Zero-temperature optical conductivity of ultraclean Fermi liquids and superconductors
Zero-temperature optical conductivity of ultraclean Fermi liquids and superconductors
复制标题
超净费米液体和超导体的零温光导率
DOI：
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发表时间：
2005
期刊：
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通讯作者：
P. Howell
中科院分区：
文献类型：
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作者：
A. Rosch;P. Howell
我们忽略了杂质和声子的影响，计算了清洁金属和超导体在零温下的低频光学电导率。一般来说，$EnsureMath{sigma}$的频率和温度依赖关系几乎没有什么共同之处。例如，对于三维(但不是二维)的小费米表面，我们发现$mathm{Re}幻影{
Ule{0.2em}{0ex}}ensuremath{sigma}(ensuremath{omega}g0)ensuremath{approx}mathrm{const}$，它对应于散射率$ensuremath{Gamma}ensuremath{propto}{ensuremath{omega}}^{2}$，即使在没有umclapp散射的情况下，当没有${T}^{2}$对$EnsureMath{Gamma}$的贡献时也是如此。在本文的主要部分中，我们详细地讨论了$d$波超导体的二维光学电导，其中$mathm{Re}模{
最小频率的ule{0.2em}{0ex}}ensuremath{sigma}(ensuremath{omega}g0)ensuremath{propto}{ensuremath{omega}}^{4}$和umkLapp进程通常平稳地设置在小于最大间隙的两倍的有限阈值${EnsureMath{omega}}_{0}$。在节点位于$(ifmmodesmse extpmfi{}ensureath{pi}/2，ifmmodesmse extpmfi{}ensureath{pi}/2)$的情况下，使得可以在它们之间直接散布umclapp，从而获得$mathm{re}幻象{
Ule{0.2em}{0ex}}ensuremath{sigma}(ensuremath{omega})ensuremath{propto}{ensuremath{omega}}^{2}$.
We calculate the low-frequency optical conductivity $ensuremath{sigma}(ensuremath{omega})$ of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of $ensuremath{sigma}$ have very little in common. For small Fermi surfaces in three dimensions (but not in two dimensions) we find, for example, that $mathrm{Re}phantom{
ule{0.2em}{0ex}}ensuremath{sigma}(ensuremath{omega}g0)ensuremath{approx}mathrm{const}$ which corresponds to a scattering rate $ensuremath{Gamma}ensuremath{propto}{ensuremath{omega}}^{2}$ even in the absence of umklapp scattering when there is no ${T}^{2}$ contribution to $ensuremath{Gamma}$. In the main part of the paper we discuss in detail the optical conductivity of $d$-wave superconductors in two dimensions where $mathrm{Re}phantom{
ule{0.2em}{0ex}}ensuremath{sigma}(ensuremath{omega}g0)ensuremath{propto}{ensuremath{omega}}^{4}$ for the smallest frequencies and the umklapp processes typically set in smoothly above a finite threshold ${ensuremath{omega}}_{0}$ smaller than twice the maximal gap $ensuremath{Delta}$. In cases where the nodes are located at $(ifmmodepmelse extpmfi{}ensuremath{pi}∕2,ifmmodepmelse extpmfi{}ensuremath{pi}∕2)$, such that direct umklapp scattering among them is possible, one obtains $mathrm{Re}phantom{
ule{0.2em}{0ex}}ensuremath{sigma}(ensuremath{omega})ensuremath{propto}{ensuremath{omega}}^{2}$.