superlattices*

When ultrathin ferroelectric layers of PbTiO₃ are embedded in superlattices with a paraelectric material, such as SrTiO₃, the interplay between elastic, electrostatic, and gradient energies produces complex patterns of the electrical polarization. In particular, nanometer scale of vortex-antivortex arrays have been recently detected [1], and exotic properties such as the emergence of a negative capacitance have been measured [2]. Performing predictive simulations in these systems is difficult due to the long spatial scales involved, the strong competition between a large number of phases and the sensitivity of the results to external perturbations like strain, periodicity, temperature or electric fields. In order to overcome these problems we employ a recently developed second-principles method [3] that can cope with all the degrees of freedom associated to a large number of atoms retaining high accuracy. Depending on the boundary conditions, our simulations predict the existence of several quasi-degenerate phases at low energies each displaying different properties including net polarization, negative capacitance [4], non-null topological constants [5] and chirality [5,6]. The later prediction supports the findings of optical activity in x-ray circular dichroism experiments [5,6]. Moreover, depending on the periodicity of the superlattice these chiral vortex phases coexist with ferroelectric phases and reversible phase transitions can be induced by external electric fields [7].

[1] A. K. Yadav et al., Nature 530, 198 (2016)
[2] P. Zubko et al., Nature 534, 524 (2016)
[3] J. Wojdel et al., J. Phys.: Condens. Matter 25, 305401 (2013)
[4] A. K. Yadav et al., Nature (in press)
[5] S. Das et al., submitted
[6] P. Shafer et al., PNAS 115, 915 (2018)
[7] A. R. Damodaran et al., Nature Mater. 16, 1003 (2017)