The impacts of the quantum-dot confining potential on the spin-orbit effect

Abstract

For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how small the well height is, there are at least two bound states in the finite square well: one has the σx = −1 symmetry and the other has the σx = 1 symmetry. When the well height is slowly tuned from large to small, the position of the maximal probability density of the first excited state moves from the center to x ≠ 0, while the position of the maximal probability density of the ground state is always at the center. A strong enhancement of the spin-orbit effect is demonstrated by tuning the well height. In particular, there exists a critical height , at which the spin-orbit effect is enhanced to maximal.

A spin dephasing mechanism mediated by the interplay between the spin–orbit coupling and the asymmetrical confining potential in a semiconductor quantum dot

“…As can be seen from the figures, with the decease of the well-height V 0 , the energies of the corresponding quantum states become smaller, i.e., more closer to the well-portal, and the qubit level splitting becomes smaller too. This phenomenon has been observed previously, the spin-orbit effect in the quantum dot can be enhanced by lowering the height of the confining potential [46]. We can understand as follows.…”

“…The boundary condition is used to determine the energy spectrum and the corresponding eigenfunctions of a quantum system. For the square well (2) we are considering, the boundary condition explicitly reads [46] Ψ(0) = 0, Ψ(a+0) = Ψ(a−0), Ψ ′ (a+0) = Ψ ′ (a−0), (3) where Ψ(x) is the eigenfunction and Ψ ′ (x) is its first derivative. It should be noted that the eigenfunction Ψ(x) = [Ψ 1 (x), Ψ 2 (x)] T here has two components due to the spin degree of freedom.…”

Charge noise induced spin dephasing in a nanowire double quantum dot with spin–orbit coupling

“…Also, in a DQD, it is easy to achieve a strong electric-dipole spin resonance, which is useful for the single qubit manipulation. The one-dimensional square well problem in the presence of both the SOC and the Zeeman field is exactly solvable [27,[41][42][43]. In order to show explicitly the underlying physics of the spin dephasing and its dependence on the DQD parameters, here the confining potential of the nanowire DQD is modeled by an infinite double square well.…”

“…, 12) to be determined, we expand the eigenfunction in each coordinate region in terms of the corresponding bulk wavefunctions [see Eq. (A1)] [27,42]. Once an eigen-energy, e.g., E n , is obtained, we can solve its corresponding coefficients c n i by combining the equation M · C = 0 with the normalization condition dxΨ † n (x)Ψ n (x) = 1.…”

“…2. When the orbital wavefunction is more un-localized, the spin-orbit effects in the system are much stronger [25,42,51].…”