Anharmonic stabilization and band gap renormalization in the perovskite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CsSnI</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

Calculations of electronic and optical properties of solids at finite temperature including electronphonon interactions and quantum zero-point renormalization have enjoyed considerable progress during the past few years. Among the emerging methodologies in this area, we recently proposed a new approach to compute optical spectra at finite temperature including phonon-assisted quantum processes via a single supercell calculation [Zacharias and Giustino, Phys. Rev. B 94, 075125 (2016)]. In the present work we considerably expand the scope of our previous theory starting from a compact reciprocal space formulation, and we demonstrate that this improved approach provides accurate temperature-dependent band structures in three-dimensional and two-dimensional materials, using a special set of atomic displacements in a single supercell calculation. We also demonstrate that our special displacement reproduces the thermal ellipsoids obtained from X-ray crystallography, and yields accurate thermal averages of the mean-square atomic displacements. At a more fundamental level, we show that the special displacement represents an exact single-point approximant of an imaginary-time Feynman's path integral for the lattice dynamics. This enhanced version of the special displacement method enables non-perturbative, robust, and straightforward ab initio calculations of the electronic and optical properties of solids at finite temperature, and can easily be used as a post-processing step to any electronic structure code. To illustrate the capabilities of this method, we investigate the temperature-dependent band structures and atomic displacement parameters of prototypical nonpolar and polar semiconductors and of a prototypical two-dimensional semiconductor, namely Si, GaAs, and monolayer MoS2, and we obtain excellent agreement with previous calculations and experiments. Given its simplicity and numerical stability, the present development is suited for high-throughput calculations of band structures, quasiparticle corrections, optical spectra, and transport coefficients at finite temperature.

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“…In fact, by combining Eqs. (18) and (16) it follows directly that σ 2 κα (T ) = U κ,αα (T ). The ADPs of Eq.…”

Section: Zg Displacement and Thermal Ellipsoidsmentioning

confidence: 94%

“…The ADPs of Eq. (18) are the values employed to generate thermal ellipsoids when visualizing crystal structures at finite temperature.…”

Section: Zg Displacement and Thermal Ellipsoidsmentioning

confidence: 99%

Theory of the special displacement method for electronic structure calculations at finite temperature

Zacharias

Giustino

2020

Phys. Rev. Research

123

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“…[1][2][3][4][5][6][7] In addition to being investigated for use in radiation detectors and light emitting diodes, 8 the all-inorganic CsMX 3 (M = Ge, Sn, Pb; X = Cl, Br, I) perovskites offer an opportunity to understand the crystal chemistry of the divalent metal-halogen network without the added complexity introduced by the organic molecular ions present in the heavily studied organic-inorganic hybrids. [9][10][11][12] These materials are distinguished from tetrahedral semiconductors and from transition metal oxides in part by the presence of a s 2 lone pair on the divalent M-site cation. The lone pair gives rise to strong optical absorption near the bandgap and an unusual band structure, with the valence band comprising a mixture of cation s states and anion p states and three conduction bands comprised of cation p states.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stereochemical Activity of the Sn²⁺ Lone Pair in Perovskite CsSnBr₃

et al. 2016

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Stable s 2 lone pair electrons on heavy main-group elements in their lower oxidation states drive a range of important phenomena, such as the emergence of polar ground states in some ferroic materials. Here we study the perovskite halide CsSnBr 3 as an embodiment of the broader materials class. We show that lone pair stereochemical activity due to the Sn s 2 lone pair causes a crystallographically hidden, locally distorted state to appear upon warming, a phenomenon previously referred to as emphanisis.The synchrotron X-ray pair distribution function acquired between 300 K and 420 K reveals emerging asymmetry in the nearest-neighbor Sn-Br correlations, consistent with dynamic Sn 2+ off-centering, despite there being no evidence of any deviation from the average cubic structure. Computation based on density functional theory supports the finding of a lattice instability associated with dynamic off-centering of Sn 2+ in its coordination environment. Photoluminescence measurements reveal an unusual blueshift with increasing temperature, closely linked to the structural evolution. At low temperatures, the structures reflect the influence of octahedral rotation. A continuous transition from an orthorhombic structure (P nma, no. 62) to a tetragonal structure (P 4/mbm, no. 127) is found around 250 K, with a final, first-order transformation at 286 K to the cubic structure (P m3m, no. 221).2

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“…This problem can be overcome by pathintegral molecular dynamics 32 , but the even greater computational cost that the method needs to incorporate the quantum character of atomic vibrations makes it challenging. To surmount these difficulties, several methods 3,4,[33][34][35][36][37][38] have been developed, mainly inspired by the self-consistent harmonic approximation (SCHA) devised by Hooton 39 . The main idea of the SCHA is to use a variational principle, the Gibbs-Bogoliubov (GB) principle, in order to approximate the free energy of the true ionic Hamiltonian with the free energy calculated with a trial harmonic density matrix for the same system.…”

Section: Introductionmentioning

confidence: 99%

Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

et al. 2017

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The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in secondorder structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e. the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

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Anharmonic stabilization and band gap renormalization in the perovskiteCsSnI3

Cited by 92 publications

References 58 publications

Theory of the special displacement method for electronic structure calculations at finite temperature

Theory of the special displacement method for electronic structure calculations at finite temperature

Dynamic Stereochemical Activity of the Sn²⁺ Lone Pair in Perovskite CsSnBr₃

Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

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Anharmonic stabilization and band gap renormalization in the perovskiteCsSnI3

Cited by 92 publications

References 58 publications

Theory of the special displacement method for electronic structure calculations at finite temperature

Theory of the special displacement method for electronic structure calculations at finite temperature

Dynamic Stereochemical Activity of the Sn2+ Lone Pair in Perovskite CsSnBr3

Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

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Product

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Dynamic Stereochemical Activity of the Sn²⁺ Lone Pair in Perovskite CsSnBr₃