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首页> 外文期刊>Physical review >Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires
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Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

机译：Luttinger液体线的正常-超导体-正常结的重归一化基团流的系统稳定性分析

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摘要

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an S matrix representing small deviations from a given fixed point S matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2k_F) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.
机译：我们研究了两条Luttinger液体线的超导结的两个末端电导的重整化群流。我们使用SU（4）组的生成器计算与围绕该系统各个固定点的重归一化组流相关的幂定律，以生成S矩阵的适当参数化，该S矩阵表示与给定的固定点S矩阵的小偏差。早在S. Das，S。Rao和A. Saha，物理学。 Rev. B 77，155418（2008）]，然后我们进行全面的稳定性分析。特别是，对于具有中间值的透射，反射，Andreev反射和Andreev交叉反射的非平凡不动点，我们显示出有11个独立的方向可以扰动系统，这些方向是相关的或不相关的，还有五个方向这是边际的。我们获得与这些相关和不相关的扰动相关的幂定律。与两线电荷守恒结的情况不同，这里我们证明存在幂律，它们是V（0）和V（2k_F）的非线性函数[其中V（k）表示电子间相互作用势的傅立叶变换在动量k]。我们还获得了线性响应电导与该固定点附近的电压偏置或温度的幂律关系。

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