Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
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DOI：
10.3952/lithjphys.52207
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发表时间：
2012-04
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影响因子：
--
通讯作者：
H. Pal;V. Yudson;D. Maslov
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文献类型：
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作者：
H. Pal;V. Yudson;D. Maslov
虽然众所周知，电子-电子（\ee {}）相互作用不会影响伽利略不变费米液体（FL）的电阻率，但相反的说法不一定正确：非伽利略不变FL的电阻率不一定遵循T^2行为。T^2行为只有在允许Umklapp过程的情况下才能得到保证;然而，如果费米面（FS）很小或者电子-电子相互作用的范围很长，Umklapp就会被抑制。在这种情况下，T^2项只能由电子-杂质相互作用和电子-杂质相互作用的组合效应产生，但与量子干涉校正不同。T^2项是否存在取决于1）维度（二维（2D）与三维（3D）），2）拓扑（单连通与多连通），3）FS的形状（凸与凹）。特别是，对于任何二维和三维的二次（但不一定是各向同性）光谱，都不存在T^2项。对于一个凸的、单连通的、但在其他方面任意各向异性的二维FS，T^2项也是不存在的。这种无效的根源是电子运动在二维FS上的近似可积性，其中能量和动量守恒定律不允许电流弛豫到T/E_F（E_F是费米能）中的第二阶。如果T^2项被守恒律抵消，则第一个非零项表现为T^4。这同样适用于Pomeranchuk不稳定性附近的量子临界金属，条件是电阻率中的前导（第一个非零）项标度为T^{\frac{D+2}{3}}（T^{\frac{D+8}{3}}）。我们讨论了一些情况下，可积性弱破，例如，通过准二维金属中的面间跳跃或通过如Bi_2Te_3族拓扑绝缘体的表面态中的FS的翘曲。
While it is well-known that the electron-electron (\emph{ee}) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T^2 behavior. The T^2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T^2 term can result only from a combined--but distinct from quantum-interference corrections-- effect of the electron-impurity and \emph{ee} interactions. Whether the T^2 term is present depends on 1) dimensionality (two dimensions (2D) vs three dimensions (3D)), 2) topology (simply- vs multiply-connected), and 3) shape (convex vs concave) of the FS. In particular, the T^2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T^2 term is also absent for a convex and simply-connected but otherwise arbitrarily anisotropic FS in 2D. The origin of this nullification is approximate integrability of the electron motion on a 2D FS, where the energy and momentum conservation laws do not allow for current relaxation to leading --second--order in T/E_F (E_F is the Fermi energy). If the T^2 term is nullified by the conservation law, the first non-zero term behaves as T^4. The same applies to a quantum-critical metal in the vicinity of a Pomeranchuk instability, with a proviso that the leading (first non-zero) term in the resistivity scales as T^{\frac{D+2}{3}} (T^{\frac{D+8}{3}}). We discuss a number of situations when integrability is weakly broken, e.g., by inter-plane hopping in a quasi-2D metal or by warping of the FS as in the surface states of Bi_2Te_3 family of topological insulators.