g-factor symmetry and topology in semiconductor band states

Abstract

The $\mathbf{g}$ tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but it inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. Here we uncover new symmetry and topological features of $\mathbf{g}={\mathbf{g}}_{\mathbf{L}}+{\mathbf{g}}_{\mathbf{S}}$ for important valence and conduction bands in silicon, germanium, and gallium arsenide. For all crystals with high (cubic) symmetry, we show that large departures from the nonrelativistic value $g=2$ are guaranteed by symmetry. In particular, considering the spin part ${\mathbf{g}}_{\mathbf{S}}(\mathbf{k})$, we prove that the scalar function $det({\mathbf{g}}_{\mathbf{S}}(\mathbf{k}))$ must go to zero on closed surfaces in the Brillouin zone, no matter how weak the spin-orbit coupling is. We also prove that for wave vectors $\mathbf{k}$ on these surfaces, the Bloch states $|u_{n\mathbf{k}}⟩$ have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces $det(\mathbf{g}(\mathbf{k}))=0$ exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory.

arXiv comment15 pages, 8 figures

References in corpus (11)

• Quantum Computation with Quantum Dots
• Berry Phase Effects on Electronic Properties
• Dirac semimetal in three dimensions
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Charge noise and spin noise in a semiconductor quantum device
• Model for the on-site matrix elements of the tight-binding hamiltonian of a strained crystal: Application to silicon, germanium and their alloys
• Topological Lifshitz transitions
• Theory of Orbital Magnetization in Solids
• Coherent wave-packet evolution in coupled bands
• Blueprint of a scalable spin qubit shuttle device for coherent mid-range qubit transfer in disordered Si/SiGe/SiO${}_2$
• SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits

Cited by in corpus (1)

• Magnetic-field dependence of spin-phonon relaxation and dephasing due to g-factor fluctuations from first principles