The special displacement method as a unified treatment of anharmonicity and electron-phonon coupling in solids

Including quantum nuclear effects in electronic structure calculations of solids has been the focus of intensive research over the last decade. These effects drive electron-phonon and phonon-phonon couplings, playing a key role in addressing compelling scientific questions in condensed matter physics [1]. For example, quantum nuclear dynamics leads to the zero-point renormalization of electron energy levels, as well as to phonon-assisted optical transitions and transport coefficients [1]. In this talk, I will discuss first how the recent advances in nonperturbative supercell calculations can account separately for electron-phonon and phonon-phonon interactions. Then, I will present the special displacement method (SDM) [2,3] as a unified approach to the many-body problem and show some of its capabilities, including the calculation of temperature-dependent anharmonic phonons, band structures, absorption coefficients, and exciton-phonon spectra. I will demonstrate that SDM is designed to replace the vibrational sampling performed in Monte Carlo or Molecular dynamics simulations [5] to the point that only a single thermal nuclei configuration is enough for obtaining accurate results. Applications of SDM for typical semiconductors, 2D materials, perovskites, and quantum dots will be discussed [2,3,4,5,6]. I will also explain the physical concepts hidden in SDM, discuss its merits and drawbacks, and indicate avenues for future work in ab-initio calculations at finite temperatures. Finally, I will present our recent work on the role of polymorphism and anharmonicity in the vibrational properties and electron-phonon physics of cubic perovskites [6].

[1] F. Giustino, Rev. Mod. Phys. 89, 015003 (2017).

[2] M. Zacharias and F. Giustino, Phys. Rev. B 89, 075125 (2016).

[3] M. Zacharias and F. Giustino, Phys. Rev. Res. 2, 013357 (2020).

[4] M. Zacharias M. Scheffler, and C. Carbogno, Phys. Rev. B 102, 045126 (2020).

[5] T. A. Huang et al., J. Phys. Chem. Lett. 12, 15 (2021).

[6] M. Zacharias, J. Even, et al., "The role of disorder and anharmonicity in cubic halide and oxide perovskites", submitted.