Table 1 Calculated parameters.

From: Strong spin–orbit quenching via the product Jahn–Teller effect in neutral group IV qubits in diamond

 

SiV0

GeV0

SnV0

PbV0

\({\rho }_{0}^{(1)}\) [Å]

0.171

0.166

0.154

0.145

\({\rho }_{0}^{(2)}\) [Å]

−0.006

−0.022

−0.038

−0.051

\(\hbar\)ωE [meV]

87.3

86.6

87.7

90.8

Λ [meV]

81.6

86.4

98.2

112.5

\({E}_{{\rm{JT}}}^{(1)}\) [meV]

258

244

217

200

\({\delta }_{{\rm{JT}}}^{(1)}\) [meV]

82.2

75.5

63.5

64.5

\({E}_{{\rm{JT}}}^{(2)}\) [meV]

0.289

4.61

14.9

29.9

\({\delta }_{{\rm{JT}}}^{(2)}\) [meV]

0.147

0.307

0.226

2.18

γ(1) [meV]

7.18

7.59

8.96

10.4

γ(2) [meV]

3.21

4.06

6.22

7.90

ZPL (3Eu) [eV]

1.361

1.813

1.833

2.216

γ(2) + SOC [meV]

3.17

3.77

4.76

2.03

ZPL (3Eu) + SOC [eV]

1.361

1.812

1.825

2.170

pu

0.012

0.017

0.032

0.043

pg

0.012

0.012

0.023

0.040

λu + λg [meV]

0.089

0.622

3.15

11.31

  1. We determine the parameters \({\rho }_{0}^{{\mathrm{(i)}}}\), \({E}_{{\rm{JT}}}^{{\mathrm{(i)}}}\), \({\delta }_{{\rm{JT}}}^{{\mathrm{(i)}}}\) and Λ directly from the DFT potential energy surface (e.g., Fig. 1d). The effective vibrational energy \(\hbar\)ωE can be found from these parameters similarly to the case of the single Jahn–Teller (see Supplementary Note 2). The vibronic splitting between the lowest levels to first and second order are given by γ(1) and γ(2), respectively. SO effects are included nonperturbatively and we find significant quenching of the pure electronic SO splitting (pu,g ≪ 1), a consequence of the strong electron–phonon coupling induced by the pJT. The energy λu + λg corresponds to the energy splitting between the ms = ±1 levels of the lowest Eu vibronic eigenstates.
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