Electron and hole $g$ factors in semiconductors and nanostructures (Review)

TL;DR

This review surveys how charge-carrier spins in semiconductors respond to external magnetic fields, focusing on the g factor as the linear spin response. It synthesizes experimental techniques from ESR/EPR to spin noise and time-resolved Kerr measurements, and surveys theoretical treatments across bulk, two-dimensional, and nanostructured systems, anchored by the Roth formula and k·p/Luttinger formalisms. Key takeaways include strong g-factor anisotropy in low-symmetry nanostructures, size- and shape-dependent g factors in quantum dots and nanocrystals, and significant contributions from remote bands and valence-band warping to hole g factors; yet notable discrepancies remain in certain NCs, driving ongoing theoretical development. The work has broad implications for spintronics and quantum information, where precise g-factor control supports coherent spin manipulation and readout in diverse materials, including TMDCs and lead-halide perovskites.

Abstract

We present a review of experimental and theoretical studies of the spin response of charge carriers to an external magnetic field in bulk semiconductors and semiconductor nanostructures. The linear response is quantitatively characterized by the magnitude of the electron or hole g factor. Various experimental methods for measuring the electron g factor are considered, beginning with historical works and including modern research. A detailed analysis of theoretical methods for calculating the electron and hole g factors in bulk semiconductors and nanostructures of various shapes also includes fundamental work from previous years and the present time.

Figures (10)

• Figure 1: (a) EPR spectrum ($f_{mw}$ = 9.5 GHz, $T=4.5$ K) of a bulk In$_{0.53}$Ga$_{0.47}$As crystal, recorded from the first derivative of the resonant absorption line. (b) ODMR spectrum ($f_{mw}$ = 24 GHz, $T =1.6$ K), recorded from the magnetically induced circular polarization of the exciton PL of a bulk In$_{0.53}$Ga$_{0.47}$As crystal. The inset shows the resonance after subtracting the linear background and approximating it using a Lorentzian contour. Figure adapted from Ref. Kowalski.
• Figure 2: (a -- c) Spin-flip Raman spectra of 4 monolayer thick CdSe nanoplatelets measured under resonant excitation at $\hbar \omega =2.497$ eV, power density P = 20 W cm$^{-2}$, $B$ = 5 T, and $T$ = 2 K. (a) Spectra in Voigt geometry measured in co- (blue) and cross- (red) linear polarizations. Faraday spectra measured in co- and cross-linear polarizations [panel (b)] and in co- and cross-circular polarizations [panel (c)]. Figure adapted from Ref. Kudlasik2020.
• Figure 3: Photoluminescence spectra measured in $\sigma_+$ (black) and $\sigma_-$ (red) circular polarization in a WSe$_2$ monolayer under linearly polarized photoexcitation. Panel (b) shows experimental curves in the absence of a magnetic field. The symbols $X^0$ and "Trion" denote the emission lines of the neutral exciton and the negatively charged exciton X$^{-}$ (trion). The monolayer lies on a SiO$_2$/Si substrate. Figure adapted from Ref. TMDC.
• Figure 4: Kerr rotation as a function of time in a 10 nm thick GaAs/Al$_x$Ga$_{1-x}$As quantum well in a magnetic field of 1 T and at T=1.6 K. The black line shows the experimental data, the thick gray line corresponds to the results of the approximation according to Eq. (\ref{['St']}) with parameters $\Omega_L=23.4$ GHz and $T_2=\tau_s$ =880 ps. The inset shows the Zeeman splitting (left scale) and the spin beat frequency $\Omega_L$ (right scale) as functions of the magnetic field. Figure adapted from Ref. Kiselev2007.
• Figure 5: Kerr rotation noise spectra in a single 20 nm wide GaAs/AlAs quantum well (placed in a microcavity) measured in magnetic fields ranging from 9.5 to 29 mT with equal increments. Experimental parameters are shown in the panel. Figure adapted from Ref. Poltavtsev.