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arXiv 1402.4878cond-mat.mes-hall
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介观电容器中的电流形变和量子电感

Current deformation and quantum inductance in mesoscopic capacitors

Yue Yin

摘要:

本文对单通道介观电容器的低频动力学进行了理论分析,该电容器由一个量子点通过一个量子信道连接到一个电子库组成。在低频下,已知Wigner-Smith延迟时间$τ_W$起主导作用,并且其可以被解释为离开点的电流与进入点的电流之间的时间延迟。在更高的频率下,我们发现另一个特征时间$τ_S$也很重要。它描述了离开电流对进入电流的变形,因此可以称为变形时间。在足够低的温度下,变形时间$τ_S$可以通过简单的关系式$τ"_W/τ^3_S=24/\hbar^2$从$τ_W$的二阶导数近似。随着温度的升高,这种关系被打破,取而代之的是处于高温极限的$τ"_W/τ^3_S \to 0$。我们进一步表明,变形时间$τ_S$可以有一个显着的影响上的量子电感$L_q$的介观电容器,导致功能不同于量子电容。最引人注目的是,随着温度的升高,$L_q$可以改变其符号:它可以从低温时的正值变为高温时的大负值。上述结果证明了变形时间$τ_S$对介观电容器的交流电导的重要性。

英文摘要:

We present a theoretical analysis of low frequency dynamics of a single-channel mesoscopic capacitor, which is composed by a quantum dot connected to an electron reservoir via a single quantum channel. At low frequencies, it is known that the Wigner-Smith delay time $τ_W$ plays a dominant role and it can be interpreted as the time delay between the current leaving the dot and the current entering the dot. At higher frequencies, we find that another characteristic time $τ_S$ can also be important. It describes the deformation of the leaving current to the entering one and hence can be referred as the deformation time. At sufficient low temperatures, the deformation time $τ_S$ can be approximated from the second-order derivative of $τ_W$ via a simple relation $τ"_W/τ^3_S=24/\hbar^2$. As the temperature increases, this relation breaks down and one has instead $τ"_W/τ^3_S \to 0$ in the high temperature limit. We further show that the deformation time $τ_S$ can have a pronounced influence on the quantum inductance $L_q$ of the mesoscopic capacitor, leading to features different from the ones of the quantum capacitance. The most striking one is that $L_q$ can change its sign as the temperature increases: It can go from positive values at low temperatures to large negative values at high temperatures. The above results demonstrate the importance of the deformation time $τ_S$ on the ac conductance of the mesoscopic capacitor.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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