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Transparency Enhancement for SrVO 3 by SrTiO 3 Mixing: A First- Principles Study Z. T. Y. Liu 1, N. J. Podraza 1, S. V. Khare 1*, P. Sarin 2 1 Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA 2 School of Materials Science and Engineering, Oklahoma State University, Tulsa, OK 74106, USA *Corresponding author: sanjay.khare@utoledo.edu Supplemental Materials

A. Magnetism and potential choices for V We justify the choice of U = 4 ev for V. Figure S1 shows the energy-dependent complex dielectric function spectra!! and!! for SrVO 3, and Figure S2 shows the band structures calculated with different parameter sets. In Figure S1, there are curves from six variations, ferromagnetic (FM) or non-magnetic (NM) with PBE potentials and U = 0 or 4 ev, or using the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06). In agreement with previous calculations 1, FM/U = 0 matches the experimental measurements well. Comparing FM/U = 0 and NM/U = 0, the lack of consideration of magnetization has a small influence on the complex dielectric functions, consistent with previous calculations 1. It red-shifts (lower) the rise of!! at ~2.8 ev by 0.2 ev. On the other hand, within FM, the introduction of the GGA+U scheme with U = 4 ev red-shifts the rise of!! greatly, by 0.8 ev, while within NM, it merely blue-shifts (higher) the rise by 0.2 ev, overlapping with the FM/U = 0 curve. Generally, GGA+U widens the band gap for semiconductors and insulators, and blue-shifts the overall complex dielectric function curves, as in the NM case. Further calculations reveal that for FM, U = 0 results in the magnetic moment of V 4+ being 0.5!!, and a value of U beyond 2 ev increases the effective on-site Coulomb repulsion and raises the magnetic moment to 1!!. At U = 4 ev, there is a larger separation between the spin-up and spin-down channels of the V-t 2g bands around the Fermi energy level (E F ) as shown in Figure S2(a) and (b). Each channel then gets closer to the adjacent bands, i.e. the lower-lying O-p and higher-lying V-e g bands, facilitating interband transitions. GGA+U leads to little change of the NM band structure, because there is no such spin channel separation occurring in the FM case. Only NM/U = 4 ev is shown in Figure S2(c), similar to FM/U = 0 in Figure S2(a). The FM and NM HSE06 curves in Figure S1 deviate greatly from the experimental observations. In short, considering the correlated nature of SrVO 3, small magnetic moments, and agreement of complex dielectric functions with the experimental measurements, we used NM/U = 4 ev for all calculations in this work.

Figure S1. Calculated complex dielectric function spectra!! and!! of SrVO 3 with different parameter settings. FM stands for the ferromagnetic configuration for V 4+ and NM for nonmagnetic. The first four cases were calculated with PBE potentials, and last two with HSE06.

Figure S2. Calculated band structures of SrVO3 with (a) FM/U = 0, (b) FM/U = 4 ev, (c) NM/U = 4 ev, all with PBE potentials. FM stands for the ferromagnetic configuration for V4+ and NM for non-magnetic. In cases of FM, the solid blue and dashed red curves stand for the spin-up and spin-down channels, respectively.

B. Cluster expansion Below we provide detailed information of the cluster set used in the fitting process. Figure S3. Effective cluster interactions (ECIs) of SrTi 1-x V x O 3. ECI values have been multiplied by their multiplicities. Blue circles and red squares triangles indicate pair and triplet interactions. Connecting lines are a guide to the eye. Table S1. Cluster sets and effective cluster interactions (ECIs) of SrTi 1-x V x O 3. Type Index Diameter (Å) Multiplicity Coordinates ECI (mev) empty 1 0.00 1 25.777 point 1 0.00 1 [[1.0, 1.0, 1.0]] 8.794 pair 1 3.87 3 [1.0, 0.0, 1.0]] -7.326 pair 2 5.47 6 pair 3 6.70 4 pair 4 7.73 3 [1.0, 0.0, 0.0]] [0.0, 0.0, 0.0]] [1.0, 1.0, -1.0]] -1.738-0.006 2.152 trip 1 5.47 12 [1.0, 1.0, 0.0], [1.0, 0.0, 0.0]] 0.668

