Polarons in materials

Abstract

Polarons are quasiparticles that easily form in polarizable materials due to the coupling of excess electrons or holes with ionic vibrations. Polarons manifest themselves in many different ways and have a profound impact on materials properties and functionalities. As one of the most studied subject in physics, chemistry and material science, polarons have been the testing ground for the development of numerous theories, and their manifestations have been studied by many different experimental probes. This review aims to provide a map of the enormous amount of data and knowledge accumulated on polaron effects in materials, ranging from early studies and standard treatments to emerging experimental techniques and novel theoretical and computational approaches. 2/40 Theoretical account of polaron propertiesThis section provides a brief overview of the theoretical constructs and computational models developed in the last 90 years to describe, interpret and compute the properties of polarons loosely following a chronological order from the classical work of Landau to the ab initio theory of polarons (schematized in Tab. 1). Theoretical models and computational approaches YearTheoretical and Computational models Polaron properties 1933 6 Dielectric theory: charge moving in a dielectric crystal Auto-localization due to lattice deformation 1946-1948 4, 99-101 Self-consistent theory of a large polaron Enhancement of effective mass Landau-Pekar model Localization of the wave function 1950' 7-9, 102, 103 Quantum-mechanical variational theory of large polarons Effective mass, energy, mobility Fröhlich large polaron Hamiltonian (continuum approx.) Intermediate electron-phonon interaction 1955-2017 12,13,[104][105][106] All-coupling continuum polaron theory Energy, effective mass, mobility

Rational Design of Semiconductor Heterojunctions for Photocatalysis

“… [119] The vertical excitation was followed by a structural relaxation that leads to hole and electron localization and polaron formation. [ 120 , 121 , 122 ] The generation of charge carriers upon photon absorption starts at the (001) surface with formation of delocalized holes in the VB and electrons in the CB. The structural relaxation induces hole localization on a single O ion on the (001) side of the junction and migration of the excited electron to the (101) side, where it localizes to form a Ti 3+ ion, as shown by the spin density plots, Figure 9 .…”

Light‐Induced Migration of Spin Defects in TiO2 Nanosystems and their Contribution to the H2 Evolution Catalysis from Water

“…However, the photocatalytic performances of various TiO 2 ‐based systems tested so far, despite the system's advantages shown above, display severe limitations as witnessed in the low rate of H 2 production; one of the material's limitations is linked to thermodynamic boundaries, which are associated to the large bandgap energy (3.0–3.2 eV); the large optical bandgap translates into the limited absorption of the solar spectrum, which is confined to the sole UV region (≈4 % of the total energy spectrum), thus leaving unused the majority of the solar energy input that can potentially drive the water splitting catalysis [17,18] . During the photocatalytic process, electron–hole pairs are generated, [19] but only a small fraction of the photoexcited e − are effectively delivered to H + and thus actively feed the reaction sequence 2H + +2e − →2H . →H 2 .…”

“…The detailed structural/electronic characteristics associated to the oxygen vacancy ( S = ) spin specie that gives the g≈ 2.000 EPR signal remain matter of discussions [51] . However, experimental and theoretical results, especially obtained on TiO 2 materials containing rutile phase, show that at least one of the two excess electrons lost upon formation of the oxygen vacancy (neutral V O form) remains tightly localized on the Ti 4+ atoms close to the vacant oxygen site, and the electron‘s localization is accompanied by a local lattice distortion, which results in the formation of a polaron that is essentially immobile in anatase [19,52] . In anatase, V O defects reside almost exclusively in the subsurface regions.…”

Band-selective Holstein polaron in Luttinger liquid material A0.3MoO3 (A = K, Rb)

“…1c). Up to date, although polarons have been widely observed and well understood in two-or threedimensional materials [11][12][13][14][15][16] , they are yet to be discovered in Q1D materials.…”