Department of Physics, Cornell University, Ithaca, NY 14853.
Proc Natl Acad Sci U S A. 2023 Mar 14;120(11):e2217816120. doi: 10.1073/pnas.2217816120. Epub 2023 Mar 10.
Superconductivity is a macroscopic manifestation of a quantum phenomenon where pairs of electrons delocalize and develop phase coherence over a long distance. A long-standing quest has been to address the underlying microscopic mechanisms that fundamentally limit the superconducting transition temperature, . A platform which serves as an ideal playground for realizing "high"-temperature superconductors are materials where the electrons' kinetic energy is quenched and interactions provide the only energy scale in the problem. However, when the noninteracting bandwidth for a set of isolated bands is small compared to the interactions, the problem is inherently nonperturbative. In two spatial dimensions, is controlled by superconducting phase stiffness. Here, we present a theoretical framework for computing the electromagnetic response for generic model Hamiltonians, which controls the maximum possible superconducting phase stiffness and thereby , without resorting to any mean-field approximation. Our explicit computations demonstrate that the contribution to the phase stiffness arises from i) "integrating out" the remote bands that couple to the microscopic current operator and ii) the density-density interactions projected on to the isolated narrow bands. Our framework can be used to obtain an upper bound on the phase stiffness and relatedly for a range of physically inspired models involving both topological and nontopological narrow bands with density-density interactions. We discuss a number of salient aspects of this formalism by applying it to a specific model of interacting flat bands and compare the upper bound against the known from independent numerically exact computations.
超导性是一种宏观量子现象，其中电子对离域并在长距离上发展出相位相干性。长期以来，人们一直在研究基本限制超导转变温度的微观机制。一个可以作为实现“高温”超导体的理想平台的材料是电子动能被猝灭且相互作用提供问题中唯一能量尺度的材料。然而，当一组孤立能带的无相互作用带宽与相互作用相比很小时，问题本质上是非微扰的。在二维空间中，由超导相位硬度控制。在这里，我们提出了一个计算任意模型哈密顿量的电磁响应的理论框架，该框架控制着最大可能的超导相位硬度，从而控制着。无需采用任何平均场近似。我们的显式计算表明，相位硬度的贡献来自于：i）“积分”与微观电流算子耦合的远程能带，以及 ii）密度-密度相互作用在孤立窄带的投影。我们的框架可用于获得与物理启发模型相关的相位硬度和相关的上限，这些模型涉及具有密度-密度相互作用的拓扑和非拓扑窄带。我们通过将其应用于相互作用的扁平能带的特定模型并将上限与独立的数值精确计算得到的已知进行比较，讨论了该形式主义的一些突出方面。
