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Intrinsic Floquet generation and 1/I quantum oscillations in a sliding charge-density wave

Yi Zhou*

  • *Contact author: yizhou@iphy.ac.cn
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Phys. Rev. Research 8, 043049 – Published 14 October, 2026

DOI: https://doi.org/10.1103/5tjw-9z42

Abstract

Recent experiments [Phys. Rev. B 109, 245123 (2024)] revealed striking inverse-current (1/I) quantum oscillations in quasi-one-dimensional charge-density-wave (CDW) insulators and proposed an intrinsic Floquet sideband mechanism arising from the sliding condensate. Here, we develop the complete theoretical framework underlying this proposal. We provide an exact Floquet diagonalization of the uniformly sliding CDW problem, yielding split gap edges and a ladder of Floquet sidebands with explicit unitary transformation and spectral functions. Using this exact solution, we formulate weak-probe tunneling spectroscopy and demonstrate that the local Floquet spectrum naturally yields 1/I oscillations as successive sideband edges cross a fixed contact chemical potential. The measured period fixes Neffε≃4.80eV, where ε is the local contact-to-gap-edge offset. Combining this relation with the experimentally resolved low-temperature oscillations constrains the effective coherent channel count to be at most of order 103, far below the geometric estimate Ngeom∼3×104, while ε=10meV gives the representative value Neff≃480. This reduced coherent scale is naturally realized by a spatially nonuniform percolating network, but does not require Neff independent end-to-end wires. Furthermore, using a segmented multiterminal model, we show that inelastic phase-slip dephasing near the contacts explains the experimentally observed suppression of oscillation visibility on outer voltage probes. Finally, we contrast the persistent-current-driven multiterminal geometry with a homogeneous voltage-biased two-terminal reference calculation. Our results establish a nonequilibrium transport framework for the observed 1/I oscillations and identify an observability condition in which the Floquet spacing must exceed collective and quasiparticle broadening.

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References (40)

