Imaging charge and spin transport at high density in semiconductors
The numerous investigations of charge and spin transport aimed at applications such as spin lasers and spin field-effect transistors have mostly laid emphasis on ‘ clean’ experimental conditions. In these scenarios, the charge density is spatially homogeneous,1 enabling observation of pure spin diffusive currents, which is of particular interest to developers of bipolar components and spin lasers. Recently, we revealed novel phenomena in spin-dependent transport in high-density carrier conditions, by tightly focusing a circularly polarized laser beam to a diffraction-limited spot, and then imaging the spatial profiles of luminescence intensity and the degree of circular polarization.2 As shown in Figure 1, the decrease in charge and spin density profiles with distance from the excitation spot gives the charge and spin diffusion lengths, respectively. This technique is analogous to continuous wave (CW) measurements of cathodoluminescence intensity profiles,3 and to transient measurements of the spin density profile using Kerr microscopy.4 However, unlike these two techniques, our approach gives access to both charge and spin transport, and is therefore suitable for investigating their possible couplings. Furthermore, we can also explore drift transport (see Figure 2) by applying an electric field. In this work, we describe two examples of novel physical phenomena that we have explored using this experimental technique.
The first is the appearance of an effective spin-spin coupling, due to ambipolar effects originating from the differential diffusivities of electrons and holes.5 When we increase the pump power, the electron diffusion constant is replaced by an ambipolar one, as shown from the narrowing of the charge spatial profile near the excitation spot.6 Although electrical quasi-neutrality is preserved throughout the sample, an internal electric field builds up. This field induces drift currents toward the excitation spot. The currents are approximately equal for the two spin species, and therefore reduce the electronic polarization at the excitation spot. Figure 3(a) shows this decrease for p-type gallium arsenide (GaAs) (NA≈1017 cm−3) at 300K, which reveals that the polarization at r=0 decreases by almost a factor of six to ∼2% at the maximum accessible power (3mW). This effect is not caused by a decrease in the spin relaxation time, since the spatially averaged polarization does not change with excitation power: see Figure 3(a). Figure 3(b) shows the profiles calculated by numerically solving the coupled diffusion equations for electronic spins + and −.
The second physical phenomenon we explored concerns the appearance of a charge coupling effect due to the Pauli principle in p-type GaAs (NA≈1018 cm−3) at 15K.7, 8 At low excitation power (see Figure 4, left), the polarization profile exhibits a featureless decrease with distance, characteristic of spin relaxation during diffusion. We observe the effect of the Pauli principle under degeneracy, i.e., for an increased excitation power P, such that the electronic concentration is larger than the effective density of states of the conduction band. For P=2.55mW (see Figure 4, right), there appears a counterintuitive volcano-like shape, reflecting how spin polarization initially increases with diffusion. A simple interpretation of this effect, illustrated in Figure 4 (center), is that, under degeneracy, the diffusion constant is larger for majority spin electrons than for minority. Thus, the more efficient removal by diffusion from the excitation spot induces a depletion of majority electrons, with an accumulation some distance away from this spot. Our interpretation of these findings can be found in detail elsewhere.8
We have shown that at high excitation power, ambipolar diffusion opposes the outward diffusion of electrons, and increases the electron concentration at the excitation spot. This renders the electrons degenerate at lower powers than would otherwise be necessary, and makes Pauli blockade phenomena on spin transport experimentally accessible. In the absence of ambipolar diffusion higher powers are needed, and this heats the electron gas to the extent that it becomes non-degenerate.
In conclusion, our studies will enable other investigations seeking to demonstrate new effects of spin transport at high density. Our future work may explore the spin dependence of currents induced by the spatial gradient of the electronic temperature, and of the photoelectron mobility. It would also be interesting to extend these studies to systems of lower dimensionality, such as semiconducting quantum wells, quantum wires, or transition metal dichalcogenides.