Charge-Noise-Induced Dephasing in Silicon Hole-Spin Qubits

We investigate, theoretically, charge-noise-induced spin dephasing of a hole confined in a quasi-two-dimensional silicon quantum dot. Central to our treatment is accounting for higher-order corrections to the Luttinger Hamiltonian. Using experimentally reported parameters, we find that the new terms give rise to sweet spots for the hole-spin dephasing, which are sensitive to device details: dot size and asymmetry, growth direction, and applied magnetic and electric fields. Furthermore, we estimate that the dephasing time at the sweet spots is boosted by several orders of magnitude, up to on the order of milliseconds.

Figure 1

(a) Lateral quantum dot hosting a spin qubit. A hole is confined by a triangular potential along the growth direction $z$, and an in-plane harmonic potential with axes $x$ and $y$ rotated by $\delta$ with respect to the crystallographic directions [100] and [010]. (b) The basis states in the calculation, showing the heavy hole and light hole subbands of the unperturbed Hamiltonian. The red area shows the states used in the perturbation series of Eq. (6).

Figure 2

Heavy-hole qubit $g$-tensor components for a dot with $z$ axis along [001]. The horizontal axis represents (a) the average dot energy $\overline{ϵ}=({ϵ}_x+{ϵ}_y)/2$, (b) dot asymmetry $\eta =({ϵ}_y-{ϵ}_x)/2\overline{ϵ}$, (c) dot orientation $\delta$, and (d) vertical confinement electric field $E_z$. The dashed line, defined by ${ϵ}_x=-1\mathrm{meV},{ϵ}_y=-3\mathrm{meV},\delta =\pi /4$, and $E_z=10\mathrm{mV}/\mathrm{nm}$, denotes a common reference point.

Figure 3

Dephasing time $T_2^{*}$ calculated from the Luttinger model (top) and the full Hamiltonian (bottom). Figure axes: the vertical electric field $E_z$ and the in-plane-direction angle $\varphi$ of the magnetic field $\mathbf{B}=B(\cos \varphi ,\sin \varphi ,0)$. Other parameters: $B=1\mathrm{T}$, confinement lengths $l_x=\hslash \sqrt{({\gamma }_1+{\gamma }_2)/m_0{ϵ}_x}=20\mathrm{nm}$, $l_y=15\mathrm{nm}$, the dot-orientation angle $\delta =0$, the noise magnitude $A=450{\mathrm{V}}^2/{\mathrm{m}}^2$ [73, 74], and the frequency cutoffs $f_{\mathrm{ir}}=1\mathrm{Hz}$, $t=10\mu \mathrm{s}$.