Why g-factor tunability matters for spin devices
The g-factor sets how strongly a carrier's spin responds linearly to a magnetic field, so its value for electrons and holes shapes how spin-based quantum devices can be engineered. The paper frames two useful regimes: a g-factor near zero suits architectures such as quantum repeaters and makes a system resilient to magnetic noise, which can lengthen coherence time, while large g-factors give large Zeeman splittings that support reliable spin initialization and efficient quantum information transfer.
Strain has already been shown to tune g-factors in conventional III-V systems, but the paper states that a systematic description of strain tunability in halide perovskites had not been fully established. That gap is what this work addresses for the inorganic lead-halide perovskites CsPbX3 with X = Cl, Br, I.
Why an 18-band k.p model is needed
In conventional III-V bulk semiconductors such as InAs, InP, or GaAs, g-factors are often evaluated with the Roth formula from the eight-band k.p model, where values follow from the band gap, the Kane energy, and the spin-orbit splitting. For perovskites, however, the electron g-factor is strongly influenced by coupling to remote bands, which motivates a description beyond eight bands.
The authors therefore use an 18-band k.p model covering six lowest conduction bands grouped into R8c- and R6c- blocks and twelve highest valence bands grouped into R6v+, R8w+, R6w+, and R8t+ blocks. Its parameters are determined from target band structures obtained from DFT calculations, and the strain part is a Bir-Pikus Hamiltonian adapted to the perovskite band ordering, with deformation potentials ac, bc, dc, and av. The paper notes that only the R8c-, R6c-, and R6v+ bands are treated as strain-dependent, while other bands are neglected because they lie farther in energy.
Bulk g-factors agree best for electrons
For unstrained bulk crystals at the R point, the DFT-derived parameter set gives electron g-factors that agree well with experiment for CsPbBr3 and CsPbI3, and for both carriers in CsPbCl3. Larger discrepancies appear for the hole g-factor in CsPbBr3 and CsPbI3. The paper emphasizes that its calculations assume an ideal cubic structure, whereas the reference experimental values correspond to a low-temperature phase of lower symmetry.
To test whether the mismatch comes from the band-gap energy, the authors also apply a scissor shift setting E6c to the experimental gap while keeping the DFT-derived spin-orbit splitting. This correction barely changes CsPbCl3, improves the hole g-factor in CsPbBr3 but worsens the electron agreement there, and for CsPbI3 moves the hole value from -2.218 to -1.103 and the electron value from 3.204 to 2.073. The comparison is therefore sensitive to which parameter set is used, not just to the model order.
Hydrostatic strain moves electrons and holes oppositely
Under hydrostatic strain, the electron g-factor decreases under tensile strain and increases under compressive strain, while the hole g-factor shows the opposite trend and increases under tensile strain. The dependence is pronounced for both carriers, indicating that moderate lattice deformation provides substantial control. The largest slopes appear for CsPbI3, which the paper attributes to its smallest band gap relative to the strain-related contributions.
For CsPbBr3, the hole g-factor changes sign, meaning a zero g-factor can be reached by proper strain. Biaxial strain with exx = eyy and ezz = 0 and uniaxial strain with exx = eyy = 0 and ezz nonzero produce dependencies resembling the hydrostatic case, with slopes modified by the bc deformation potential and by splitting in the E8c manifold. The authors note that the orthorhombic phase relevant to low-temperature experiments could modify this behavior, since a nonmonotonic pressure dependence of the band gap has been reported for that phase, but such calculations are beyond the scope of this work.
Nanocrystal size sets the g-factor before strain does
For nanocrystals, the authors perform real-space k.p simulations in the envelope-function approximation, replacing kn by -i d/dxn and introducing the magnetic field through the spin-Zeeman term and gauge-invariant phase factors. The hole-state energy is defined as the negative of the corresponding valence-band electron energy, Eh = -Ev, and the calculations use the scissor-shifted parameters.
The electron-hole pair energy of the ground states increases significantly as the nanocrystal size L, the cube edge length, decreases, as expected from quantum confinement. The electron g-factor increases and the hole g-factor decreases with increasing nanocrystal size, and both approach their bulk limits as size grows. For the electron in CsPbCl3 and for both carriers in CsPbI3, the g-factor crosses zero as a function of size.
Confinement weakens the nanocrystal strain response
With the unstrained cube edge length fixed at L = 50 a0, the electron-hole pair energy under hydrostatic strain depends approximately linearly on strain, with a slope governed by the deformation potential ag, approximately as 3ag times strain. The corresponding electron and hole g-factors, taken from the lowest Zeeman doublets, follow the bulk trend: the electron g-factor increases and the hole g-factor decreases under compressive strain.
The key difference is magnitude. The strain dependence in nanocrystals is less pronounced than in bulk because of the confinement effect, and the paper states that carrier g-factors in CsPbX3 nanocrystals are considerably less sensitive to strain due to quantum confinement. The introduction also singles out CsPbCl3 nanocrystals as considerably less sensitive to strain than the other systems because of that material's large band gap.
Where strain tuning works best and where it stops
The practical split from this paper is between bulk and nanocrystal regimes rather than between halides alone. In bulk cubic CsPbX3, moderate strain tunes carrier g-factors widely, and in some cases, including the CsPbBr3 hole, strain can drive the g-factor through zero, the regime the paper links to robustness against magnetic noise. Among the bulk compounds, CsPbI3 shows the largest g-factor slopes because of its smallest band gap.
In nanocrystals, size already sets the g-factor through confinement, and hydrostatic strain shifts it only weakly, with CsPbCl3 nanocrystals the least strain-sensitive of the systems studied. The most decision-relevant comparison is therefore not which halide has the largest g-factor but whether the target is a bulk crystal, where strain is an effective tuning knob, or a confined nanocrystal, where size and confinement dominate and strain offers much less leverage. The paper also leaves open whether the low-temperature orthorhombic phase would behave differently, since a nonmonotonic pressure dependence of the band gap has been reported there.
Sources used in this answer
Strain tunability of electron and hole g-factors in CsPb X 3 : bulk and nanocrystals
Using an 18-band k.p model parameterized from DFT band structures, the authors show that bulk CsPbX3 electron and hole g-factors can be tuned over a wide range by external strain, in some cases through zero, whereas carrier g-factors in CsPbX3 nanocrystals are considerably less strain-sensitive due to quantum confinement.