trip 2 5.47 8 trip 3 6.70 24 trip 4 7.73 3 trip 5 7.73 12 trip 6 7.73 12 [0.0, 1.0, 0.0], [1.0, 0.0, 0.0]] [1.0, 1.0, 0.0], [0.0, 0.0, 0.0]] [1.0, 1.0, 0.0], [1.0, 1.0, -1.0]] [1.0, 0.0, 0.0], [1.0, 1.0, -1.0]] [0.0, 0.0, 0.0], [1.0, 1.0, -1.0]] 0.534-0.180 1.612 0.152-0.423 Volumes of random solid solutions deviate from linearity slightly with down-bowing behavior. Figure S4. Volume deviations from linearity of SrTi 1-x V x O 3. Curves indicate CE-fitted values of the random solid solution configurations. C. Special quasi-random structure (SQS) prototypes Here we provide the ionic configurations of the SQS s of SrTi 1-x V x O 3 at x = 8/9, 7/9,, 1/9. Each SQS is a cubic supercell with a lattice constant of 11.6 Å of 3 3 3 5-atom unit cells. The 27 exchangeable sites are listed for Ti and V. Coordinates of the other ions are provided at the end.

Table S2. Ionic configurations of the SQS s of SrTi 1-x V x O 3 at x = 8/9, 7/9,, 1/9. x = 8/9: Ti 0.333 0.333 1.000 Ti 1.000 0.333 0.333 Ti 0.667 0.333 0.333 V 1.000 1.000 1.000 V 1.000 0.667 0.333 V 0.333 1.000 1.000 V 0.333 0.667 0.333 V 0.667 1.000 1.000 V 0.667 0.667 0.333 V 1.000 0.333 1.000 V 1.000 1.000 0.667 V 0.667 0.333 1.000 V 0.333 1.000 0.667 V 1.000 0.667 1.000 V 0.667 1.000 0.667 V 0.333 0.667 1.000 V 1.000 0.333 0.667 V 0.667 0.667 1.000 V 0.333 0.333 0.667 V 1.000 1.000 0.333 V 0.667 0.333 0.667 V 0.333 1.000 0.333 V 1.000 0.667 0.667 V 0.667 1.000 0.333 V 0.333 0.667 0.667 V 0.333 0.333 0.333 V 0.667 0.667 0.667 x = 7/9: Ti 0.333 1.000 1.000 Ti 0.667 0.333 1.000 Ti 0.333 0.667 1.000 Ti 0.667 0.667 1.000 V 0.667 0.333 0.333 Ti 0.333 0.333 0.333 V 1.000 0.667 0.333 Ti 0.333 1.000 0.667 V 0.333 0.667 0.333 V 1.000 1.000 1.000 V 0.667 0.667 0.333 V 0.667 1.000 1.000 V 1.000 1.000 0.667 V 1.000 0.333 1.000 V 0.667 1.000 0.667 V 0.333 0.333 1.000 V 1.000 0.333 0.667 V 1.000 0.667 1.000 V 0.333 0.333 0.667 V 1.000 1.000 0.333 V 0.667 0.333 0.667 V 0.333 1.000 0.333 V 1.000 0.667 0.667 V 0.667 1.000 0.333 V 0.333 0.667 0.667 V 1.000 0.333 0.333 V 0.667 0.667 0.667 x = 6/9:

Ti 0.333 1.000 1.000 Ti 1.000 0.333 1.000 Ti 1.000 0.667 1.000 Ti 0.667 0.667 1.000 V 0.333 0.333 0.333 Ti 0.333 1.000 0.333 V 0.667 0.333 0.333 Ti 0.667 1.000 0.333 V 0.667 0.667 0.333 Ti 1.000 0.333 0.333 V 1.000 1.000 0.667 Ti 1.000 0.667 0.333 V 0.333 1.000 0.667 Ti 0.333 0.667 0.333 V 0.667 1.000 0.667 V 1.000 1.000 1.000 V 1.000 0.333 0.667 V 0.667 1.000 1.000 V 0.333 0.333 0.667 V 0.333 0.333 1.000 V 0.667 0.333 0.667 V 0.667 0.333 1.000 V 1.000 0.667 0.667 V 0.333 0.667 1.000 V 0.333 0.667 0.667 V 1.000 1.000 0.333 V 0.667 0.667 0.667 x = 5/9: Ti 1.000 1.000 1.000 Ti 0.333 1.000 1.000 Ti 0.667 1.000 1.000 Ti 1.000 0.333 1.000 V 0.333 1.000 0.333 Ti 0.333 0.333 1.000 V 1.000 0.333 0.333 Ti 1.000 0.667 1.000 V 0.333 0.333 0.333 Ti 0.667 0.667 1.000 V 0.667 0.333 0.333 Ti 0.667 1.000 0.333 V 1.000 0.667 0.333 Ti 0.333 0.667 0.333 V 0.333 1.000 0.667 Ti 0.667 0.667 0.333 V 0.667 1.000 0.667 Ti 1.000 1.000 0.667 V 1.000 0.333 0.667 Ti 0.333 0.667 0.667 V 0.333 0.333 0.667 V 0.667 0.333 1.000 V 0.667 0.333 0.667 V 0.333 0.667 1.000 V 1.000 0.667 0.667 V 1.000 1.000 0.333 V 0.667 0.667 0.667 x = 4/9:

