Charge-Noise Resilience of Two-Electron Quantum Dots in $\mathrm{Si}/\mathrm{SiGe}$ Heterostructures

Charge-Noise Resilience of Two-Electron Quantum Dots in $Si / SiGe$ Heterostructures

H. Ekmel Ercan, Mark Friesen, and S. N. Coppersmith

Phys. Rev. Lett. 128, 247701 – Published 16 June 2022

Abstract

The valley degree of freedom presents challenges and opportunities for silicon spin qubits. An important consideration for singlet-triplet states is the presence of two distinct triplets, composed of valley vs orbital excitations. Here, we show that both of these triplets are present in the typical operating regime, but that only the valley-excited triplet offers intrinsic protection against charge noise. We further show that this protection arises naturally in dots with stronger confinement. These results reveal an inherent advantage for silicon-based multielectron qubits.

Received 3 June 2021
Revised 30 March 2022
Accepted 7 April 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.247701

Physics Subject Headings (PhySH)

Noise Quantum information with solid state qubits

Interfaces Quantum dots

Configuration interaction Tight-binding model

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Ekmel Ercan ¹, Mark Friesen ¹, and S. N. Coppersmith ^1,2

¹Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
²School of Physics, The University of New South Wales, Sydney, New South Wales 2052, Australia

Strong electron-electron interactions in Si/SiGe quantum dots

H. Ekmel Ercan, S. N. Coppersmith, and Mark Friesen

Phys. Rev. B 104, 235302 (2021)

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Vol. 128, Iss. 24 — 17 June 2022

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Figure 1
Effects of $e − e$ interactions and electrical noise on singlet-triplet states in a two-electron $Si / SiGe$ quantum dot. (a) Noninteracting electrons. Single-electron energy levels (black lines) include valley and orbital excited states, with $E_{val} < E_{orb}$ . Two-electron states ( $S$ , $T_{val}$ , and $T_{orb}$ ) are formed from combinations of spin, valley, and orbital states (red arrows). Charge distributions are shown schematically, with darker colors indicating higher densities. The two $T_{orb}$ states have distinct $p_{x}$ or $p_{y}$ character. (b) Including $e − e$ interactions. In the high- $E_{orb}$ regime, we find $E_{{S T}_{val}} < E_{{S T}_{orb}}$ . The resulting low-energy states ( $S$ and $T_{val}$ ) have very similar charge distributions. (c) Stronger $e − e$ interactions (low- $E_{orb}$ regime). Here, $E_{{S T}_{orb}} < E_{{S T}_{val}}$ , and the low-energy states ( $S$ and $T_{orb}$ ) have very different charge distributions. (d),(e) The responses of $S$ , $T_{orb}$ , and $T_{val}$ to a charge trap (CT) depend on their charge distributions. (d) Dissimilar distributions give large $E_{S T_{orb}}$ fluctuations. (e) Similar distributions give small $E_{S T_{val}}$ fluctuations.
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Figure 2
Overview of theoretical methods. (a) Schematic of the 2D TB method used to compute single-electron wave functions, while accounting for atomic-scale disorder at the quantum well interface. Si sites are shown as white and SiGe sites are shown as gray. Interface steps have width $W$ , the harmonic dot confinement potential (red) has diameter $D$ , and we take the dot to be centered halfway between two steps, $d = W / 2$ . Hopping parameters $t_{1}$ , $t_{2}$ , and $t_{3}$ and on-site parameters are discussed in the main text. (b) Typical results for single-electron energies $ϵ_{i}$ . (c) FCI step: Slater determinants $ψ_{α}$ are computed for spin orbitals $χ_{i}$ , obtained from TB valley orbitals $ϕ_{i}$ , combined with spin coordinates. The two-electron Hamiltonian $H^{2 e}$ is diagonalized in this Slater basis, with enough spin-orbit basis states (84) to ensure convergence. (d) Typical results for two-electron energies $E_{q}$ .
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Figure 3
Effects of $e - e$ interactions, interface steps, and a charge trap on the excitation energies of a two-electron dot. Solid symbols refer to the lowest $S T$ excitation, which defines the qubit, and open symbols refer to the higher $S T$ excitation. (a) $S T$ splittings for fixed terrace width, $W = 101 nm$ , with the dot center equidistant between two steps. [See Fig. 2 for device geometry.] The single-electron valley splitting $E_{val}$ is also shown. $E_{{S T}_{orb}}$ is strongly suppressed below $E_{orb}$ (not shown) over its entire range, due to strong $e − e$ interactions. A crossover is observed between regions dominated by $S T_{orb}$ vs $S T_{val}$ . Here, $E_{{S T}_{orb}}$ is typically too small to form practical qubits in the small- $ℏ ω$ regime. Insets: charge densities of $S$ , $T_{orb}$ , and $T_{val}$ states, for two different confinement strengths. (b) $S T$ splittings for fixed $W / D = 2$ , where the dot diameter $D$ depends on $ℏ ω$ (so $W$ also depends on $ℏ ω$ ). Here, $E_{{S T}_{val}} \approx E_{val}$ is approximately constant, indicating that VOC is mainly determined by the overlap of the wave functions with interface steps. Insets: the same quantities are plotted as a function of $W / D$ for fixed $ℏ ω$ , showing that $E_{{S T}_{val}}$ is more strongly affected by the steps than $E_{{S T}_{orb}}$ . In (a) and (b), the triplet crossover occurs in an experimentally relevant regime. (c) Shift in $E_{S T}$ , and corresponding qubit dephasing rate $Γ_{2}^{*}$ , as a function of the shift in detuning, $ϵ$ , due to the occupation of a charge trap near the top gate. Results are only shown for the low-lying excitations, just below or above the triplet crossover in (a). $Γ_{2}^{*}$ is significantly lower for qubits defined by $T_{val}$ since $S$ and $T_{val}$ have nearly identical charge distributions. Lower inset: schematic of the full double-dot geometry, with the smaller FCI simulation domain indicated. Upper inset: shift of the detuning $ϵ$ of a double dot, for dots separated by 200 nm, due to the occupation of a charge trap at lateral position $x_{CT}$ , defined in the lower inset.
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Physical Review Letters

Charge-Noise Resilience of Two-Electron Quantum Dots in $Si / SiGe$ Heterostructures

H. Ekmel Ercan, Mark Friesen, and S. N. Coppersmith

Phys. Rev. Lett. 128, 247701 – Published 16 June 2022

Abstract

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Strong electron-electron interactions in Si/SiGe quantum dots

H. Ekmel Ercan, S. N. Coppersmith, and Mark Friesen

Phys. Rev. B 104, 235302 (2021)

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Physical Review Letters

Charge-Noise Resilience of Two-Electron Quantum Dots in Si/SiGe Heterostructures

H. Ekmel Ercan, Mark Friesen, and S. N. Coppersmith

Phys. Rev. Lett. 128, 247701 – Published 16 June 2022

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

See Also

Strong electron-electron interactions in Si/SiGe quantum dots

H. Ekmel Ercan, S. N. Coppersmith, and Mark Friesen

Phys. Rev. B 104, 235302 (2021)

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Charge-Noise Resilience of Two-Electron Quantum Dots in $Si / SiGe$ Heterostructures