Electron spin decoherence in silicon carbide nuclear spin bath

Rapid Communication

Electron spin decoherence in silicon carbide nuclear spin bath

Li-Ping Yang, Christian Burk, Matthias Widmann, Sang-Yun Lee, Jörg Wrachtrup, and Nan Zhao

Phys. Rev. B 90, 241203(R) – Published 22 December 2014

Abstract

In this Rapid Communication, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of ${}^{29}{Si}$ ( $p_{Si} = 4.7 %$ ) is about four times larger than that of $^{13} C$ ( $p_{C} = 1.1 %$ ), the electron spin coherence time of defect centers in SiC nuclear spin bath in a strong magnetic field ( $B > 300 G$ ) is longer than that of nitrogen-vacancy (NV) centers in $^{13} C$ nuclear spin bath in diamond. In addition to the smaller gyromagnetic ratio of ${}^{29}{Si}$ , and the larger bond length in SiC lattice, a crucial reason for this counterintuitive result is the suppression of the heteronuclear-spin flip-flop process in a finite magnetic field. Our results show that electron spin of defect centers in SiC are excellent candidates for solid state spin qubit in quantum information processing.

Received 2 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.241203

Authors & Affiliations

Li-Ping Yang¹, Christian Burk², Matthias Widmann², Sang-Yun Lee², Jörg Wrachtrup², and Nan Zhao^1,2,3,*

¹Beijing Computational Science Research Center, Beijing 100084, China
²3. Physikalisches Institut and Research Center SCOPE, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
³Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

^*nzhao@csrc.ac.cn; http://www.csrc.ac.cn/∼nzhao/

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Issue

Vol. 90, Iss. 24 — 15 December 2014

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Images

Figure 1
(a) Schematic for the $V_{Si}$ defect in 4H-SiC. The $z$ direction is chosen along the $c$ axis of the crystal. Black and gray spheres represent carbon and silicon atoms, respectively. (b) Schematic for SiC nuclear spin bath. The flip-flop process between the heteronuclear spins is significantly suppressed in finite magnetic fields.
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Figure 2
(a) Pseudospin model of a homonuclear spin pair in the strong magnetic field. The polarized states are well decoupled due to the large Zeeman splitting $Δ$ . The unpolarized states form a pseudospin with frequency splitting $δ$ and transition rate $Ω$ . (b) Energy levels of the heteronuclear spin pair in the strong magnetic field. Both level splittings $Δ$ and $δ$ are proportional to the magnetic field strength. In additional to the secular flip-flop between the unpolarized states, the nonsecular single spin flipping, induced by the vertical component of the hyperfine field $A_{⊥}$ , can also happen with comparable probability (see text). However, all the spin transitions are significantly suppressed in strong magnetic fields.
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Figure 3
The contributions of single nuclear spin pairs to the electron spin coherence (Hahn echo). The red solid line, blue dashed line, and gray dashed-dotted line correspond to the ${}^{29}{Si} -^{13} C$ pair, the $^{13} C -^{13} C$ pair, and the ${}^{29}{Si} - {}^{29}{Si}$ pair, respectively. The magnetic field is $B = 1000$ G. The inset shows a close-up of the contribution of the ${}^{29}{Si} -^{13} C$ heteronuclear spin pair. All these pairs have similar internuclei separations and distances to the defect center.
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Figure 4
The typical FID of the $T_{V 2}$ center in the cases of zero field (dashed blue line) and strong field (solid red line) are presented. The inset gives the histogram of the FID coherence time $T_{2}^{*}$ distribution of 1000 randomly generated bath configurations under zero and strong fields.
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Figure 5
(a) Hahn echo of the $T_{V 2}$ center spin coherence between $| 1 / 2 〉$ and $| 3 / 2 〉$ states as a function of total evolution time $t$ and magnetic field $B$ . The strong, medium, and weak magnetic field regimes, in which the $T_{V 2}$ center spin has different decoherence behavior, are separated by the horizontal dashed lines. (b) Calculated Hahn echo coherence with different CCE orders. (c)–(e) The typical Hahn echo coherence behavior for weak, medium, and strong magnetic fields, respectively.
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Figure 6
(a) The influence of heteronuclear spin pairs on the Hahn echo in zero field. The red solid line is the electron spin coherence in real SiC nuclear spin bath. The blue dashed line is calculated with all the ${}^{29}{Si}$ spins replaced by $^{13} C$ spins. The gray dashed-dotted line is calculated with all the $^{13} C$ spins replaced by ${}^{29}{Si}$ spins. (b) The same as (a), but in a strong magnetic field.
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