发表机构
Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学卡弗里纳米科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究短超导结的环境诱导基态和附加能量的相互作用修正，推导通用公式，分析两种环境模型及三种特殊情况，发现无量纲尺度$L G_Q \Delta$是更优估计，指出非超导贡献并概述非微扰模型。
AI 中文摘要
本文对短超导结中环境诱导的基态和附加能量的相互作用修正进行了详细的理论研究。我们推导了这些修正的通用公式，将其与结的频率相关导纳和环境阻抗关联起来。我们指定了两种环境模型：外部阻抗模型和Mattis-Bardeen模型。在这两种模型中，我们假设$G_Q Z \ll 1$，其中$G_Q$是电导量子，$Z$是典型环境电阻。虽然预期相对修正的典型尺度为$G_Q Z$量级，但我们发现，在许多情况下，无量纲尺度$L G_Q \Delta$能提供更好的估计，其中$\Delta$是超导能隙，$L$是外部电感。我们讨论了能量受低频和高频相位涨落的对数重整化，并指出了与传输本征值重整化相关的非超导贡献。我们详细研究了以下情况中修正的特殊性：i. 小相位下，相互作用导致电流跳变；ii. 安德烈夫束缚态能量接近能隙边缘；iii. 安德烈夫束缚态能量接近费米能级。在所有这些情况下，即使$G_Q Z \ll 1$，修正也可能与未受扰能量相当，并且我们简要概述了适用于这些情况的非微扰模型。
英文摘要
Here we present a detailed theoretical investigation of the environment-induced interaction correction to the ground states and addition energies in a short superconducting junction. We derive general formulas for these corrections linking them to the frequency-dependent admittance of the junction and the environment impedance. We specify two environmental models: that of an external impedance and the Mattis-Bardeen model. In both cases we assume $G_Q Z \ll 1$, where $G_Q$ is the conductance quantum and $Z$ the typical environmental resistance. While an expectation is that the typical scale of the relative correction is of the order $G_Q Z$, we have found that in many cases the dimensionless scale $L G_Q Δ$ provides a better estimation, where $Δ$ is the superconducting energy gap and $L$ an external inductance. We discuss the logarithmic renormalizations of the energies by low- and high-frequency phase fluctuations and single out a non-superconducting contribution related to the renormalization of transmission eigenvalues. We investigate in detail the peculiarities of the corrections at: i. small phases, where the interaction causes a current jump, ii. Andreev bound state energies close to the gap edge, iii. Andreev bound state energies close to Fermi level. In all these cases the correction may become comparable with the unperturbed energy, even for $G_Q Z \ll 1$, and we briefly sketch non-perturbative models relevant for the situations.
Comments18 + 18 pages, 12 + 4 figures
