Bardeen's 1973 Solid State Communications note proposed that the paraconductivity of the quasi-one-dimensional organic conductor TTF-TCNQ above its Peierls transition arises from Fröhlich's one-dimensional model of superconductivity, in which a traveling charge-density wave carries current without dissipation. Five decades of charge-density-wave research have substantiated the fluctuating Fröhlich contribution to the paraconductivity and established the pinned, classically sliding and dissipative regime of real materials, but the central question this account raises remains open: whether a charge-density-wave condensate in a real quasi-one-dimensional conductor can carry genuine Fröhlich superconductivity — dissipationless, quantum-coherent collective transport, including a superconducting-like high-frequency response below the Peierls transition. Contested modern claims of h/2eh/2e quantum interference in charge-density-wave rings at 77 K and of nearly unlimited Fröhlich conductivity in (TaSe4)2I(TaSe_4)_2I nanowires keep this question active; no demonstration or refutation is accepted by the field.

Background

In the early 1970s the charge-transfer salt TTF-TCNQ (tetrathiafulvalene–tetracyanoquinodimethane), the first highly conducting 'organic metal', became the testing ground for theories of one-dimensional (1D) electron-phonon physics: its conductivity rises on cooling to a peak near 60 K, above a metal-insulator transition near 54 K now identified as a Peierls transition (a lattice distortion with wave vector 2kF2k_F, twice the Fermi wave vector, that opens a gap at the Fermi level and makes the equilibrium low-temperature state insulating). Coleman et al. interpreted the peak as paraconductivity — a fluctuation-enhanced conductivity above a transition, by analogy with the excess conductivity above a superconducting transition temperature — arising from superconducting fluctuations of the BCS type (BCS: the Bardeen-Cooper-Schrieffer theory of superconductivity based on electron pairs). Bardeen's note argued instead that the paraconductivity is that of Fröhlich's 1954 one-dimensional model of superconductivity. In that model, electrons in a 1D metal with strong electron-phonon coupling self-consistently build a lattice distortion with wave vector 2kF2k_F that travels as a whole; because a uniformly translating wave lattice does not scatter electrons, the moving distortion carries an electric current without dissipation — a 'superconductor without Cooper pairs'. In real quasi-1D materials the same distortion is static in equilibrium, and the coupled electron-lattice modulation is called a charge-density wave (CDW). The fluctuating Fröhlich contribution obeys the 1D fluctuation law (σ−σn)/σn∝(T−Tc)−3/2(\sigma-\sigma_n)/\sigma_n \propto (T-T_c)^{-3/2} (where σ\sigma is the conductivity, σn\sigma_n its normal-state value, and TcT_c the transition temperature), as established for TTF-TCNQ above ~60 K, while the absence of a DC superconducting state below TcT_c is attributed to the relaxation of the traveling waves to the static Peierls distortion. The question recorded here is whether the Fröhlich mechanism can ever yield genuine superconductivity — dissipationless, quantum-coherent collective transport — in a real material. In every established case the depinned ('sliding') CDW moves classically and dissipatively, overcoming a threshold electric field set by pinning (the anchoring of the CDW phase to the lattice by impurities, commensurability, or Coulomb interchain coupling). No real quasi-one-dimensional conductor has been shown to carry a dissipationless, quantum-coherent CDW current — genuine 'Fröhlich superconductivity' — yet a modern experimental program claims exactly that: quantum interference of CDW currents in ring-shaped crystals with magnetic-flux period h/2eh/2e at 77 K (an Aharonov-Bohm effect — quantum interference of a charged condensate's wave function around enclosed magnetic flux, the same period as in superconductors), 'quantum fluidic' CDW transport, and reports of nearly unlimited Fröhlich conductivity in (TaSe4)2I(TaSe_4)_2I nanowires. These claims are contested, and the question of whether genuine Fröhlich superconductivity can occur — including a superconducting-like high-frequency response below the Peierls transition — remains open.

Problem Statement

Bardeen's 1973 account raised, but did not settle, whether the Fröhlich mechanism can yield genuine superconductivity in a real material. The aspects of that account which subsequent work has established — the tight-binding formulation; the fluctuating Fröhlich contribution to the paraconductivity; the relaxation of moving lattice waves to the static Peierls distortion through pinning; the quantitative determination of the electron-phonon coupling and related parameters; and the identification of the Fröhlich mode with the phase mode of the Peierls condensate — are excluded from the open target. The open question is: does genuine Fröhlich superconductivity — collective charge transport by a charge-density-wave condensate that is dissipationless and quantum-coherent, rather than pinned or classically sliding and dissipative — occur in any real quasi-one-dimensional conductor? This includes whether a superconducting-like high-frequency response can be observed below the Peierls transition when the condensate is driven at frequencies exceeding the inverse of the relaxation (pinning) time.

References

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