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arXiv 0904.4385cond-mat.mes-hall
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分子结输运中的电压诱导奇异性

Voltage-induced singularities in transport through molecular junctions

O. Entin-Wohlman, Y. Imry, A. Aharony

摘要:

通过单分子结携带电流的电子的非弹性散射由量子点模拟,通过两个引线耦合到电子库。当电子在点上时,它被耦合到频率为$ω_0$的单个谐振子。在零温时,线性响应电导中的共振峰由于与振动模式的耦合而总是变窄。然而,这种窄化仅针对窄共振由弗兰克-康登因子给出。与文献中的一些说法相反,线性响应电导在零温度下不表现出任何边带。在有限的温度下确实会出现$\exp [-β\hbar ω_0]$级的小边带。由于自能的虚部和实部,单粒子态密度在对应于非弹性通道开口的频率处表现出不连续性和对数奇异性。同样的奇异性也会在非弹性阈值处和附近的微分电导中产生不连续性和对数发散。这些不连续性通常涉及向上的台阶,但这些台阶在接合处的弹性透明度的相当窄的范围内变为负值。当激发能超过裸共振宽度时,该范围进一步缩小。

英文摘要:

The inelastic scattering of electrons which carry current through a single-molecule junction is modeled by a quantum dot, coupled to electron reservoirs via two leads. When the electron is on the dot, it is coupled to a single harmonic oscillator of frequency $ω_0$. At zero temperature, the resonance peak in the linear-response conductance always narrows down due to the coupling with the vibrational mode. However, this narrowing down is given by the Franck-Condon factor only for narrow resonances. Contrary to some claims in the literature, the linear-response conductance does not exhibit any side-bands at zero temperature. Small side-bands, of order $\exp [-β\hbar ω_0]$, do arise at finite temperatures. The single-particle density of states exhibits discontinuities and logarithmic singularities at the frequencies corresponding to the opening of the inelastic channels, due to the imaginary and real parts of the self-energy. The same singularities also generate discontinuities and logarithmic divergences in the differential conductance at and around the inelastic thresholds. These discontinuities usually involve upwards steps, but these steps become negative within a rather narrow range of the elastic transparency of the junction. This range shrinks further as the the excitation energy exceeds the bare resonance width.

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