Energy relaxation due to two-phonon scattering of electrons: Breakdown of the energy diffusion model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914494333059072 |
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| author | Covey, Joshua Maslov, Dmitrii L. |
| author_facet | Covey, Joshua Maslov, Dmitrii L. |
| contents | Recent THz spectroscopy of the quantum paraelectric SrTiO$_3$ (arXiv:2501.15771) and a high-$T_c$ cuprate (arXiv:2503.15646) has renewed interest in energy relaxation in correlated electron systems. We consider a situation in which single-phonon scattering is forbidden by symmetry or momentum conservation, while two-phonon scattering is allowed. Solving the Boltzmann equation, we show that above the Bloch-Grüneisen temperature the energy relaxation rate from two soft transverse optical phonons exceeds the single-phonon one: while the latter scales as $1/T$, the former is linear in $T$. This dominance of two-phonon scattering invalidates the usual picture of energy diffusion due to frequent scattering by subthermal phonons; instead, energy relaxes via rare scattering events involving thermal phonons. Below the Bloch-Grüneisen temperature, the energy relaxation rate scales as the single-particle rate, namely as $T^3$ for soft phonons. For anisotropic electron bands, an intermediate regime appears between two Bloch-Grüneisen temperatures, in which both allowed single-phonon and two-phonon processes scale as $T^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Energy relaxation due to two-phonon scattering of electrons: Breakdown of the energy diffusion model Covey, Joshua Maslov, Dmitrii L. Strongly Correlated Electrons Recent THz spectroscopy of the quantum paraelectric SrTiO$_3$ (arXiv:2501.15771) and a high-$T_c$ cuprate (arXiv:2503.15646) has renewed interest in energy relaxation in correlated electron systems. We consider a situation in which single-phonon scattering is forbidden by symmetry or momentum conservation, while two-phonon scattering is allowed. Solving the Boltzmann equation, we show that above the Bloch-Grüneisen temperature the energy relaxation rate from two soft transverse optical phonons exceeds the single-phonon one: while the latter scales as $1/T$, the former is linear in $T$. This dominance of two-phonon scattering invalidates the usual picture of energy diffusion due to frequent scattering by subthermal phonons; instead, energy relaxes via rare scattering events involving thermal phonons. Below the Bloch-Grüneisen temperature, the energy relaxation rate scales as the single-particle rate, namely as $T^3$ for soft phonons. For anisotropic electron bands, an intermediate regime appears between two Bloch-Grüneisen temperatures, in which both allowed single-phonon and two-phonon processes scale as $T^2$. |
| title | Energy relaxation due to two-phonon scattering of electrons: Breakdown of the energy diffusion model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2604.19037 |