Ti 1.000 1.000 1.000 Ti 0.333 1.000 1.000 Ti 1.000 0.333 1.000 Ti 0.667 0.333 1.000 V 0.667 1.000 1.000 Ti 0.667 0.667 1.000 V 0.333 0.333 1.000 Ti 1.000 0.333 0.333 V 1.000 0.667 1.000 Ti 0.333 0.667 0.333 V 0.333 0.667 1.000 Ti 0.333 1.000 0.667 V 1.000 1.000 0.333 Ti 0.667 1.000 0.667 V 0.333 1.000 0.333 Ti 1.000 0.333 0.667 V 0.667 1.000 0.333 Ti 0.333 0.333 0.667 V 0.333 0.333 0.333 Ti 0.667 0.333 0.667 V 0.667 0.333 0.333 Ti 1.000 0.667 0.667 V 1.000 0.667 0.333 Ti 0.333 0.667 0.667 V 0.667 0.667 0.333 Ti 0.667 0.667 0.667 V 1.000 1.000 0.667 x = 3/9: Ti 1.000 1.000 1.000 Ti 0.333 0.333 1.000 Ti 1.000 0.667 1.000 Ti 0.667 0.667 1.000 Ti 1.000 0.667 0.667 Ti 0.333 1.000 0.333 Ti 0.333 0.667 0.667 Ti 1.000 0.333 0.333 Ti 0.667 0.667 0.667 Ti 0.333 0.333 0.333 V 0.333 1.000 1.000 Ti 1.000 0.667 0.333 V 0.667 1.000 1.000 Ti 0.333 0.667 0.333 V 1.000 0.333 1.000 Ti 0.667 0.667 0.333 V 0.667 0.333 1.000 Ti 0.333 1.000 0.667 V 0.333 0.667 1.000 Ti 0.667 1.000 0.667 V 1.000 1.000 0.333 Ti 1.000 0.333 0.667 V 0.667 1.000 0.333 Ti 0.333 0.333 0.667 V 0.667 0.333 0.333 Ti 0.667 0.333 0.667 V 1.000 1.000 0.667 x = 2/9: Ti 1.000 1.000 1.000 Ti 0.333 1.000 1.000

Ti 0.667 1.000 1.000 Ti 1.000 0.333 1.000 Ti 1.000 0.333 0.667 Ti 0.333 0.333 1.000 Ti 0.333 0.333 0.667 Ti 1.000 0.667 1.000 Ti 0.667 0.333 0.667 Ti 0.333 0.667 1.000 Ti 1.000 0.667 0.667 Ti 0.667 0.667 1.000 Ti 0.333 0.667 0.667 Ti 0.667 1.000 0.333 Ti 0.667 0.667 0.667 Ti 0.333 0.333 0.333 V 0.667 0.333 1.000 Ti 1.000 0.667 0.333 V 1.000 1.000 0.333 Ti 0.333 0.667 0.333 V 0.333 1.000 0.333 Ti 0.667 0.667 0.333 V 1.000 0.333 0.333 Ti 1.000 1.000 0.667 V 0.667 0.333 0.333 Ti 0.333 1.000 0.667 V 0.667 1.000 0.667 x = 1/9: Ti 1.000 1.000 1.000 Ti 0.333 1.000 1.000 Ti 1.000 0.333 1.000 Ti 0.333 0.333 1.000 Ti 0.667 0.667 0.333 Ti 0.667 0.333 1.000 Ti 1.000 1.000 0.667 Ti 1.000 0.667 1.000 Ti 0.333 1.000 0.667 Ti 0.333 0.667 1.000 Ti 1.000 0.333 0.667 Ti 0.667 0.667 1.000 Ti 0.333 0.333 0.667 Ti 0.333 1.000 0.333 Ti 0.667 0.333 0.667 Ti 0.667 1.000 0.333 Ti 1.000 0.667 0.667 Ti 1.000 0.333 0.333 Ti 0.333 0.667 0.667 Ti 0.333 0.333 0.333 Ti 0.667 0.667 0.667 Ti 0.667 0.333 0.333 V 0.667 1.000 1.000 Ti 1.000 0.667 0.333 V 1.000 1.000 0.333 Ti 0.333 0.667 0.333 V 0.667 1.000 0.667 Other ions: Sr 0.167 0.167 0.167 O 1.000 1.000 0.167 Sr 0.500 0.167 0.167 O 0.333 1.000 0.167 Sr 0.833 0.167 0.167 O 0.667 1.000 0.167 Sr 0.167 0.500 0.167 O 1.000 0.333 0.167

