Microscopic identification, pinning theory, and forced-diffusion kinetics of quenching defects in the Peierls conductor o-TaS$_3$

Orthorhombic TaS$_3$ ($o$-TaS$_3$) crystals quenched during synthesis contain mobile 'quenching defects' that pin the charge-density wave (CDW) in a way fundamentally different from ordinary impurities and point defects: the pinning disappears during thermocycling below the Peierls transition, leaves a non-uniform defect distribution, obeys $\Delta T_P \propto E_T$ instead of the local-pinning law $\Delta T_P \propto \sqrt{E_T}$ (equivalently, $E_T \propto \Delta T_P^2$), and barely smears the Peierls transition. A 2020 follow-up established the phenomenological scalings $E_T \propto n$ and $\Delta T_P \propto n$ for defect concentration $n$ and proposed that the defects are interstitial sulfur impurities in the van der Waals gaps, correlated with the CDW below $T_P$, whose forced diffusion ejects them from the crystal during thermocycling. What remains open is the microscopic substance behind this phenomenology: no structural probe has ever imaged or diffracted these defects, no microscopic theory of CDW pinning by such correlated or extended defect ensembles exists, the forced-diffusion kinetics has only order-of-magnitude estimates near room temperature, and the phenomenon is untested in any other Peierls conductor. The problem is to convert this observed phenomenology into a microscopically modeled pinning-and-diffusion mechanism.

Background

A charge-density wave (CDW) is a modulation of the electron density in a metal, coupled to a periodic lattice distortion, that forms below a Peierls transition temperature $T_P$ in quasi-one-dimensional conductors; $o$-TaS$_3$ is a classic example, with $T_P \approx 220$ K in pure crystals (Monceau 2012, Adv. Phys. 61, 325). A static CDW distorts around imperfections, which 'pin' it: the current-voltage characteristic stays linear until the electric field exceeds a threshold $E_T$ at which the CDW starts to slide. For local pinning centers (substitutional impurities, irradiation-induced point defects) the theory of strong pinning ($E_T \propto n$ for defect concentration $n$, with $\Delta T_P \propto \sqrt{n}$) and weak pinning ($E_T \propto n^2$, with $\Delta T_P \propto n$) is classical, and in both cases $\Delta T_P \propto \sqrt{E_T}$, where $\Delta T_P$ is the defect-induced suppression of $T_P$; local defects also strongly smear the Peierls transition. A precedent for mobile defects exists: indium impurities diffusing in NbSe$_3$ and $o$-TaS$_3$ redistribute under the influence of the CDW and change $E_T$ and $T_P$ on observable timescales (Gill 1996, Phys. Rev. B 53, 15586; Nasretdinova et al. 2015, Physica B 460, 180). Minakova, Nikitina, and Zaitsev-Zotov (JETP Lett. 110, 62 (2019)) studied a different defect class: defects created by rapidly quenching $o$-TaS$_3$ crystals from growth temperature. In about 10% of crystals these defects make the transport 'unstable': thermocycling between room temperature and $T < T_P$ progressively raises $T_P$ and lowers $E_T$, the total growth of $T_P$ over many cycles reaching up to 15 K and $E_T$ decreasing by up to a factor 2.5, with changes concentrated in the temperature region where the CDW forms or its configuration changes, and short samples evolve faster — evidence that the CDW itself forces the defects to diffuse out of the crystal. The pinning they produce is non-local: the $E_T$–$\Delta T_P$ relation is linear ($\Delta T_P \propto E_T$) rather than the $\Delta T_P \propto \sqrt{E_T}$ law of local pinning, and, unlike any local pinning case, the sharpness of the Peierls transition — measured by the peak height and half-width of the logarithmic derivative $d\ln R/d(1/T)$ of the resistance $R$, whose maximum marks the transition — is almost unaffected. The 2019 paper conjectured the defects are extended objects, probably lattice dislocations, and noted that this pinning type had never been studied theoretically or experimentally. A same-group follow-up (Minakova et al. 2020, JETP Lett. 112, 346) pinned down the phenomenology: $E_T \propto n$ and $\Delta T_P \propto n$, ordinary diffusion of the defects detectable near 300 K with an estimated diffusion coefficient and energy barrier, and a revised microscopic picture — interstitial sulfur impurities lodged in the van der Waals gaps between the chain structure, partially ordered (correlated with the CDW) below $T_P$, which drastically lowers the barrier for forced diffusion whenever thermocycling changes the CDW configuration. This identification, like the earlier dislocation conjecture, is inferred entirely from transport kinetics: a direct energy-dispersive search for excess sulfur in the 2020 work found the difference between quenched and as-grown crystals to be below measurement accuracy, leaving only indirect evidence (copper-sulfide overgrowth on stored copper wires), and no structural or microscopic probe has ever directly observed these defects. The 2020 conclusion speculates that such effects may be inherent to a wide class of layered or chain metals with strong interaction between the electronic superstructure and impurities. No theory derives the observed laws from a microscopic model.

