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Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling

机译:非平衡中的Kondo模型:电压,温度以及从弱耦合到强耦合的交叉之间的相互作用

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摘要

We consider an open quantum system in contact with fermionic metallic reservoirs in a nonequilibrium setup. For the case of spin, orbital, or potential fluctuations, we present a systematic formulation of real-time renormalization group at finite temperature, where the complex Fourier variable of an effective Liouvillian is used as flow parameter. We derive a universal set of differential equations free of divergencies written as a systematic power series in terms of the frequency-independent two-point vertex only, and solve it in different truncation orders by using a universal set of boundary conditions. We apply the formalism to the description of the weak to strong coupling crossover of the isotropic spin-1/2 nonequilibrium Kondo model at zero magnetic field. From the temperature and voltage dependence of the conductance in different energy regimes, we determine various characteristic low-energy scales and compare their universal ratio to known results. For a fixed finite bias voltage larger than the Kondo temperature, we find that the temperature dependence of the differential conductance exhibits nonmonotonic behavior in the form of a peak structure. We show that the peak position and peak width scale linearly with the applied voltage over many orders of magnitude in units of the Kondo temperature. Finally, we compare our calculations with recent experiments.
机译:我们考虑在非平衡装置中与费米金属储层接触的开放量子系统。对于自旋,轨道或势能波动的情况,我们提出了在有限温度下实时重归一化组的系统表示,其中有效Liouvillian的复傅立叶变量用作流量参数。我们仅根据频率独立的两点顶点派生了一个无散度的通用微分方程组,这些散度被写为系统幂级数,并通过使用一组通用的边界条件以不同的截断阶数求解。我们将形式主义应用于零磁场下各向同性自旋1/2非平衡近藤模型的弱到强耦合交叉的描述。从不同能量状态下电导的温度和电压依赖性,我们确定了各种低能特征量,并将它们的通用比与已知结果进行了比较。对于大于近藤温度的固定有限偏置电压,我们发现差分电导的温度依赖性以峰结构的形式表现出非单调行为。我们显示,峰的位置和峰宽与所施加的电压呈线性关系,且以近藤温度为单位在多个数量级上变化。最后,我们将计算结果与最近的实验进行比较。

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