Local vibrational modes of Si vacancy spin qubits in SiC

Abstract

Silicon carbide is a very promising platform for quantum applications because of the extraordinary spin and optical properties of point defects in this technologically friendly material. These properties are strongly influenced by crystal vibrations, but the exact relationship between them and the behavior of spin qubits is not fully investigated. We uncover the local vibrational modes of the Si vacancy spin qubits in as-grown 4H-SiC. We apply microwave-assisted spectroscopy to isolate the contribution from one particular type of defects, the so-called V2 center, and observe the zero-phonon line together with seven equally separated phonon replicas. Furthermore, we present first-principles calculations of the photoluminescence line shape, which are in excellent agreement with our experimental data. To boost up the calculation accuracy and decrease the computation time, we extract the force constants using machine-learning algorithms. This allows us to identify the dominant modes in the lattice vibrations coupled to an excited electron during optical emission in the Si vacancy. A resonance phonon energy of 36 meV and a Debye-Waller factor of about 6% are obtained. We establish experimentally that the activation energy of the optically induced spin polarization is given by the local vibrational energy. Our findings give insight into the coupling of electronic states to vibrational modes in SiC spin qubits, which is essential to predict their spin, optical, mechanical, and thermal properties. The approach described can be applied to a large variety of spin defects with spectrally overlapped contributions in SiC as well as in other threeand two-dimensional materials.

Photoluminescence line shapes for color centers in silicon carbide from density functional theory calculations

“…Experimental data from Refs. [24] (Shang, 2020) and [25] (Udarvhelyi, 2020) measured at T = 15 and <30 K, respectively, are shown by the shaded areas. The intensity of the experimental line shapes from Ref.…”

“…As a result, 4H-SiC can host several defects with distinct photoluminescence (PL) peaks within the band gap. The most important ones are as follows: (i) The negatively charged silicon vacancy (V −1 Si ) in h or k sites with a zero-phonon line (ZPL) in the range of 1.352-1.445 eV [24][25][26][27]. It offers two excitation possibilities at each vacancy site.…”

“…Although all these defects have been the subject of several publications, the experimental results are usually focused on an individual color center. The only well-reported signatures of defects are the spectrally narrow emission spectra at a certain wavelength at low temperatures [19,[24][25][26][27][28][29][30][31][33][34][35][36][37][40][41][42][43]. Electronic structure calculations can be extremely useful to obtain detailed insight and understanding of defects, at a level inaccessible to experiment.…”

“…Accordingly, they have been routinely used to analyze, e.g., charge transition levels, spin states, and ZPLs [22,23,28,[48][49][50]. It was, however, only very recently [24,25] that the PSBs of V Si were calculated and compared to experimental data. While DWFs were reported, the contributions from different vibrational modes to them remain poorly understood.…”

Efficient construction of linear models in materials modeling and applications to force constant expansions

“…The second-order FCs of systems with many atoms and/or low symmetry can be tedious to obtain by the direct approach. This applies in particular to the FCs of defect configurations, which are needed for example for computing the vibrational contribution to the free energy of defect formation 16 , analyzing the impact of defects on the thermal conductivity 18,38,39 or predicting the vibrational broadening of optical spectra 40,41 . In this section, we therefore analyze the extraction of second-order FCs for the vacancy in body-centered cubic (BCC) Ta as a prototypical case, using both the direct approach as implemented in PHONOPY 25 and the regression approach as implemented in HIPHIVE 15 .…”