Effective mass suppression upon complete spin-polarization in an isotropic two-dimensional electron system

We measure the effective mass $\left(m^{\ast }\right)$ of interacting two-dimensional electrons confined to a 4.5-nm-wide AlAs quantum well. The electrons in this well occupy a single out-of-plane conduction-band valley with an isotropic in-plane Fermi contour. When the electrons are partially spin polarized, $m^{\ast }$ is larger than its band value and increases as the density is reduced. However, as the system is driven to full spin-polarization via the application of a strong parallel magnetic field, $m^{\ast }$ is suppressed down to values near or even below the band mass. Our results are consistent with the previously reported measurements on wide AlAs quantum wells where the electrons occupy an in-plane valley with an anisotropic Fermi contour and effective mass, and suggest that the effective mass suppression upon complete spin-polarization is a genuine property of interacting two-dimensional electrons.

Figure 1

(Color online) Effective mass, normalized to the band mass, measured as a function of density for a 2DES confined to a 4.5-nm-wide AlAs quantum well. Open and closed symbols represent $m^{\ast }$ measured in partially and fully spin-polarized 2DESs, respectively. Black squares and red circles correspond to $m^{\ast }$ values deduced either assuming a constant quantum lifetime ${\tau }_q$ or that the relative temperature dependence of ${\tau }_q$ is half the size of the relative temperature dependence of the background resistance, respectively. Each data point represents $m^{\ast }$ averaged over different Landau level filling factors, $\nu$, and the error bars include the variation of $m^{\ast }$ with $\nu$. The dashed curves through the data points are guides to the eye.

Figure 2

(Color online) Magnetoresistance traces at a density of $3.93\times {10}^{11}{\text{cm}}^{-2}$ and $\theta =53.0°$. The traces were taken at $T\cong 0.34$, 0.71, 1.03, and 1.30 K. Insets show the energy level diagram at this tilt angle (left) and the Dingle fit at $\nu =11$ assuming a constant ${\tau }_q$ and $R_o$ (right).

Figure 3

(Color online) Magnetoresistance traces at a density of $2.38\times {10}^{11}{\text{cm}}^{-2}$ and $\theta =80.1°$. The traces were taken at $T\cong 0.35$, 1.74, and 4.28 K. Insets show the energy level diagram at this tilt angle (left) and the Dingle fit at $\nu =3$ assuming a constant ${\tau }_q$ and $R_o$ (right).

Figure 4

(Color online) Magnetoresistance traces at a density of $1.52\times {10}^{11}{\text{cm}}^{-2}$ and $\theta =31.8°$. The traces were taken at $T\cong 0.31$, 0.49, 0.65, 0.83, 0.95, and 1.09 K. Insets show the energy level diagram at this tilt angle (right) and the Dingle fit at $\nu =5$ using a constant ${\tau }_q$ and $R_o$ (left).

Figure 5

(Color online) Magnetoresistance traces for the same density as in Fig. 4 at $\theta =80.4°$. The traces were taken at $T\cong 0.43$, 0.63, 0.78, 1.07, 1.15, and 1.30 K. Insets show the energy level diagram for this tilt angle (left) and the Dingle fit at $\nu =4$ using a constant ${\tau }_q$ and $R_o$ (right).

Figure 6

(Color online) Dingle plots of $\Delta R/\left[\xi /\text{sinh}\left(\xi \right)\right]$ vs $1/B$ summarizing data taken for the partially spin-polarized case for: (a) a density of $3.93\times {10}^{11}{\text{cm}}^{-2}$ in the range $0.3\lesssim T\lesssim 1.3\text{K}$ and $11\le \nu \le 25$; and (b) a density of $1.52\times {10}^{11}{\text{cm}}^{-2}$ in the range $0.3\lesssim T\lesssim 1.1\text{K}$ and $5\le \nu \le 11$.

Figure 7

(Color online) Normalized effective mass and spin susceptibilities of both narrow and wide AlAs QWs as a function of the interaction strength, $r_s$. Black and red circles are $g^{\ast }{m}^{\ast }/g_b{m}_b$ of 4.5 nm- and 15-nm-wide AlAs QWs taken from Refs. 23, 10, respectively. The thin curves through the data points are guides to the eye. Open and closed red squares are $m^{\ast }/m_b$ for partially and fully spin-polarized system, respectively, for 11 to 15-nm-wide AlAs QWs from Ref. 26. Black squares are $m^{\ast }/m_b$ data measured in our sample for a 4.5-nm-wide AlAs QW.