[论文解读] Generalization of BCS theory to short coherence length superconductors: A BCS--Bose-Einstein crossover scenario

Qijin Chen|arXiv (Cornell University)|Jan 19, 2018

Physics of Superconductivity and Magnetism参考文献 2被引用 9

一句话总结

该论文通过BCS-Bose-Einstein凝聚（BEC）交叉框架，将BCS理论推广至短相干长度超导体，将动量非零的成对态与单粒子态同等处理。该理论解释了欠掺杂铜氧化物中的序参量Δsc与能隙Δ的差异，定量再现了相图、穿透深度、比热，并预测了与实验一致的低温幂律行为。

ABSTRACT

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.

研究动机与目标

• 将BCS理论从弱耦合区扩展至描述短相干长度超导体。
• 解决标准BCS理论在解释欠掺杂铜氧化物中序参量与能隙差异时的失效问题。
• 提供一个统一框架，使费米子超导与玻色子BEC成为同一现象的两种视角。
• 定量预测高Tc超导体中的实验可观测量，如穿透深度与比热。
• 通过非相干成对激发解释比热中线性-T项与低温幂律行为的起源。

提出的方法

• 发展了一套适用于任意配对强度的BCS–Bose-Einstein凝聚交叉形式化方法。
• 利用Dyson方程与T矩阵方法，描述超越平均场BCS理论的配对关联。
• 在自洽平均场方案中，将单粒子准粒子与动量非零的库珀对同等处理。
• 通过有限温度下低于Tc的赝能隙态，引入非相干成对贡献。
• 从正常态的稳定性条件推导出超导转变温度Tc。
• 将该形式化方法应用于铜氧化物，仅使用一个自由参数即可拟合实验相图并提取物理量。

实验结果

研究问题

• RQ1 BCS理论如何推广以描述短相干长度超导体？
• RQ2 欠掺杂铜氧化物中序参量Δsc与能隙Δ的物理起源是什么？
• RQ3 统一的BCS–Bose-Einstein凝聚交叉框架能否定量描述高Tc超导体的热力学性质？
• RQ4 非相干、动量非零的成对态在决定低温比热异常中起什么作用？
• RQ5 费米子准粒子与玻色子成对激发的共同贡献如何解释超流密度的准普遍行为？

主要发现

• 该理论仅用一个自由参数即可定量再现铜氧化物的相图，与不同空穴掺杂下的实验数据高度吻合。
• 归一化的平面内超流密度随归一化温度表现出准普遍行为，其物理机制源于准粒子与成对激发的补偿性贡献。
• 比热中的线性-T项源于非相干成对通道中的玻色子成对激发，具有内在起源。
• 低温比热的幂律行为由非相干成对贡献预测得出，与现有实验观测一致。
• 在Tc处出现的比热尖锐特征，源于长程超导序的出现，尽管能隙本身保持平滑，与实验观测相符。
• Δ与Δsc之间的差异可物理地归因于随着配对强度增强，动量非零成对态的主导性逐渐增强。