Gurzhi effect explained

R of a finite size conductor with increasing of its temperature T (i.e. the situation dR/dT < 0 for some temperature interval). Gurzhi effect usually being considered as the evidence of electron hydrodynamic transport^{[3] [4] [5] [6] [7] [8]} in conducting media. The mechanism of Gurzhi effect is the following. The value of the resistance of the conductor is inverse to the l _{lost} =min \{l _{boundary} , l _{V\}} — a mean free path corresponding to the momentum loss from the electrons+phonons system$$R\backslash propto\; \backslash frac,$$where l _{boundary} is the average distance which electron pass between two consecutive interactions with a boundary, and l _{V} is a mean free path corresponding to other possibilities of momentum loss. The electron reflection from the boundary is assumed to be diffusive.

When temperature is low we have ballistic transport with

l _{ee} \gg d , l _{lost} ≈ l _{boundary} ≈ d , where d is a width of the conductor, l _{ee} is a mean free path corresponding to effective normal electron-electron collisions (i.e. collisions without total electrons+phonons momentum loss). For low temperatures phonon emitted by electron quickly interacts with another electron without loss of total electron+phonons momentum and l _{ee} ≈ l _{ep} , where l _{ep} \propto T ^{-5} is a mean free path corresponding to the electron-phonon collisions. Also we assume d \ll l _{V} . Thus the resistance for lowest temperatures is a constant R \propto d ^{-1} (see the picture). The Gurzhi effect appears when the temperature is increased to have l _{ee} \ll d . In this regime the electron diffusive length between two consecutive interactions with the boundary can be considered as momentum loss free path: l _{lost} ≈ l _{boundary} ≈ d ^{2 /l} _{ee} , and the resistance is proportional to R \propto l _{ee} (T)/d ^{2} \propto T ^{-5} d ^{-2} , and thus we have a negative derivative dR/dT < 0 . Therefore, Gurzhi effect can be observed when l _{ee} \ll d \ll d ^{2 /l} _{ee} \ll l _{V} .

Gurzhi effect corresponds to unusual situation when electrical resistance depends on a frequency of normal collisions. As one can see this effect appears due to the presence of a boundaries with finite characteristic size

d . Later Gurzhi's group discovered a special role of electron hydrodynamics in a spin transport.^{[9] [10]} In such a case magnetic inhomogeneity plays role of a "boundary" with spin-diffusion length^[11] as a characteristic size instead of d as before. This magnetic inhomogeneity stops electrons of the one spin component which becomes an effective scatterers for electrons of another spin component. In this case magnetoresistance of a conductor depends on the frequency of normal electron-electron collisions as well as in the Gurzhi effect.

Notes and References

1. Minimum of resistance in impurity-free conductors . Gurzhi, R. N. . J Exp Theor Phys . 17 . 521 . 1963.
2. Gurzhi, R. N. . 1968 . HYDRODYNAMIC EFFECTS IN SOLIDS AT LOW TEMPERATURE . Soviet Physics Uspekhi . 11 . 2 . 255–270 . 10.1070/PU1968v011n02ABEH003815.
3. Negative Temperature Derivative of Resistivity in Thin Potassium Samples: The Gurzhi Effect?. Yu, Z. -Z.. Haerle, M.. Zwart, J. W. . Bass, J. . Pratt, W. P. . Schroeder, P. A.. Phys. Rev. Lett.. 52. 5. 368–371. 1984. 10.1103/PhysRevLett.52.368.
4. Hydrodynamic electron flow in high-mobility wires . de Jong, M. J. M. . Molenkamp, L. W. . Phys. Rev. B . 51 . 19 . 13389–13402 . 1995 . 10.1103/PhysRevB.51.13389. cond-mat/9411067 .
5. Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons . Alekseev, P. S. . Phys. Rev. Lett. . 117 . 16 . 166601 . 2016 . 10.1103/PhysRevLett.117.166601. 1603.04587 .
6. Narozhny, Boris N. . Gornyi, Igor V. . Mirlin, Alexander D. . Schmalian, Jörg. Hydrodynamic Approach to Electronic Transport in Graphene. Annalen der Physik. 529. 11. 1700043. 2017. 10.1002/andp.201700043. free. 1704.03494.
7. Moll, Philip J. W.. Kushwaha, Pallavi. Nandi, Nabhanila. Schmidt, Burkhard. Mackenzie, Andrew P. . Evidence for hydrodynamic electron flow in PdCoO2 . 351 . 6277 . 1061–1064 . 2016 . Science . 10.1126/science.aac8385. 10023/8262. free.
8. Hydrodynamic Electron Flow and Hall Viscosity . Scaffidi, Thomas . Nandi, Nabhanila . Schmidt, Burkhard . Mackenzie, Andrew P. . Moore, Joel E. . Phys. Rev. Lett. . 118 . 22 . 226601 . 2017 . 10.1103/PhysRevLett.118.226601. free . 10023/11223 . free .
9. Dynamics of a spin-polarized electron liquid: Spin oscillations with a low decay . Gurzhi, R. N. . Kalinenko, A. N. . Kopeliovich, A. I. . Pyshkin, P. V. . Yanovsky, A. V. . Phys. Rev. B . 73 . 15 . 153204 . 2006 . 10.1103/PhysRevB.73.153204. 1109.1872 .
10. Gurzhi, R. N. . Kalinenko, A. N. . Kopeliovich, A. I. . Pyshkin, P. V. . Yanovsky, A. V.. Electrical resistance of spatially varying magnetic interfaces. The role of normal scattering. Low Temperature Physics. 37. 2. 149–156. 2011. 10.1063/1.3556662. 1109.0555.
11. Spin-diffusion lengths in metals and alloys, and spin-flipping at metal/metal interfaces: an experimentalist's critical review . Bass, J. . Pratt, W. P. . Journal of Physics: Condensed Matter . 19 . 183201 . 10.1088/0953-8984/19/18/183201 . 2007. cond-mat/0610085 .