Absorption Spectrum Around $\nu =1$: Evidence for a Small-Size Skyrmion

We measure the absorption spectrum of a two-dimensional electron system (2DES) in a GaAs quantum well in the presence of a perpendicular magnetic field. We focus on the absorption spectrum into the lowest Landau level around $\nu =1$. We find that the spectrum consists of bound electron-hole complexes, trionlike and excitonlike. We show that their oscillator strength is a powerful probe of the 2DES spatial correlations. We find that near $\nu =1$ the 2DES ground state consists of Skyrmions of small size (a few magnetic lengths).

Figure 1

(a) Photocurrent spectra for $n_e=1.7\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ and $I_L=0.3\mathrm{m}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. The dashed lines are guides to the eye. (b),(c) Spectra at both polarizations (solid line) for $\nu <1$, where both the singlet trion $T$ and the exciton $X$ are present for heavy and light holes. The dotted lines are the fitted functions.

Figure 2

Evolution of the spectra of both heavy- and light-hole excitons $X$ and trions $T$ as a function of the density at $B=-9\mathrm{T}$ and $I_L=3\mu \mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. The $\nu =1$ spectrum is emphasized by a thick line. It is seen that both $X$ lines appear abruptly below $\nu =1$.

Figure 3

(a) The oscillator strength of $T_{\mathrm{L}\mathrm{H}}$ for both polarizations at constant $n_e=1.8\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$. (b) The calculated values of $|M_{T,\uparrow }{|}^2$ and $|M_{T,\downarrow }{|}^2$ with $u_m={\delta }_{m,0}$ as $B$ is scanned. The dotted line corresponds to independent electrons model ($u_m=0$). The values of $|M{|}^2$ are normalized by dividing by $N_{\varphi }{|}_{\upsilon =1}$.

Figure 4

(a) The energy of $X_{\mathrm{L}\mathrm{H},\downarrow }$ and $T_{\mathrm{L}\mathrm{H},\downarrow }$ as a function of $n_e$ at constant $B$. The scale was shifted by 1530.3 meV for clarity. (b) FWHM of the $T_{\mathrm{L}\mathrm{H},\downarrow }$. Notice the symmetry of the energy and width around $\nu =1$.