Influence of magnetic quantum confined Stark effect on the spin lifetime of indirect excitons

We report on the unusual and counterintuitive behavior of spin lifetime of excitons in coupled semiconductor quantum wells (CQWs) in the presence of in-plane magnetic field. Instead of conventional acceleration of spin relaxation due to the Larmor precession of electron and hole spins, we observe a strong increase of the spin relaxation time at low magnetic fields followed by saturation and decrease at higher fields. We argue that this nonmonotonic spin relaxation dynamics is a fingerprint of the magnetic quantum confined Stark effect. In the presence of electric field along the CQW growth axis, an applied magnetic field efficiently suppresses the exciton spin coherence, due to inhomogeneous broadening of the $g$-factor distribution.

Figure 1

(a) Color map of the excitonic absorption in a CQW structure studied in this work, calculated as a function of applied electric bias. Sketch of the CQW band structure in the presence (c), (e), or absence (b), (d) of electric bias along the $z$ axis. Red and blue parabolas in (d) and (e) are dispersions of two direct and two indirect states corresponding to optical transitions indicated in (b) and (c).

Figure 2

(a) Waterfall plot of Kerr rotation measured at zero electric bias as a function of the pump-probe delay at different magnetic field intensities, $E_{pp}=1.571$ eV, $E_{pr}=1.569$ eV. (b) Same measurements at $B=0$ for two different pump energies. (c) Magnetic field dependence of the slowest relaxation time measured at zero electric bias for two different excitation energies. Lines are fit to two models, based on the Liouville equation with Lindblad term (solid line) and on the microscopic analysis of the Schrödinger equation (dashed line).

Figure 3

(a) Kerr rotation measured at $V_g=0.8$ V as a function of the pump-probe delay at $B=0$ and $B=1$ T, $E_{pp}=1.568$ eV, $E_{pr}=1.569$ eV. (b) Three characteristic decay times extracted from Kerr rotation measurements at $V_g=0.8$ V and at different in-plane magnetic fields. These decay times are ascribed to DX, IX, and 2DEG spin relaxation. Solid lines are fits to the spin dephasing model, assuming $g$-factor distribution $\mathrm{\Delta }g=0.016$ for IX and $\mathrm{\Delta }g=0.006$ for 2DEG. (c) Fourier spectra of Kerr rotation measured at $B=1$ T. Zero bias spectrum is compared to $V_g=0.8$ V. (d) Two precession frequencies extracted from Kerr rotation measurements at $V_g=0.8$ V and at different in-plane magnetic fields. These frequencies are ascribed to IX and 2DEG spin precession.

Figure 4

Gate voltage dependence of (a) the slowest decay time measured in Kerr rotation scans at different gate voltages and in-plane magnetic fields. (b) Gate voltage dependence of $g$ factor, associated with this slowest component. Two regimes can be identified. At sufficiently small $V_g$, such that DX state remains below IX (direct regime), decay time increases with magnetic field. Under gate voltage such that IX becomes the lowest exciton state in the system (indirect regime), the dependence is inverse, decay time drops dramatically in the presence of the magnetic field.