1. Negative magnetoresistance in Poiseuille flow of two-dimensional electrons P. S. Alekseev 1 and M. I. Dyakonov A. F. Ioffe Physico-Technical Institute, St. Petersburg, Russia 2 Université Montpellier 2, CNRS, France
Outline:
Experiments
Viscous flow of electronic fluid
Decrease of viscosity in magnetic field
Interpretation of experimental magnetoresistance data
Prediction: temperature and magnetic field dependent Hall resistance
Unresolved problems

2. « colossal » « giant » Goal « huge »
Recently, several groups reported strong negative magnetoresistance in 2D electron gas at low temperatures and moderate magnetic fields.
« colossal »
« huge »
« giant »
So far, there is no explanation of these results
We propose a new mechanism, which might be responsible
(However, we still have some problems)

3. Brief review of experimental results

4. Giant negative magnetoresistance in high-mobility 2D electron systems
A.T. Hatke, M.A. Zudov, J.L. Reno, L.N. Pfeiffer, K.W. West
Phys. Rev. B 85, (R) (2012)

5. Size-dependent giant magnetoresistance in millimeter scale GaAs/AlGaAs 2D electron devices. R. G. Mani, A. Kriisa, and W. Wegscheider (2013)

6. L. Bockhorn, A. Hodaei, D. Schuh, W. Wegscheider, R. J. Haug
HMF-20, Journal of Physics: Conference Series 456 (2013)
« We observe for each sample geometry a strong negative magnetoresistance around zero magnetic field which consists of a peak around zero magnetic field and of a huge magnetoresistance at larger fields».

7. Colossal negative magnetoresistance in a 2D electron gas
Q. Shi, P.D. Martin, Q.A. Ebner, M.A. Zudov, L.N. Pfeiffer, K.W. West (2014)

8. Announcing our main ideas
The resistance might be due to the viscosity of the electronic fluid
Then resistivity is proportional to viscosity
2) The viscosity decreases in magnetic field on the scale defined by
As a consequence, negative magnetoresistance appears
3) There should be a corresponding correction to the Hall resistance

9. Electronic viscosity - electron-electron collision time
- Fermi velocity,
- electron-electron collision time
For degenerate electrons at low temperatures
Viscosity is relevant when the mean free path lee = vFτee is << sample width w
The idea of a viscous flow of electronic fluid was put forward by Gurzhi more than 50 years ago:
R. N. Gurzhi, Sov. Phys. JETP 17, 521 (1963)
R. N. Gurzhi and S. I. Shevchenko, Sov. Phys. JETP 27, 1019 (1968)
R. N. Gurzhi, Sov. Phys. Uspekhi 94, 657 (1968)

10. More recently, this idea was discussed in connection with 2D transport
L. W. Molenkamp and M. J. M. de Jong, Phys. Rev. B 49, 5038 (1994)
R. N. Gurzhi, A. N. Kalinenko, and A. I. Kopeliovich, Phys. Rev. Lett., 72, 3872 (1995)
H. Buhmann et al, Low Temp. Phys. 24, 737 (1998)
H. Predel et al, Phys. Rev. B 62, 2057 (2000)
Z. Qian and G. Vignale, Phys. Rev. B 71, (2005)
A. Tomadin, G. Vignale, and M. Polini, Phys. Rev. Lett. 113, (2014)

11. Calculated e-e and e-ph mean free paths as functions of temperature
lee
lph

12. Viscous flow of electronic fluid in 2Dx y E
(Poiseuille parabolic profile)
Jean Léonard Marie Poiseuille (1797 – 1869)
Boundary condition:
Steady state solution:
(total current ~ w3)

13. Pure viscous resistivity
Unusual temperature dependence!
These results are modified if the momentum relaxation time τ due to interaction with phonons and static defects is comparable to τ*. In this case, the usual friction term −v/ τ should be added to the right-hand side of the Navier-Stocks equation.

14. Taking in account electron viscosity scattering by phonons and defects
[Gurzhi-Shevchenko (1968)] ,
(Here l is the mean free path for scattering by phonons and defects)
Interestingly, this formula can be replaced (with an accuracy better than 12%) by:
Which means that the effect of viscosity can be considered as
a parrallel channel of electron momentum relaxation !

15. Calculated resistivity at B=0 as a function of temperature
Poiseuille flow regime – below the minimum at ~ 8K

16. Main point: decrease of viscosity in magnetic field
Like other kinetic coeeficients, e.g. conductivity, in magnetic field the viscosity becomes a tensor with B-dependent components

17. THE VISCOSITY OF A PLASMA IN A STRONG MAGNETIC FIELD
Yu. M. Aliev
Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp , 1965

19. Physical reason for the decrease of viscosity in magnetic field
In magnetic field electrons carry their momentum to adjacent layers on a smaller distance. Thus the internal friction (viscosity) must diminish

20. Equations for viscous electronic liquid in electric and magnetic fields

21. Under stationary conditions and in the absence of Hall
current vy = 0 for all y, while
The first equation says that the resistance is given by previous formulas, where η is replaced by ηxx (which decreases with magnetic field!!).
The second equation serves for finding the Hall field Ey

22. This is for pure viscous flow! (Terms – v/τ are ignored)
New prediction: correction to Hall resistance
(depending on sample width, magnetic field, and temperature)
This is for pure viscous flow!
(Terms – v/τ are ignored)

23. Calculated resistivity as function of magnetic field for different temperatures, assuming 1/τee ~ T2 down to zero temperature + phonon scattering

24. Calculated resistivity as function of magnetic field for different temperatures assuming 1/τee = aT2+b (b is a fitting parameter) + phonon scattering
T = 1, 5, 9, 12, 15, 18, 21, 24, 27, 30 K

25. Comparison of our calculations with
the experimental results of Shi et al
experimental
« theoretical »

26. Hall resistance calculated with 1/τee =aT^2+b

27. Problems
1. To fit the experimental data reasonably well we need to assume that τee remains finite in the limit T 0
2. We also need to assume that electron-phonon scattering time τph behaves as 1/T down to very low temperatures
(this was already noted by Q. Shi et al (2014))

28. Conclusions: our theory in a nutshell
Simplified Drude-like equations:
Results

29. That’s the end
Thank you!