arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1403.3452cond-mat.mes-hallcond-mat.str-el
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小偏压和温度下纳米器件的非平衡自能、Ng逼近和热流

Nonequilibrium self-energies, Ng approach and heat current of a nanodevice for small bias voltage and temperature

A. A. Aligia

摘要:

利用二阶非平衡重整化微扰理论计算了一般非对称情况下描述量子点电流的杂质Anderson模型的小$Σ^<$和大$Σ^>$自能.虽然在一般情况下,需要一个数值积分来评估微扰的结果,我们推导出一个解析近似的小频率$ω$,偏置电压$V$和温度$T$,这是确切的总二阶在这些数量。当相应的能量$\hbar ω$、$eV$和$k_B T$小于$k_B T_K$时,近似是有效的,其中$T_K$是近藤温度。数值积分的结果进行了比较,与解析和与Ng近似,其中$Σ^<$和$Σ^>$被假定成正比的延迟自能$Σ^r$倍的平均费米函数。虽然它在$T=0$中对于$\hbar|ω| \lesssim eV$失败,但我们发现Ng近似对于$k_B T > eV/2$是极好的,并且改善了与引线的不对称耦合。即使在$T=0$下,Ng近似对点处的总占据的影响也非常小。$ω$和$V$的依赖性进行了讨论比较与沃德身份,这是由三种方法完成。我们还计算了在有限的偏置电压点和任何引线之间的热流。在有限温度下,其中一个热电流随着所施加的偏置电压而改变符号。

英文摘要:

Using non-equilibrium renormalized perturbation theory to second order in the renormalized Coulomb repulsion, we calculate the lesser $Σ^<$ and and greater $Σ^>$ self-energies of the impurity Anderson model, which describes the current through a quantum dot, in the general asymmetric case. While in general a numerical integration is required to evaluate the perturbative result, we derive an analytical approximation for small frequency $ω$, bias voltage $V$ and temperature $T$ which is exact to total second order in these quantities. The approximation is valid when the corresponding energies $\hbar ω$, $eV$ and $k_B T$ are small compared to $k_B T_K$, where $T_K$ is the Kondo temperature. The result of the numerical integration is compared with the analytical one and with Ng approximation, in which $Σ^<$ and $Σ^>$ are assumed proportional to the retarded self-energy $Σ^r$ times an average Fermi function. While it fails at $T=0$ for $\hbar|ω| \lesssim eV$ we find that the Ng approximation is excellent for $k_B T > eV/2$ and improves for asymmetric coupling to the leads. Even at $T=0$, the effect of the Ng approximation on the total occupation at the dot is very small. The dependence on $ω$ and $V$ are discussed in comparison with a Ward identity that is fulfilled by the three approaches. We also calculate the heat currents between the dot and any of the leads at finite bias voltage. One of the heat currents changes sign with the applied bias voltage at finite temperature.

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