Counterflows in viscous electron-hole fluid

P. S. Alekseev, A. P. Dmitriev, I. V. Gornyi, V. Yu. Kachorovskii, B. N. Narozhny, and M. Titov

Phys. Rev. B 98, 125111 – Published 6 September 2018

Abstract

In ultrapure conductors, the collective motion of charge carriers at relatively high temperatures may become hydrodynamic such that electronic transport may be described similarly to a viscous flow. In confined geometries (e.g., in ultrahigh quality nanostructures), the resulting flow is Poiseuille-like. When subjected to a strong external magnetic field, the electric current in semimetals is pushed out of the bulk of the sample towards the edges. Moreover, we show that the interplay between viscosity and fast recombination leads to the appearance of counterflows. The edge currents possess a nontrivial spatial profile and consist of two stripelike regions: the outer stripe carrying most of the current in the direction of the external electric field and the inner stripe with the counterflow.

Received 25 May 2018
Revised 17 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.125111

Physics Subject Headings (PhySH)

Electrical conductivity Magnetoresistance Magnetotransport Transport phenomena Viscosity

Semimetals

Hydrodynamic models

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. S. Alekseev¹, A. P. Dmitriev¹, I. V. Gornyi^1,2,3,4, V. Yu. Kachorovskii^1,2,4, B. N. Narozhny^3,5, and M. Titov^6,7

¹A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
²Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
³Institut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
⁴L.D. Landau Institute for Theoretical Physics, Kosygina Street 2, 119334 Moscow, Russia
⁵National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia
⁶Radboud University Nijmegen, Institute for Molecules and Materials, NL-6525 AJ Nijmegen, The Netherlands
⁷ITMO University, 197101 St. Petersburg, Russia

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Vol. 98, Iss. 12 — 15 September 2018

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Images

Figure 1
Schematic plot of the inhomogeneous electric current density in the regime of fast recombination and a strong enough magnetic field. The color map emphasizes the positive (i.e., parallel to the external electric-field) current at the edge (red) contrasted to the negative (i.e., opposite to the external electric-field) current in the intermediate stripe (blue). The black curve illustrates the magnitude of the current density at a given point along the sample. The dashed line indicates the zero value of the current.
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Figure 2
Electric current density (8a) in the regime of fast recombination (14) and strong enough magnetic-fields $B > B_{*}$ . Left panel: evolution of the current density with increasing magnetic field. The three curves (blue, green, and red) correspond to $ω_{c} τ_{e e} = 4, 10, 40$ , respectively, calculated with the values $ℓ_{G} (0) / ℓ_{R} = 0.25, W / ℓ_{R} = 0.25$ , and $τ τ_{*} / τ_{e e}^{2} = 300$ . Right panel: the fine structure of the edge current in a strong magnetic field in the narrow range of values near zero. The numerical values correspond to the choices of $ℓ_{G} (0) / ℓ_{R} = 0.25, W / ℓ_{R} = 0.25, τ τ_{*} / τ_{e e}^{2} = 1000$ , and $ω_{c} τ_{e e} = 50$ . The vertical grid lines indicate the sample edges, and the horizontal dashed line indicates the zero value $j = 0$ .
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Figure 3
Sample resistance (25) as a function of the magnetic field. The numerical values correspond to the following choice of parameters: $ℓ_{G} (0) / ℓ_{R} = 0.2, W / ℓ_{R} = 0.2$ , and $τ τ_{*} / τ_{e e}^{2} = 1000$ . The green dashed line indicates the negative parabolic magnetoresistance in weak fields [26], see Eq. (26a). The blue dashed line shows the positive linear magnetoresistance (26b).
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Figure 4
Sample resistance (25) as a function of the magnetic field for $ℓ_{G} (0) / ℓ_{R} = 0.005, W / ℓ_{R} = 0.01$ , and $τ τ_{*} / τ_{e e}^{2} = 10^{10}$ . The dashed lines indicate the three asymptotic regimes: parabolic (green), Eq. (27); linear (blue), Eq. (26b); and the power-law $R \sim B^{3 / 2}$ , (black) Eq. (28). The insets zoom into the range of weak (up) and intermediate (down) fields.
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Figure 5
Individual electron (left) and hole (right) flows computed with the same choice of parameters as in Fig. 2: $ℓ_{G} (0) / ℓ_{R} = 0.25, W / ℓ_{R} = 0.25$ , and $τ τ_{*} / τ_{e e}^{2} = 300$ . The color map indicates the magnitude of the currents (according to the “hue” scheme: low magnitude—red, high magnitude—violet) and the arrows—their direction. The top panels show data for $ω_{c} τ_{e e} = 4$ (same as the blue curve in the left panel in Fig. 2); the bottom panels show data for $ω_{c} τ_{e e} = 10$ (same as the green curve in the left panel in Fig. 2).
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