Interaction effects on magneto-oscillations in a two-dimensional electron gas

Motivated by recent experiments, we study the interaction corrections to the damping of magneto-oscillations in a two-dimensional electron gas (2DEG). We identify leading contributions to the interaction-induced damping which are induced by corrections to the effective mass and quantum scattering time. The damping factor is calculated for Coulomb and short-range interaction in the whole range of temperatures, from the ballistic to the diffusive regime. It is shown that the dominant effect is that of the renormalization of the effective electron mass due to the interplay of the interaction and impurity scattering. The results are relevant to the analysis of experiments on magneto-oscillations (in particular, for extracting the value of the effective mass) and are expected to be useful for understanding the physics of a high-mobility 2DEG near the apparent metal-insulator transition.

Figure 1

The logarithmic term $\tilde{\Omega }$, Eq. (7), in the thermodynamic potential, Eq. (3), is a sum of closed loop diagrams with self-energy insertions $\Sigma$. This term is responsible for magneto-oscillations.

Figure 2

Self-energy diagrams in the first order in the effective interaction (wavy line). Black triangles denote impurity ladders $\Gamma$ dressing interaction vertices, Fig. 3. (a) “Simple” self-energies ${\Sigma }_{ij}^a$; and (b) Hikami-box self-energies ${\Sigma }_{ij}^b$ generated by covering each of ${\Sigma }_{ij}^a$ by an impurity line (dashed).

Figure 3

Interaction vertex renormalized by the impurity ladder, $\Gamma (i{\omega }_k,\mathbf{q})$. Dashed line represents scattering on impurity.

Figure 4

Schematic illustration of the scattering off Friedel oscillations. The black dot in the middle represents a short-range impurity which creates the oscillatory correction to the electron density around it. The circle represents the equipotential line of the effective impurity potential. The correction to the impurity cross section at the angle $\varphi$ arises due to the interference of two electronic waves (Refs. 9, 38), one of which (dashed line) scattered by the impurity and another (solid line) by the Friedel oscillations at a point parametrized by the distance $r$ from the impurity and the angle $\psi$.

Figure 5

Differential impurity cross section $S\left(\varphi \right)$ (in units of the bare cross section $S_0$) renormalized by the scattering off Friedel oscillations (with only the exchange contribution taken into account) calculated for $\nu U_0=0.2$ and (a) fixed $T=0.01E_F$ and $ϵ∕E_F=0$, 0.01, 0.02, 0.05, 0.1, and 0.2, from top to bottom; and (b) fixed $ϵ=0$ and $T∕E_F=0.005$, 0.01, 0.02, 0.05, 0.1, and 0.2, from top to bottom.

Figure 6

Diagrammatic equation for the effective interaction line (bold wavy line) in the random-phase approximation, Eqs. (71, 73). Dotted wavy line represents the bare interaction, $V_0\left(q\right)+F_0^{\rho }∕2\nu$ in the singlet channel or $F_0^{\sigma }∕2\nu$ in the triplet channel. The bubble $\Pi$ is the polarization operator, Eq. (72).

Figure 7

Temperature dependence of the singlet channel correction to the damping factor $B^{\rho }\left(T\right)$, Eq. (83), for $4\pi \Delta \tau =100$ (solid line) with the low-$T$ (dot-dashed) and high-$T$ (dashed) asymptotics, Eq. (84). (a) Wide temperature range: on this scale $B^{\rho }\left(T\right)$ is essentially indistinguishable from its high-$T$ asymptotics; and (b) low-$T$ part: the crossover between the two asymptotics occurs at $T\tau \sim 0.05$.