D. Vanderbilt, J. Phys. Chem. Solids 61, 147 (2000) 0022-3697 10.1016/S0022-3697(99)00273-5.
X. Wu, D. Vanderbilt, and D. R. Hamann, Phys. Rev. B 72, 035105 (2005) 1098-0121 10.1103/PhysRevB.72.035105.
R. M. Martin, Phys. Rev. B 5, 1607 (1972) 0556-2805 10.1103/PhysRevB.5.1607.
D. Nelson and M. Lax, Phys. Rev. B 13, 1785 (1976) 0556-2805 10.1103/PhysRevB.13.1785.
M. Stengel, N. Spaldin, and D. Vanderbilt, Nat. Phys. 5, 304 (2009) 1745-2473 10.1038/nphys1185.
J. Yu and P.-E. Janolin, J. Appl. Phys. 131, 170701 (2022) 0021-8979 10.1063/5.0079510.
D. S. P. Tanner, P.-E. Janolin, and E. Bousquet, Phys. Rev. B 106, L060102 (2022) 2469-9950 10.1103/PhysRevB.106.L060102.
D.-S. Park, M. Hadad, L. Riemer, R. Ignatans, D. Spirito, V. Esposito, V. Tileli, N. Gauquelin, D. Chezganov, D. Jannis, Science 375, 653 (2022) 0036-8075 10.1126/science.abm7497.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.106.174105 for a detailed derivation of the fixed field-fixed voltage relations presented in the paper.
D. S. P. Tanner, E. Bousquet, and P.-E. Janolin, Small 17, 2103419 (2021) 1613-6810 10.1002/smll.202103419.
R. W. Nunes and X. Gonze, Phys. Rev. B 63, 155107 (2001) 0163-1829 10.1103/PhysRevB.63.155107.
I. Souza, J. Íniguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002) 0031-9007 10.1103/PhysRevLett.89.117602.
P. Umari and A. Pasquarello, Phys. Rev. Lett. 89, 157602 (2002) 0031-9007 10.1103/PhysRevLett.89.157602.
R. A. Toupin, J. Ration. Mech. Anal. 5, 849 (1956).
H. Ymeri, Electr. Eng. 80, 163 (1997) 0948-7921 10.1007/BF01235710.
R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993) 0163-1829 10.1103/PhysRevB.47.1651.
D. Vanderbilt and R. D. King-Smith, Phys. Rev. B 48, 4442 (1993) 0163-1829 10.1103/PhysRevB.48.4442.
M. Stengel, Nat. Commun. 4, 2693 (2013) 2041-1723 10.1038/ncomms3693.
(Equation presented) is equivalent to (Equation presented) but preserving the units of electric field, where the columns of (Equation presented) are the lattice vectors (including strain). (Equation presented) is equivalent to (Equation presented), where the columns of (Equation presented) are the reciprocal lattice vectors, and similarly for (Equation presented).
V. Sundar, J.-F. Li, D. Viehland, and R. Newnham, Mater. Res. Bull. 31, 555 (1996) 0025-5408 10.1016/S0025-5408(96)00036-0.
W. Kucharczyk, Z. Kristallogr.-Cryst. Mater. 181, 109 (1987) 2196-7105 10.1524/zkri.1987.181.14.109.
J. Schreuer and S. Haussühl, J. Phys. D: Appl. Phys. 32, 1263 (1999) 0022-3727 10.1088/0022-3727/32/11/313.
M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rignanese, Comput. Phys. Commun. 226, 39 (2018) 0010-4655 10.1016/j.cpc.2018.01.012.
J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. 100, 136406 (2008) 0031-9007 10.1103/PhysRevLett.100.136406.
I. Kornev, M. Willatzen, B. Lassen, and L. C. Lew Yan Voon, in 29th International Conference on the Physics of Semiconductors, edited by M. Caldas and N. Studart, AIP Conf. Proc. No. 1199 (AIP, New York, 2010), p. 71.
L. Pedesseau, C. Katan, and J. Even, Appl. Phys. Lett. 100, 031903 (2012) 0003-6951 10.1063/1.3676666.
C. Cancellieri, D. Fontaine, S. Gariglio, N. Reyren, A. D. Caviglia, A. Fete, S. J. Leake, S. A. Pauli, P. R. Willmott, M. Stengel, P. Ghosez, and J. M. Triscone, Phys. Rev. Lett. 107, 056102 (2011) 0031-9007 10.1103/PhysRevLett.107.056102.
Z. Jiang, R. Zhang, F. Li, L. Jin, N. Zhang, D. Wang, and C.-L. Jia, AIP Adv. 6, 065122 (2016) 2158-3226 10.1063/1.4954886.
R. Yimnirun, P. J. Moses, R. E. Newnham, and R. J. Meyer, J. Electroceram. 8, 87 (2002) 1385-3449 10.1023/A:1020543610685.
Z. Meng, Y. Sun, and L. E. Cross, Mater. Lett. 2, 544 (1984) 0167577X 10.1016/0167-577X(84)90091-0.
S. W. P. van Sterkenburg, J. Phys. D 25, 992 (1992) 0022-3727 10.1088/0022-3727/25/6/016.