The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length $ξ$ is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small $ξ$ materials, this failure has the potential for widespread impact. Here we have extended BCS theory in a natural way to short $ξ$ superconductors, based on a BCS--BEC crossover scenario, and arrived at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, leading to the distinction between EG and OP. The superconductivity from the fermionic perspective and BEC from the bosonic perspective are just two sides of the same coin. Our theory is capable of making verifiable quantitative predictions. We obtain a cuprate phase diagram (with one free parameter) , in (semi-)quantitative agreement with experiment. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations provides a natural explanation for the quasi-universal behavior of the in-plane superfluid density versus T. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat. Incoherent pair contributions lead to new low T power laws, consistent with existing experiments. Finally, we demonstrated that the onset of superconducting long range order leads to sharp features in the specific heat at Tc, consistent with experiment.The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length $ξ$ is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small $ξ$ materials, this failure has the potential for widespread impact. Here we have extended BCS theory in a natural way to short $ξ$ superconductors, based on a BCS--BEC crossover scenario, and arrived at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, leading to the distinction between EG and OP. The superconductivity from the fermionic perspective and BEC from the bosonic perspective are just two sides of the same coin. Our theory is capable of making verifiable quantitative predictions. We obtain a cuprate phase diagram (with one free parameter) , in (semi-)quantitative agreement with experiment. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations provides a natural explanation for the quasi-universal behavior of the in-plane superfluid density versus T. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat. Incoherent pair contributions lead to new low T power laws, consistent with existing experiments. Finally, we demonstrated that the onset of superconducting long range order leads to sharp features in the specific heat at Tc, consistent with experiment.

arXiv:1801.06266Jan 19, 20188 citations

Applying BCS–BEC crossover theory to high-temperature superconductors and ultracold atomic Fermi gases (Review Article)

Q. Chen, K. Levin, J. Stajic

This review is written at the time of the twentieth anniversary of the discovery of high-temperature superconductors, which nearly coincides with the important discovery of the superfluid phases of ultracold trapped fermionic atoms. We show how these two subjects have much in common. Both have been addressed from the perspective of the BCS—Bose–Einstein condensation (BEC) crossover scenario, which is designed to treat short coherence length superfluids with transition temperatures which are “high” with respect to the Fermi energy. A generalized mean field treatment of BCS–BEC crossover at general temperatures T, based on the BCS–Leggett ground state, has met with remarkable success in the fermionic atomic systems. Here we summarize this success in the context of four different cold atom experiments, all of which provide indications, direct or indirect, for the existence of a pseudogap. This scenario also provides a physical picture of the pseudogap phase in the underdoped cuprates which is a central focus of high Tc research. We summarize successful applications of BCS–BEC crossover to key experiments in high Tc systems, including the phase diagram, specific heat, and vortex core STM data, along with the Nernst effect, and exciting recent data on the superfluid density in very underdoped samples.This review is written at the time of the twentieth anniversary of the discovery of high-temperature superconductors, which nearly coincides with the important discovery of the superfluid phases of ultracold trapped fermionic atoms. We show how these two subjects have much in common. Both have been addressed from the perspective of the BCS—Bose–Einstein condensation (BEC) crossover scenario, which is designed to treat short coherence length superfluids with transition temperatures which are “high” with respect to the Fermi energy. A generalized mean field treatment of BCS–BEC crossover at general temperatures T, based on the BCS–Leggett ground state, has met with remarkable success in the fermionic atomic systems. Here we summarize this success in the context of four different cold atom experiments, all of which provide indications, direct or indirect, for the existence of a pseudogap. This scenario also provides a physical picture of the pseudogap phase in the underdoped cuprates which is a central focus of high Tc research. We summarize successful applications of BCS–BEC crossover to key experiments in high Tc systems, including the phase diagram, specific heat, and vortex core STM data, along with the Nernst effect, and exciting recent data on the superfluid density in very underdoped samples.

