Exact solution for finite center-of-mass momentum Cooper pairing
Exact solution for finite center-of-mass momentum Cooper pairing
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DOI：
10.1103/physrevb.108.174506
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发表时间：
2022-09
影响因子：
3.7
通讯作者：
C. Setty;Jinchao Zhao;L. Fanfarillo;E. Huang;P. Hirschfeld;P. Phillips;Kun Yang
中科院分区：
文献类型：
--
作者：
C. Setty;Jinchao Zhao;L. Fanfarillo;E. Huang;P. Hirschfeld;P. Phillips;Kun Yang
电子对密度波 (PDW) 是由包含非零质心动量的电子“库珀对”形成的超导态。它们的特征是空间调制序参数，可能出现在各种新兴量子材料中，例如铜酸盐、过渡金属二硫化物 (TMD) 和 Kagome 金属。尽管进行了大量的理论和数值研究以寻找各种晶格和相互作用设置中的 PDW，但目前还没有通用且稳健的机制支持存在时间反转对称性的超导序参数的调制解在这里，我们研究了受各向异性（$d$波）吸引势影响的两个电子的问题，我们精确地求解了二体薛定谔波动方程，以确定作为质心动量函数的电子对结合能。解决方案中，我们构建了类似BCS的变分多体波函数，并计算了作为质心动量函数的自由能和超导能隙。能量的零温度分析表明，二体问题的结论在多体极限下是稳健的，我们的结果为PDW的存在奠定了理论和微观基础。
Pair density waves (PDWs) are superconducting states formed by ``Cooper pairs"of electrons containing a non-zero center-of-mass momentum. They are characterized by a spatially modulated order parameter and may occur in a variety of emerging quantum materials such as cuprates, transition metal dichalcogenides (TMDs) and Kagome metals. Despite extensive theoretical and numerical studies seeking PDWs in a variety of lattices and interacting settings, there is currently no generic and robust mechanism that favors a modulated solution of the superconducting order parameter in the presence of time reversal symmetry. Here, we study the problem of two electrons subject to an anisotropic ($d$-wave) attractive potential. We solve the two-body Schrodinger wave equation exactly to determine the pair binding energy as a function of the center-of-mass momentum. We find that a modulated (finite momentum) pair is favored over a homogeneous (zero momentum) solution above a critical interaction. Using this insight from the exact two-body solution, we construct a BCS-like variational many-body wave function and calculate the free energy and superconducting gap as a function of the center-of-mass momentum. A zero temperature analysis of the energy shows that the conclusions of the two-body problem are robust in the many-body limit. Our results lay the theoretical and microscopic foundation for the existence of PDWs.