Chaos in Jahn–Teller Rattling

Hotta, Takashi; Shudo, Akira

doi:10.7566/jpsj.83.083705

Cited by 2 publications

(6 citation statements)

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“…The above Hamiltonian was used to obtain the renormalized phonon dispersions (TDEP spectra) accounting for both the anharmonic shifts Δ and broadenings Γ of the mode ⃗ . These are derived from the real and imaginary parts of the cubic self-energies Σ (3) , respectively [32]…”

Section: Temperature-dependent Effective Potential Methodmentioning

confidence: 99%

“…Although ( ; ⃗ 1 1 ; ⃗ 2 2 ) and ( ; ; ⃗ 1 1 ; − ⃗ 1 1 ) change with 1 and 2 , an average over modes, ⟨ (⋅)⟩ = ∑ 1,2 ( ; ⃗ 1 1 ; ⃗ 2 2 )/ ∑ 1,2 1, is needed by the fitting, where 1 and 2 under the summation symbol represent ⃗ . We define the cubic and quartic fitting parameters as (3)…”

Section: Fine Structures Of Phonon-phonon Interaction Channelsmentioning

confidence: 99%

“…To the leading order of cubic and quartic anharmonicity, the broadening of the Raman peaks is 2Γ (3) ( ; Ω). The frequency shift of the Raman peaks is Δ + Δ (3) + Δ (3 ) + Δ (4) , where the quasiharmonic part is denoted by Δ .…”

Section: Fine Structures Of Phonon-phonon Interaction Channelsmentioning

confidence: 99%

“…The frequency shift of the Raman peaks is Δ + Δ (3) + Δ (3 ) + Δ (4) , where the quasiharmonic part is denoted by Δ . These quantities can be written as functions of (Ω, 1 , 2 ) and (Ω, 1 , 2 ), weighted by average anharmonic coupling strengths [25,26,40] Γ (3)…”

Section: Fine Structures Of Phonon-phonon Interaction Channelsmentioning

confidence: 99%

“…Some particular responses of electronic band structures to the lattice variation may cause strong phonon anharmonicity too. Typical examples may include rigid-unit modes, rattling ions in structural cages, orbital driven ferroelectric-like lattice instability, charge disproportionation, valence fluctuations, and vibrational driven hybridization [1][2][3][4][5][6]. At low temperatures the harmonic part is dominant in most materials but examples of extremely anharmonic potentials are also seen.…”

Section: Introductionmentioning

confidence: 99%

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Renormalized Phonon Microstructures at High Temperatures from First-Principles Calculations: Methodologies and Applications in Studying Strong Anharmonic Vibrations of Solids

Lan

Zhu

2016

Advances in Condensed Matter Physics

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While the vibrational thermodynamics of materials with small anharmonicity at low temperatures has been understood well based on the harmonic phonons approximation, at high temperatures, this understanding must accommodate how phonons interact with other phonons or with other excitations. To date the anharmonic lattice dynamics is poorly understood despite its great importance, and most studies still rely on the quasiharmonic approximations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems and essentially modify the equilibrium and nonequilibrium properties of materials, for example, thermal expansion, thermodynamic stability, heat capacity, optical properties, thermal transport, and other nonlinear properties of materials. The review aims to introduce some recent developements of computational methodologies that are able to efficiently model the strong phonon anharmonicity based on quantum perturbation theory of many-body interactions and first-principles molecular dynamics simulations. The effective potential energy surface of renormalized phonons and structures of the phonon-phonon interaction channels can be derived from these interdependent methods, which provide both macroscopic and microscopic perspectives in analyzing the strong anharmonic phenomena while the traditional harmonic models fail dramatically. These models have been successfully performed in the studies on the temperature-dependent broadenings of Raman and neutron scattering spectra, high temperature phase stability, and negative thermal expansion of rutile and cuprite structures, for example.

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Section: Temperature-dependent Effective Potential Methodmentioning

confidence: 99%

Section: Fine Structures Of Phonon-phonon Interaction Channelsmentioning

confidence: 99%

Section: Fine Structures Of Phonon-phonon Interaction Channelsmentioning

confidence: 99%

Section: Fine Structures Of Phonon-phonon Interaction Channelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Renormalized Phonon Microstructures at High Temperatures from First-Principles Calculations: Methodologies and Applications in Studying Strong Anharmonic Vibrations of Solids

Lan

Zhu

2016

Advances in Condensed Matter Physics

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Kondo Effect of a Jahn–Teller Ion Vibrating in a Cubic Anharmonic Potential

Hotta

2014

J. Phys. Soc. Jpn.

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We discuss the Kondo effect in a spinless two-orbital conduction electron system coupled with anharmonic Jahn-Teller vibration by employing a numerical renormalization group technique. When a temperature T is decreased, we encounter a plateau of log 3 entropy due to quasi-triple degeneracy of local low-energy states, composed of vibronic ground states and the first excited state with an excitation energy of ∆E. Around at T ≈∆E, we observe an entropy change from log 3 to log 2. This log 2 entropy originates from the rotational degree of freedom of the vibronic state and it is eventually released due to the screening by orbital moments of conduction electrons, leading to the Kondo effect of a Jahn-Teller ion. The Kondo temperature is explained by the effective s-d model with anisotropic exchange interactions.

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Chaos in Jahn–Teller Rattling

Cited by 2 publications

References 45 publications

Renormalized Phonon Microstructures at High Temperatures from First-Principles Calculations: Methodologies and Applications in Studying Strong Anharmonic Vibrations of Solids

Renormalized Phonon Microstructures at High Temperatures from First-Principles Calculations: Methodologies and Applications in Studying Strong Anharmonic Vibrations of Solids

Kondo Effect of a Jahn–Teller Ion Vibrating in a Cubic Anharmonic Potential

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