Ballistic and hydrodynamic magnetotransport in narrow channels

Abstract

An increasing number of low carrier density materials exhibit a surprisingly large transport mean free path due to inefficient momentum relaxation. Consequently, charge transport in these systems is markedly non-ohmic but rather ballistic or hydrodynamic, features which can be explored by driving current through narrow channels. Using a kinetic equation approach we theoretically investigate how a non-quantizing magnetic field discerns ballistic and hydrodynamic transport, in particular in the spatial dependence of the transverse electric field, Ey: We find that at weak magnetic fields, the curvature of Ey at the middle of the channel has an opposite sign in the ballistic and hydrodynamic regimes; Moreover, at a magnetic field corresponding to a cyclotron radius near one quarter of the channel width, the spatial profile of Ey not only reflects the transport regime but it can also be used to diagnose the specularity of the boundary. Our results demonstrate that a purely hydrodynamic approach is insufficient in the Gurzhi regime once a magnetic field is introduced. arXiv:1901.08546v1 [cond-mat.mes-hall]

Optical conductivity in graphene: Hydrodynamic regime

“…Similar argument can be applied to the electric field. Magnetic field is typically not treated within linear response 15 leading to the field-dependent viscosity and Hall viscosity 8,16,[40][41][42] . Treating the time derivative in the Liouville's operator in the same manner leads to frequency-dependent dissipative coefficients.…”

Electron hydrodynamics in anisotropic materials

“…heoretical and experimental studies have revealed that electrons in condensed matter can behave hydrodynamically, exhibiting fluid phenomena such as Stokes flow and vortices [1][2][3][4][5][6][7][8][9] . Unlike classical fluids, preferred directions inside crystals lift isotropic restrictions, necessitating a generalized treatment of electron hydrodynamics.…”

Ballistic flow of two-dimensional electrons in a magnetic field

“…As was shown in [36,38], in the presence of weak electron-electron scattering, in almost all magnetic fields below the critical one (B < B c ), specifically, when 2 − ω c W ≫ γW , the electron flow is ballistic. In this case, in the main order in the scattering rate γ, such flows are described by kinetic equation ( 6) with an omitted arrival term [36,38]:…”

“…In the magnetic field B = B c , in which the diameter of the electron cyclotron orbit 2R c becomes equal to the sample width W and some electrons start to make a complete revolution without scattering at the edges, the longitudinal and Hall resistances as functions of the magnetic field experience a jump. In [38], the Poiseuille flow of 2D electrons in a magnetic field was studied in more detail; specifically, the Hall-field distributions over the sample cross section were numerically calculated for B < B c and B > B c and an analytical solution of the kinetic equation in the ballistic region B < B c was constructed. This allowed the authors to explain the evolution of the Hall-field profile curvature upon a variation in the magnetic field, which was observed experimentally in [10].…”