Problem Statement

Give a microscopic account of the non-local (correlated) pinning of the charge-density wave by quenching defects in $o$-TaS$_3$, as discovered by Minakova, Nikitina, and Zaitsev-Zotov (2019) and elaborated phenomenologically in their 2020 follow-up. The open core posed by the sources consists of two parts: (1) construct a microscopic theory of CDW pinning by such correlated/extended defect ensembles from which the established phenomenology follows: the linear law $\Delta T_P \propto E_T$ in place of the local-pinning law $\Delta T_P \propto \sqrt{E_T}$, the concentration scalings $E_T \propto n$ and $\Delta T_P \propto n$, and the anomalously weak suppression of the Peierls-transition sharpness (the maximum and half-width of $d\ln R/d(1/T)$) compared with all local-pinning cases; and (2) provide a quantitative microscopic model of the CDW-driven forced diffusion and exit of these defects during thermocycling below $T_P$, including activation energies and diffusion coefficients as functions of temperature and the mechanism by which changes of the CDW configuration lower the diffusion barrier. An answer must confront the published transport phenomenology; a complete answer identifies the mechanism and shows quantitatively how it produces the observed laws. Context for the mechanism to be modeled: the identity of the quenching defects remains a probabilistic inference from transport kinetics — lattice dislocations (2019) versus interstitial sulfur impurities in the van der Waals gaps correlated with the CDW (2020). Direct structural identification of the defects, and tests of whether this pinning class operates in other Peierls conductors with independent defect populations, are desirable directions but are not required components of an answer to this problem.

References

1. V. E. Minakova, A. M. Nikitina, S. V. Zaitsev-Zotov, 'A new type of charge-density-wave pinning in orthorhombic TaS$_3$ crystals with quenching defects', JETP Letters 110, 62–67 (2019). DOI: 10.1134/S0021364019130034, https://doi.org/10.1134/S0021364019130034 (preprint arXiv:1907.00226, https://arxiv.org/abs/1907.00226)
2. V. E. Minakova, A. M. Nikitina, S. V. Zaitsev-Zotov, 'Forced Diffusion of Correlated Impurities in the Peierls Conductor o-TaS$_3$', JETP Letters 112, 346–351 (2020). DOI: 10.1134/S0021364020180022, https://doi.org/10.1134/S0021364020180022
3. A. V. Frolov, A. P. Orlov, D. M. Voropaev, A. Hadj-Azzem, A. A. Sinchenko, P. Monceau, 'Logarithmic Relaxation of the Nonequilibrium State of the Charge Density Wave in TbTe$_3$ and HoTe$_3$ Compounds', JETP Letters 117, 170–175 (2023). DOI: 10.1134/S0021364022602998, https://doi.org/10.1134/S0021364022602998
4. J. C. Gill, 'Dislocations and the motion of weakly pinned charge-density waves: Experiments on niobium triselenide containing mobile indium impurities', Physical Review B 53, 15586–15603 (1996). DOI: 10.1103/PhysRevB.53.15586, https://doi.org/10.1103/PhysRevB.53.15586
5. V. F. Nasretdinova, E. B. Yakimov, S. V. Zaitsev-Zotov, 'Indium doping-induced change in the photoconduction spectra of o-TaS$_3$', Physica B: Condensed Matter 460, 180–184 (2015). DOI: 10.1016/j.physb.2014.11.065, https://doi.org/10.1016/j.physb.2014.11.065
6. Pierre Monceau, 'Electronic crystals: an experimental overview', Advances in Physics 61, 325–581 (2012). DOI: 10.1080/00018732.2012.719674, https://doi.org/10.1080/00018732.2012.719674