Screening of charged impurities with multielectron singlet-triplet spin qubits in quantum dots

Charged impurities in semiconductor quantum dots comprise one of the main obstacles to achieving scalable fabrication and manipulation of singlet-triplet spin qubits. We theoretically show that using dots that contain several electrons each can help to overcome this problem through the screening of the rough and noisy impurity potential by the excess electrons. We demonstrate how the desired screening properties turn on as the number of electrons is increased, and we characterize the properties of a double quantum dot singlet-triplet qubit for small odd numbers of electrons per dot. We show that the sensitivity of the multielectron qubit to charge noise may be an order of magnitude smaller than that of the two-electron qubit.

Figure 1

Model double-well potential along the interdot axis. There is also a harmonic potential along $y$ with frequency ${\omega }_0$. We have schematically shown 10 electrons filling the lowest Fock-Darwin orbitals in a finite magnetic field.

Figure 2

Ground-state energy vs number of shells kept in the full CI calculation for three (a) and five (b) electrons in a harmonic trap with frequency $\hslash {\omega }_0=24.26$ meV (a) and $\hslash {\omega }_0=21.79$ meV (b) and perpendicular magnetic field $B=2.8$ T (a) and $B=2.5$T (b) such that ${\omega }_c=2{\omega }_0/\sqrt{99}$.

Figure 3

Ground-state energy vs cutoff in the energetically truncated CI calculation for three (a) and five (b) electrons in a harmonic trap with parameters as in Fig. 2.

Figure 4

Rearrangement energy $\Delta$ (see text) vs number of electrons for an impurity on the $z$ axis. Here the impurity is repulsive and is located 17 nm (top) or 34 nm (bottom) from the dot center. There is a perpendicular field $B=2.8$T and the trap frequency is $\hslash {\omega }_0=24.26$ meV.

Figure 5

Rearrangement energy $\Delta$ (see text) vs number of electrons for an impurity on the $x$ axis. Parameters are the same as in Fig. 4.

Figure 6

Tunnel coupling vs well depth for 1, 5, 9, and 13 electrons in two dots in the frozen-core approximation.

Figure 7

Ground- and first-excited-state energies (left) for 2, 6, 10, and 14 (top to bottom) electrons and the difference between the two (right) vs energy cutoff.

Figure 8

Splitting between ground- and first-excited-state energies vs energy cutoff for 2, 6, 10, and 14 electrons.

Figure 9

Spectrum vs trap frequency for 2, 6, 10, and 14 (top to bottom) electrons. Inset: Exchange energy vs trap frequency using cutoff energy and frozen-core approximations for comparison.

Figure 10

Fractional change in exchange energy due to impurity vs impurity distance for different numbers of electrons using the energy-cutoff approximation with $E_c=35,26,24,17$ for $N=2,6,10,14$ electrons, respectively.

Figure 11

Fractional change in exchange energy due to impurity vs impurity distance for (a) 2, (b) 6, (c) 10, and (d) 14 electrons with various energy cutoffs.