Sr 0.500 0.500 0.167 O 0.333 0.333 0.167 Sr 0.833 0.500 0.167 O 0.667 0.333 0.167 Sr 0.167 0.833 0.167 O 1.000 0.667 0.167 Sr 0.500 0.833 0.167 O 0.333 0.667 0.167 Sr 0.833 0.833 0.167 O 0.667 0.667 0.167 Sr 0.167 0.167 0.500 O 1.000 1.000 0.500 Sr 0.500 0.167 0.500 O 0.333 1.000 0.500 Sr 0.833 0.167 0.500 O 0.667 1.000 0.500 Sr 0.167 0.500 0.500 O 1.000 0.333 0.500 Sr 0.500 0.500 0.500 O 0.333 0.333 0.500 Sr 0.833 0.500 0.500 O 0.667 0.333 0.500 Sr 0.167 0.833 0.500 O 1.000 0.667 0.500 Sr 0.500 0.833 0.500 O 0.333 0.667 0.500 Sr 0.833 0.833 0.500 O 0.667 0.667 0.500 Sr 0.167 0.167 0.833 O 1.000 1.000 0.833 Sr 0.500 0.167 0.833 O 0.333 1.000 0.833 Sr 0.833 0.167 0.833 O 0.667 1.000 0.833 Sr 0.167 0.500 0.833 O 1.000 0.333 0.833 Sr 0.500 0.500 0.833 O 0.333 0.333 0.833 Sr 0.833 0.500 0.833 O 0.667 0.333 0.833 Sr 0.167 0.833 0.833 O 1.000 0.667 0.833 Sr 0.500 0.833 0.833 O 0.333 0.667 0.833 Sr 0.833 0.833 0.833 O 0.667 0.667 0.833 O 1.000 0.167 1.000 O 0.167 1.000 1.000 O 0.333 0.167 1.000 O 0.500 1.000 1.000 O 0.667 0.167 1.000 O 0.833 1.000 1.000 O 1.000 0.500 1.000 O 0.167 0.333 1.000 O 0.333 0.500 1.000 O 0.500 0.333 1.000 O 0.667 0.500 1.000 O 0.833 0.333 1.000 O 1.000 0.833 1.000 O 0.167 0.667 1.000 O 0.333 0.833 1.000 O 0.500 0.667 1.000 O 0.667 0.833 1.000 O 0.833 0.667 1.000 O 1.000 0.167 0.333 O 0.167 1.000 0.333 O 0.333 0.167 0.333 O 0.500 1.000 0.333 O 0.667 0.167 0.333 O 0.833 1.000 0.333 O 1.000 0.500 0.333 O 0.167 0.333 0.333 O 0.333 0.500 0.333 O 0.500 0.333 0.333 O 0.667 0.500 0.333 O 0.833 0.333 0.333 O 1.000 0.833 0.333 O 0.167 0.667 0.333 O 0.333 0.833 0.333 O 0.500 0.667 0.333

O 0.667 0.833 0.333 O 0.833 0.667 0.333 O 1.000 0.167 0.667 O 0.167 1.000 0.667 O 0.333 0.167 0.667 O 0.500 1.000 0.667 O 0.667 0.167 0.667 O 0.833 1.000 0.667 O 1.000 0.500 0.667 O 0.167 0.333 0.667 O 0.333 0.500 0.667 O 0.500 0.333 0.667 O 0.667 0.500 0.667 O 0.833 0.333 0.667 O 1.000 0.833 0.667 O 0.167 0.667 0.667 O 0.333 0.833 0.667 O 0.500 0.667 0.667 O 0.667 0.833 0.667 O 0.833 0.667 0.667 Here we show the bond lengths of Ti-O and bond angles O-Ti-O in SQS s of SrTi 1-x V x O 3 with different compositions x for completeness. Figure S5. Bond lengths of Ti-O, and bond angles of O-Ti-O in SQS s of SrTi 1-x V x O 3 with different compositions x. Each box extends from the lower to upper quartile values, with a line at the median. The whiskers extend from the box to show the range of the data. Widths of the box are scaled with respect to numbers of data points. The slightly horizontally jittered red dots are actual values. The dashed lines correspond to values in the end member SrTiO 3.

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