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  • Letter
  • Open Access

Low-frequency quantum oscillations from interactions in layered metals

Andrew A. Allocca1,* and Nigel R. Cooper1,2

  • 1TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 2Department of Physics and Astronomy, University of Florence, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy

  • *aa2182@cam.ac.uk
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Phys. Rev. Research 3, L042009 – Published 28 October, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042009

Abstract

Metals composed of weakly coupled, stacked layers possess a Fermi surface that slightly varies in size along the stacking direction. This appears in de Haas–van Alphen (dHvA) oscillations of the magnetization with a magnetic field as two close frequencies, corresponding to the two extremal Fermi-surface cross-sectional areas. We show that, for layered materials of sufficiently high mobility, Coulomb interactions can have a dramatic effect on the form of the dHvA oscillations: There is also generically an oscillation at the small difference of the two large frequencies. We determine the size and form of this effect, and show that it probes the short-range part of the Coulomb interactions within the layered material. We argue that this interaction effect may explain recent experimental observations of anomalous low-frequency dHvA oscillations in the ultrapure delafossites.

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References (39)

  1. W. J. de Haas and P. M. van Alphen, The dependence of the susceptibility of diamagnetic metals upon the field, Proc. Neth. R. Acad. Sci. 33, 1106 (1930).
  2. I. Lifshitz and A. Kosevich, Theory of magnetic susceptibility in metals at low temperature, Sov. Phys. - JETP 2, 636 (1956).
  3. A. C. Potter, I. Kimchi, and A. Vishwanath, Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals, Nat. Commun. 5, 5161 (2014).
  4. F. Arnold, M. Naumann, S.-C. Wu, Y. Sun, M. Schmidt, H. Borrmann, C. Felser, B. Yan, and E. Hassinger, Chiral Weyl Pockets and Fermi Surface Topology of the Weyl Semimetal TaAs, Phys. Rev. Lett. 117, 146401 (2016).
  5. A. Alexandradinata and L. Glazman, Geometric Phase and Orbital Moment in Quantization Rules for Magnetic Breakdown, