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Ruddelsden-Popper halide perovskites are highly versatile quasi-two-dimensional energy materials with a wide range of tunable optoelectronic properties. Here we use the all-inorganic Cs$_{n+1}$Pb$_n$X$_{3n+1}$ Ruddelsden-Popper perovskites with X=I, Br, and Cl to systematically model the effect of octahedral tilting distortions on the energy landscape, band gaps, macroscopic polarization, and the emergence of Rashba-/Dresselhaus splitting in these materials. We construct all unique $n=1$ and $n=2$ structures following from octahedral tilts and use first-principles density functional theory to calculate total energies, polarizations and band structures, backed up by band gap calculations using the $GW$ approach. Our results provide design rules for tailoring structural distortions and band-structure properties in all-inorganic Ruddelsden-Popper perovskites through the interplay of the amplitude, direction, and chemical character of the antiferrodistortive distortion modes contributing to each octahedral tilt pattern. Our work emphasizes that, in contrast to 3D perovskites, polar structures may arise from a combination of octahedral tilts, and Rashba-/Dresselhaus splitting in this class of materials is determined by the direction and Pb-I orbital contribution of the polar distortion mode.

In this work, we propose a class of ferroelectrics (which we denote "double-path" ferroelectrics), characterized by two competing polarization switching paths for which the change in polarization is different and in fact of opposite sign. Depending on which path is favorable under given conditions, this leads to different identification of up- and down-polarized states. Since the sign of piezoelectric response depends on the assignment of up- or down-polarized state for a specific structure, this means that the material can exhibit different signs of the piezoelectric response under different conditions. We focus on HfO$_2$ as a key example. Our first-principles calculations show that there are two competing paths in HfO$_2$, resulting from different displacements of the atoms from the initial to the final structures, and the change in polarization along these two paths is of opposite sign. These results provide a natural explanation for the recently observed discrepancy in the signs of piezoelectric responses in HfO$_2$ between theoretical first-principles calculations and experimental observation. Further, this allows predictions of how to favor one path over another by changes in conditions and compositional tuning. This family of materials also includes other candidates, such as CuInP$_2$S$_6$ and theoretically proposed LaVO$_3$-SrVO$_3$ superlattice. We finally note that double-path ferroelectrics possess novel electromechanical properties since the signs of their piezoelectric responses can be switched., Comment: 7 pages, 5 figures

Crystalline materials with broken inversion symmetry can exhibit a spontaneous electric polarization, which originates from a microscopic electric dipole moment. Long-range polar or anti-polar order of such permanent dipoles gives rise to ferroelectricity or antiferroelectricity, respectively. However, the recently discovered antiferroelectrics of fluorite structure (HfO$_2$ and ZrO$_2$) are different: A non-polar phase transforms into a polar phase by spontaneous inversion symmetry breaking upon the application of an electric field. Here, we show that this structural transition in antiferroelectric ZrO$_2$ gives rise to a negative capacitance, which is promising for overcoming the fundamental limits of energy efficiency in electronics. Our findings provide insight into the thermodynamically 'forbidden' region of the antiferroelectric transition in ZrO$_2$ and extend the concept of negative capacitance beyond ferroelectricity. This shows that negative capacitance is a more general phenomenon than previously thought and can be expected in a much broader range of materials exhibiting structural phase transitions.

We use first principles density functional theory calculations to investigate the effect of biaxial strain in the low-temperature structural and ferroelectric properties of [111]-oriented SrTiO$_3$. We find that [111] biaxial strain, achievable by coherent epitaxial growth along the [111] direction, induces structural distortions in SrTiO$_3$ that are not present in either bulk or [001]-oriented SrTiO$_3$. Under [111] biaxial strain, SrTiO$_3$ displays ferroelectricity at tensile strain, and paraelectricity at compressive strain. We compute the phonon spectrum and macroscopic polarization of SrTiO$_3$ as a function of [111] biaxial strain, and relate our results to the predictions of the free energy phenomenological model of Pertsev, Tagantsev and Setter [Phys. Rev. B 61, 825 (2000); Phys. Rev. B 65, 219901 (2002)].

Using first principles density functional theory calculations, we show how Rashba-type energy band splitting in the hybrid organic-inorganic halide perovskites APbX$_3$ (A=CH$_3$NH$_3^+$, CH(NH$_2$)$_2^+$, Cs$^+$ and X=I, Br) can be tuned and enhanced with electric fields and anisotropic strain. In particular, we demonstrate that the magnitude of the Rashba splitting of tetragonal (CH$_3$NH$_3$)PbI$_3$ grows with increasing macroscopic alignment of the organic cations and electric polarization, indicating appreciable tunability with experimentally-feasible applied fields, even at room temperature. Further, we quantify the degree to which this effect can be tuned via chemical substitution at the A and X sites, which alters amplitudes of different polar distortion patterns of the inorganic PbX$_3$ cage that directly impact Rashba splitting. In addition, we predict that polar phases of CsPbI$_3$ and (CH$_3$NH$_3$)PbI$_3$ with $R3c$ symmetry possessing considerable Rashba splitting might be accessible at room temperature via anisotropic strain induced by epitaxy, even in the absence of electric fields.

The Ruddlesden-Popper (RP) homologous series Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ provides a useful template for the study and control of the effects of dimensionality and quantum confinement on the excited state properties of the complex oxide SrTiO$_3$. We use ab initio many-body perturbation theory within the $GW$ approximation and the Bethe-Salpeter equation approach to calculate quasiparticle energies and absorption spectrum of Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ for $n=1-5$ and $\infty$. Our computed direct and indirect optical gaps are in excellent agreement with spectroscopic measurements. The calculated optical spectra reproduce the main experimental features and reveal excitonic structure near the gap edge. We find that electron-hole interactions are important across the series, leading to significant exciton binding energies that increase for small $n$ and reach a value of 330~meV for $n=1$, a trend attributed to increased quantum confinement. We find that the lowest-energy singlet exciton of Sr$_2$TiO$_4$ ($n=1$) localizes in the 2D plane defined by the TiO$_2$ layer, and explain the origin of its localization.

Density functional calculations are performed to investigate the experimentally-reported field-induced phase transition in thin-film ZrO2 (J. Muller et al., Nano. Lett. 12, 4318). We find a small energy difference of ~ 1 meV/f.u. between the nonpolar tetragonal and polar orthorhombic structures, characteristic of antiferroelectricity. The requisite first-order transition between the two phases, which atypically for antiferroelectrics have a group-subgroup relation, results from coupling to other zone-boundary modes, as we show with a Landau-Devonshire model. Tetragonal ZrO2 is thus established as a previously unrecognized lead-free antiferroelectric with excellent dielectric properties and compatibility with silicon. In addition, we demonstrate that a ferroelectric phase of ZrO2 can be stabilized through epitaxial strain, and suggest an alternative stabilization mechanism through continuous substitution of Zr by Hf., Comment: 5 pages, 5 figures

Density functional calculations are performed to study the effect of epitaxial strain on PbZrO3. We find a remarkably small energy difference between the epitaxially strained polar R3c and nonpolar Pbam structures over the full range of experimentally accessible epitaxial strains -3% < \eta < 4%. While ferroelectricity is favored for all compressive strains, for tensile strains the small energy difference between the nonpolar ground state and the alternative polar phase yields a robust antiferroelectric ground state. The coexistence of ferroelectricity and antiferroelectricity observed in thin films is attributed to a combination of strain and depolarization field effects., Comment: 4 pages, 3 figures