Theory of temperature dependent phonon-renormalized properties

Abstract

We present a general harmonic theory for the temperature dependence of phonon-renormalized properties of solids. Firstly, we formulate a perturbation theory in phonon-phonon interactions to calculate the phonon renormalization of physical quantities. Secondly, we propose two new schemes for extrapolating phonon zero-point corrections from temperature dependent data that improve the accuracy by an order of magnitude compared to previous approaches. Finally, we consider the low-temperature limit of the class of observables that includes the electronic band gap, obtaining a $T^4$ dependence in three dimensions, $T^2$ in two dimensions, and $T^{3/2}$ in one dimension.

10 pages, 1 figure

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• Electronic band gaps from Quantum Monte Carlo methods
• Full versus quasi-particle self consistency in vertex corrected GW approaches
• Vibrational renormalisation of the electronic band gap in hexagonal and cubic ice
• Topological semimetallic phase in PbO${}_2$ promoted by temperature
• Low temperature-semiconductor band gap thermal shifts: T^4 shifts from ordinary acoustic and T^2 from piezoacoustic coupling
• Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization
• Spectroscopic signatures of nonpolarons : the case of diamond
• Towards improved exact exchange functionals relying on GW quasiparticle methods for parametrization
• Experimental determination of the bare energy gap of GaAs without the zero-point renormalization
• Electron correlation in semiconductors and insulators via symbolic regression