of infinite extent but of finite width d. The BEC critical transition temperature then becomes an explicit function of d. We use this result to construct a model of high-Tc superconductivity in cuprates with a periodic layered atomic structure. The predicted behavior of the BEC Tc agrees with recent experimental findings in severely underdoped cuprates.

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Condensation energy of superconducting BEC of non-interacting Cooper pairs in multilayers

I. Chávez, P. Salas, J. J. Valencia +1 more

Boson-Fermion models of superconductivity are getting attention as they are able to explain some of the high temperature superconductor's properties. Here we report on the condensation energy of a 3D non-interacting mixture of paired fermions (electrons) as Cooper pairs assumed to be composite bosons, which are responsible for carrying superconductivity, plus unpaired fermions both trapped in a periodic multilayer structure like that of the cuasi-two dimensional High-Temperature superconductor planes, generated by applying an external Dirac's comb potential in the direction perpendicular to the planes where superconductivity preferably occurs, while in the other two directions parallel to the planes the mixture moves freely. For bosons we give the Bose-Einstein condensation critical temperature, which we assume is equal to the superconducting critical one, while for both bosons and fermions we give the chemical potential, the internal energy and the entropy, all of them as functions of temperature, in order to calculate the Helmholtz free energy, which we use to obtain the condensation energy of a mixture of $N_F$ ideal fermions (electrons), which after turning on the attractive pair interaction become $N_B = N_{F}/2$ ideal bosons. For several plane impenetrability magnitudes, we calculate the condensation energy as the difference between the free energies of the fermions which are in the normal state minus that of the bosons in the condensed state, where we observe that as the plane impenetrability increases: the condensation energy increases; the critical temperature decreases, as expected for example for cuprate superconductors, and the behavior of the entropy and the internal energy show a dimensional crossover from 3D to 2D.

arXiv:2503.00473•Mar 1, 2025•0 citations
Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from Bose–Einstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the Bose–Einstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures.
Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from Bose-Einstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the Bose-Einstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures.
We describe high-Tc superconductivity in layered materials within a BCS theory as a BEC of massless-like Cooper pairons satisfying a linear dispersion relation, and propagating within quasi-2D layers of finite width defined by the charge distribution about the CuO_2 planes. We obtain a closed formula for the critical temperature, Tc, that depends on the layer width, the binding energy of Cooper's pairs, and the average in-plane penetration depth. This formula reasonably reproduces empirical values of superconducting transition temperatures for several different cuprate materials near the optimal doping regime, as well as for YBCO films with different doping degrees.
Physical properties of two-dimensional (2D) superconductors is an active area of long time researches in which many, even principle, questions are still open. One of them is a possibility of a smooth crossover of the system from the standard Bardeen–Cooper–Schrieffer (BCS) regime of strongly overlapping Cooper pairs to the regime of Bose–Einstein condensation (BEC) of almost non-overlapping local pairs. The adequate to the real process description of this transition which can happen either by changing the doping or temperature would lead to a better understanding of the superconducting properties of materials. Though the crossover is not observed in one of the most important layered systems—namely, cuprate superconductors—we demonstrate that in systems with stronger electron-electron attraction it is possible. In particular, in the d-wave channel at sufficiently high doping the crossover can take place with growth of temperature two times, i.e., as BEC→BCS, and followed by reverse BCS→BEC condensation. The physical mechanisms of such transitions and possibility to detect them experimentally in real systems are discussed.
A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schrödinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. By comparing the energy of three-fermion bound clusters (trions) with the energy of one pair plus one free particle, a trion formation threshold is accurately determined, and the region of pair stability is mapped out. It is found that the “close-packed” density of fermion pairs, which is associated with a maximum pair condensation temperature in this model, is the highest in a strongly anisotropic case. It is also argued that pair superconductivity with the highest critical temperature is always close to trion formation, which makes the system prone to phase separation and local charge ordering.
Boson-Fermion models of superconductivity are getting attention as they are able to explain some of the high temperature superconductor's properties. Here we report on the condensation energy of a 3D non-interacting mixture of paired fermions (electrons) as Cooper pairs assumed to be composite bosons, which are responsible for carrying superconductivity, plus unpaired fermions both trapped in a periodic multilayer structure like that of the cuasi-two dimensional High-Temperature superconductor planes, generated by applying an external Dirac's comb potential in the direction perpendicular to the planes where superconductivity preferably occurs, while in the other two directions parallel to the planes the mixture moves freely. For bosons we give the Bose-Einstein condensation critical temperature, which we assume is equal to the superconducting critical one, while for both bosons and fermions we give the chemical potential, the internal energy and the entropy, all of them as functions of temperature, in order to calculate the Helmholtz free energy, which we use to obtain the condensation energy of a mixture of NFN_FNF​ ideal fermions (electrons), which after turning on the attractive pair interaction become NB=NF/2N_B = N_{F}/2NB​=NF​/2 ideal bosons. For several plane impenetrability magnitudes, we calculate the condensation energy as the difference between the free energies of the fermions which are in the normal state minus that of the bosons in the condensed state, where we observe that as the plane impenetrability increases: the condensation energy increases; the critical temperature decreases, as expected for example for cuprate superconductors, and the behavior of the entropy and the internal energy show a dimensional crossover from 3D to 2D.