  1. H. Fröhlich, On the theory of superconductivity: The one-dimensional case, Proc. R. Soc. London A 223, 296 (1954).
  2. R. E. Peierls, Quantum Theory of Solids (Oxford University Press, Oxford, 1955).
  3. G. Grüner, The dynamics of charge-density waves, Rev. Mod. Phys. 60, 1129 (1988).
  4. P. Monceau, Electronic crystals: An experimental overview, Adv. Phys. 61, 325 (2012).
  5. A. W. Overhauser, Giant spin density waves, Phys. Rev. Lett. 4, 462 (1960).
  6. A. W. Overhauser, Spin density waves in an electron gas, Phys. Rev. 128, 1437 (1962).
  7. G. Grüner, The dynamics of spin-density waves, Rev. Mod. Phys. 66, 1 (1994).
  8. P. A. Lee, T. M. Rice, and P. W. Anderson, Conductivity from charge or spin density waves, Solid State Commun. 14, 703 (1974).
  9. P. Monçeau, N. P. Ong, A. M. Portis, A. Meerschaut, and J. Rouxel, Electric-field breakdown of charge-density-wave-induced anomalies in NbSe3, Phys. Rev. Lett. 37, 602 (1976).
  10. H. Fukuyama and P. A. Lee, Dynamics of the charge-density wave. I. Impurity pinning in a single chain, Phys. Rev. B 17, 535 (1978).
  11. P. A. Lee and T. M. Rice, Electric field depinning of charge density waves, Phys. Rev. B 19, 3970 (1979).
  12. R. M. Fleming and C. C. Grimes, Sliding-mode conductivity in NbSe3: Observation of a threshold electric field and conduction noise, Phys. Rev. Lett. 42, 1423 (1979).
  13. J. Bardeen, Theory of non-Ohmic conduction from charge-density waves in NbSe3, Phys. Rev. Lett. 42, 1498 (1979).
  14. T. Le, R. Jiang, L. Tu, R. Bian, Y. Ma, Y. Shi, K. Jia, Z. Li, Z. Lyu, X. Cao, J. Shen, G. Liu, Y. Shi, F. Liu, Y. Zhou, L. Lu, and F. Qu, Inverse-current quantum electro-oscillations in a charge-density wave insulator, Phys. Rev. B 109, 245123 (2024).
  15. M. Grifoni and P. Hänggi, Driven quantum tunneling, Phys. Rep. 304, 229 (1998).
  16. G. Platero and R. Aguado, Photon-assisted transport in semiconductor nanostructures, Phys. Rep. 395, 1 (2004).
  17. S. Kohler, J. Lehmann, and P. Hänggi, Driven quantum transport on the nanoscale, Phys. Rep. 406, 379 (2005).
  18. M. Bukov, L. D’Alessio, and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: From dynamical stabilization to Floquet engineering, Adv. Phys. 64, 139 (2015).
  19. T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annu. Rev. Condens. Matter Phys. 10, 387 (2019).
  20. M. S. Rudner and N. H. Lindner, Band structure engineering and non-equilibrium dynamics in Floquet topological insulators, Nat. Rev. Phys. 2, 229 (2020).
  21. G. Floquet, Sur les équations différentielles linéaires à coefficients périodiques, Ann. Sci. École Norm. Sup. 12, 47 (1883).
  22. J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
  23. H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys. Rev. A 7, 2203 (1973).
  24. G. D. Mahan, Many-Particle Physics, 3rd ed. (Plenum, New York, 2000).
  25. G. S. Uhrig, M. H. Kalthoff, and J. K. Freericks, Positivity of the spectral densities of retarded Floquet Green functions, Phys. Rev. Lett. 122, 130604 (2019).
  26. M. Büttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57, 1761 (1986).
  27. A. I. Larkin and A. A. Varlamov, Theory of Fluctuations in Superconductors, International Series of Monographs on Physics, revised ed. (Oxford University Press, Oxford, 2009), Vol. 127.
  28. Y. Imry, Introduction to Mesoscopic Physics, 2nd ed. (Oxford University Press, Oxford, 2002).
  29. A.-P. Jauho, N. S. Wingreen, and Y. Meir, Time-dependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B 50, 5528 (1994).
  30. G. Stefanucci and R. van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge University Press, Cambridge, 2013).
  31. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, 2nd ed., Springer Series in Solid-State Sciences Vol. 123 (Springer, Berlin, 2008).
  32. S. Ghosh, N. Sesing, Z. E. Nataj, T. Salguero, S. Rumyantsev, R. K. Lake, and A. A. Balandin, A quieter state of charge and ultra-low-noise of the collective current in quasi-1D charge-density-wave nanowires, Nat. Commun. 17, 116 (2026).
  33. A. V. Chaplik, Energy spectrum and electron scattering processes in inversion layers, Zh. Eksp. Teor. Fiz. 60, 1845 (1971) [Sov. Phys. JETP 33, 997 (1971)].
  34. C. Hodges, H. Smith, and J. W. Wilkins, Effect of Fermi-surface geometry on electron-electron scattering, Phys. Rev. B 4, 302 (1971).
  35. G. F. Giuliani and J. J. Quinn, Lifetime of a quasiparticle in a two-dimensional electron gas, Phys. Rev. B 26, 4421 (1982).
  36. yizhou76-sudo, Sliding-CDW: Documents for sliding CDW theory, GitHub, 2026, https://github.com/yizhou76-sudo/Sliding-CDW.
  37. J. S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2, 407 (1961).
  38. L. V. Keldysh, Diagram technique for nonequilibrium processes, J. Exptl. Theoret. Phys. (U.S.S.R.) 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)].
  39. J. Rammer and H. Smith, Quantum field-theoretical methods in transport theory of metals, Rev. Mod. Phys. 58, 323 (1986).
  40. A. Kamenev and A. Levchenko, Keldysh technique and non-linear σ-model: Basic principles and applications, Adv. Phys. 58, 197 (2009).

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Phys. Rev. Research 8, 043049– Published 14 October, 2026
  • Received 28 May 2026
  • Accepted 2 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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