Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
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DOI：
10.1103/physrevb.93.205432
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发表时间：
2016-03
影响因子：
3.7
通讯作者：
I. Burmistrov;I. Gornyi;A. Mirlin
中科院分区：
文献类型：
--
作者：
I. Burmistrov;I. Gornyi;A. Mirlin
我们发展了无序超导体局域态密度（LDOS）的理论，采用非线性σ模型形式主义和重整化群框架。该理论考虑了所有通道中无序和相互作用耦合的相互作用，平等对待短程和库仑相互作用的系统。我们探讨了在没有相互作用的情况下是安德森绝缘体的二维系统和在没有相互作用的情况下经历安德森转变的二维或三维系统。我们评估了正常无序系统中与LDOS多重分形相关的平均隧穿态密度及其介观涨落。所获得的平均LDOS在费米能附近显示出明显的耗尽，无论是在金属相中（即，在超导临界温度T_c以上）和在超导体-绝缘体转变（SIT）附近的绝缘相中。LDOS的波动被发现是特别强的情况下，短程相互作用-特别是，在政权时，T_c$增强安德森本地化。另一方面，长程库仑排斥减小了介观LDOS的涨落。然而，同样在具有库仑相互作用的模型中，当系统接近SIT时，波动变得很强。
We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the non-linear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore 2D systems that would be Anderson insulators in the absence of interaction and 2D or 3D systems that undergo Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature $T_c$) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions -- especially, in the regime when $T_c$ is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approaches the SIT.