Kinetic coefficients of two-dimensional electrons with strong Zeeman splitting

Abstract

In nanostructures with two-dimensional (2D) electrons and very low defect densities, a hydrodynamic transport regime has recently been realized. In this regime, 2D electrons form a viscous fluid due to frequent electron-electron collisions. Many unusual and mysterious magnetotransport and high-frequency effects have been observed in these systems. Their understanding is crucial for a general comprehending the formation of hydrodynamic transport. Two-component electronic systems, where there are two types of carriers with different concentrations and relaxation times, are of particularly interest. These systems can be realized by filling two lower subbands in a quantum well with electrons, or by filling one subband and applying a strong magnetic field in the well plane, leading to a Zeeman splitting of the subband. In this work, we construct the hydrodynamic equations for a viscous two-component electronic fluid for a Zeeman-type two-component 2D electronic system. By solving the kinetic equation, we calculate the relaxation rates of the first and second harmonics of the two-component distribution function. The resulting balance hydrodynamic equations take into account the effect of shear viscosity in each component and the effect of the friction between the two components. The lastleads to the alignment of the velocities of the two components of the fluid. The obtained equations can be used to explain magnetotransport measurements in ultra-pure nanostructures in an inclined magnetic field, where two-component electronic fluid is formed.

Figures (4)

• Figure 1: ($a$): Equilibrium electron distribution of the two components and the corresponding parameters of the two components. ($b$): Notation for the scattering angles of two electrons.
• Figure 2: Kinematics of inter-zone ($a$) and intra-zone collisions ($b$). The initial and final pulses correspond to the conservation of the total momentum during collisions and small energy changes.
• Figure 3: Visual explanations of kinematic the reasons for the absence of the 'second harmonic entrainment effect" (the effect of occurrence perturbations of the distribution function corresponding to shear stresses in one subzone due to the presence of such a perturbation of the distribution function of this type in another subzone).
• Figure 4: Different contributions to the relaxation rates of the first and second harmonics of the distribution function, calculated for the system studied in dai2011response (GaAs/AlGaAs quantum well in an inclined magnetic field). The horizontal axis represents the splitting in Fermi energy units. The positive semi-axis corresponds to the case $p_1^F<p_2^F,$ the negative one - to the case $p_1^F>p_2^F.$ : $(a)$ Elements of the relaxation rate matrix of the first moment ${\alpha_{11}^{(1)}}$ and ${\alpha_{22}^{(1)}}$;$(b)$ the only non-zero eigenvalue $\lambda^{(1)}$ of the relaxation matrix of the first moment (\ref{['lll']}) ${\alpha^{(1)}}$ is the relaxation rate of the relative velocity; $(c)$ Elements of the relaxation matrix of the second moment corresponding to intersubband collisions ${\alpha_{11}^{(2)}}$ and ${\alpha_{22}^{(2)}}$; $(d)$ Elements of the relaxation matrix of the second moment corresponding to intrasubband collisions${\beta_{11}^{(2)}}$ and ${\beta_{22}^{(2)}}$. It is worth noting that they are relatively small. The following parameter values were used: $\kappa=12.9,~T=0.3~K,~m=0.067 m_0,~n=2.9\cdot10^{11}cm^{-1}$