By Alexandre S. Alexandrov, Jozef T. Devreese (auth.)
While easy beneficial properties of polarons have been good well-known decades in the past and feature been defined in a couple of evaluate papers and textbooks, curiosity within the position of electron-phonon interactions and polaron dynamics in modern fabrics has lately passed through a full of life revival. Electron-phonon interactions were proven to be proper in high-temperature superconductors and substantial magnetoresistance oxides, and delivery via nanowires and quantum dots additionally usually depends upon vibronic displacements of ions. the continuing curiosity in polarons extends past actual description of complicated fabrics. the sphere has been a trying out floor for analytical, semi-analytical, and numerical concepts, similar to direction integrals, strong-coupling perturbation enlargement, complicated variational, special diagonalization, density-matrix renormalization workforce, dynamic mean-field, and quantum Monte Carlo strategies. unmarried and multi-polaron theories have provided a brand new perception in our knowing of high-temperature superconductivity, mammoth magnetoresistance, and the correlated delivery via molecular quantum dots. This booklet stories a few contemporary advancements within the box of polarons, beginning with the fundamentals and overlaying a couple of lively instructions of study.
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Extra info for Advances in Polaron Physics
Numerically rigorous polaron characteristics (groundstate energy, number of phonons in the polaron cloud, eﬀective mass, and isotope exponent) for such a lattice polaron, valid for arbitrary EPI, were 26 2 Continuum Polaron Fig. 4. 5 (dotted line), α = 1 (solid line), and α = 2 (dashed line) with energy counted from the ground-state energy of the polaron. The initial fragment of the spectral density for α = 1 is shown in the inset (from ) obtained using a path-integral continuous-time quantum Monte Carlo technique (CTQMC) [37, 60, 61].
Peeters and Devreese  rederived the DSG result using the memory function formalism (MFF). The DSG approach is successful at weak electron–phonon coupling and is able to identify the excitations at intermediate electron–phonon coupling (3 α 6). In the strong-coupling limit, DSG still gives an accurate ﬁrst moment for the polaron optical absorption but does not reproduce the broad phonon sideband structure (cf. [98,99]). A comparison of the DSG results with the optical conductivity spectra given by recently developed “approximation-free” numerical  and approximate analytical [67, 101] approaches was carried out recently , see also the review articles [58, 66].
9) where + and − in the second equation correspond to a- and c-polarized vibrations, respectively. 11) is the harmonic oscillator wave function. 12) with Ep = fc2 /2k. Here, Hn (ξ) are the Hermite polynomials, and n = 0, 1, 2, 3, . .. Hence, the c-axis single-ion deformation leads to the polaron level shift but without any renormalization of the hopping integral t. In contrast, a-polarized vibrations with the opposite shift of the electron energy on the left and right sites strongly renormalize the hopping integral.