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arXiv 1502.06486cond-mat.supr-concond-mat.mtrl-sci
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纯晶体的声子剩余电阻

Phonon residual resistance of pure crystals

A. I. Agafonov

摘要:

利用Boltzmann输运方程,研究了有限厚度的理想金属晶体$d$在弱恒电场$E$作用下的声子剩余电阻.这种电阻是$\propto d^{-5}E^{-3}$,是由于电场加热的电子的散射和长波声学声子的发射。这种电子-声子相互作用是由完美晶格中原子的零点振动引起的。在1 mV/cm量级的场中,对厚度约为1 cm的Cu、Ag和Au单晶进行考虑。根据Matthiessen规则,纯晶体的电阻,其厚度远大于电子平均自由程,表示为杂质和声子剩余电阻的总和。在厚度$d$和场$E$的条件下,找到了场加热电子的声子散射占主导地位。在此条件下,纯晶体的低温电阻不再依赖于晶体的纯度,而是决定了理想晶体的声子剩余电阻率。对纯度至少为99.9999%的Cu进行计算。

英文摘要:

Using the Boltzmann transport equation, we study phonon residual resistance of perfect metallic crystals of a finite thickness $d$ along which a weak constant electric field $E$ is applied. This resistance which is $\propto d^{-5}E^{-3}$, is due to scattering of electric field-heated electrons with emission of long-wave acoustic phonons. This electron-phonon interaction is caused by zero-point vibrations of the atoms in the perfect crystal lattice sites. Consideration is carried out for Cu, Ag and Au single crystals with the thickness of about 1 cm, in the fields of the order of 1 mV/cm. Following the Matthiessen rule, the resistance of the pure crystals the thicknesses of which are much larger than the electron mean free path, is represented as the sum of the impurity and phonon residual resistances. The condition on the thickness $d$ and the field $E$ is found at which the phonon scattering of the field-heated electrons dominates. Under this condition, the low-temperature resistances of pure crystals do not depend on the their purity and determine the phonon residual resistivity of the ideal crystals. The calculations are performed for Cu with a purity of at least 99.9999%.

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