arXiv:cond-mat/0508603Low Temperature PhysicsApr 1, 200643 citations

a Generalized BCS Approach to the Theory of Superconductivity

Yibin Zheng

Jan 1, 19920 citations

Tracking unconventional superconductivity in the presence of strongly correlated Fermi arcs

Xinyu Zhou, Fei Yang, Miao Liu +2 more

One of the primary reasons that superconductivity in underdoped cuprates is enigmatic is that it emerges from an incoherent Fermi-arc state, so the applicability of the Bardeen-Cooper-Schrieffer (BCS) theory is questionable. Here we approach this problem by investigating unconventional $d$ -wave superconductivity in a recently proposed solvable model for strongly correlated Fermi arcs. We show analytically that the exact incorporation of Fermi arcs fundamentally modifies the BCS equations, which enables us to isolate a many-body effect that suppresses the superconducting transition temperature $T_c$ beyond the simple reduction expected from a shrinking Fermi surface. The theory unambiguously produces: (i) a $T_c$ tracing out a dome as a function of hole doping, (ii) a new low-energy mode upon entering superconductivity, (iii) a suppressed superfluid stiffness in the underdoped regime, and (iv) a gap-to- $T_c$ ratio far exceeding the BCS limit, all consistent with experimental observations in cuprate superconductors. These findings provide an analytic benchmark for understanding how superconductivity emerges from a correlated Fermi-arc state in high- $T_c$ superconductors.One of the primary reasons that superconductivity in underdoped cuprates is enigmatic is that it emerges from an incoherent Fermi-arc state, so the applicability of the Bardeen-Cooper-Schrieffer (BCS) theory is questionable. Here we approach this problem by investigating unconventional $d$-wave superconductivity in a recently proposed solvable model for strongly correlated Fermi arcs. We show analytically that the exact incorporation of Fermi arcs fundamentally modifies the BCS equations, which enables us to isolate a many-body effect that suppresses the superconducting transition temperature $T_c$ beyond the simple reduction expected from a shrinking Fermi surface. The theory unambiguously produces: (i) a $T_c$ tracing out a dome as a function of hole doping, (ii) a new low-energy mode upon entering superconductivity, (iii) a suppressed superfluid stiffness in the underdoped regime, and (iv) a gap-to-$T_c$ ratio far exceeding the BCS limit, all consistent with experimental observations in cuprate superconductors. These findings provide an analytic benchmark for understanding how superconductivity emerges from a correlated Fermi-arc state in high-$T_c$ superconductors.

arXiv:2603.24977Mar 26, 20260 citations

The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length

ξ

is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small

ξ

materials, this failure has the potential for widespread impact. Here we have extended BCS theory in a natural way to short

ξ

superconductors, based on a BCS--BEC crossover scenario, and arrived at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, leading to the distinction between EG and OP. The superconductivity from the fermionic perspective and BEC from the bosonic perspective are just two sides of the same coin. Our theory is capable of making verifiable quantitative predictions. We obtain a cuprate phase diagram (with one free parameter) , in (semi-)quantitative agreement with experiment. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations provides a natural explanation for the quasi-universal behavior of the in-plane superfluid density versus T. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat. Incoherent pair contributions lead to new low T power laws, consistent with existing experiments. Finally, we demonstrated that the onset of superconducting long range order leads to sharp features in the specific heat at Tc, consistent with experiment.

d

-wave superconductivity in a recently proposed solvable model for strongly correlated Fermi arcs. We show analytically that the exact incorporation of Fermi arcs fundamentally modifies the BCS equations, which enables us to isolate a many-body effect that suppresses the superconducting transition temperature

T_c

beyond the simple reduction expected from a shrinking Fermi surface. The theory unambiguously produces: (i) a

T_c

tracing out a dome as a function of hole doping, (ii) a new low-energy mode upon entering superconductivity, (iii) a suppressed superfluid stiffness in the underdoped regime, and (iv) a gap-to-

T_c

ratio far exceeding the BCS limit, all consistent with experimental observations in cuprate superconductors. These findings provide an analytic benchmark for understanding how superconductivity emerges from a correlated Fermi-arc state in high-

T_c

superconductors.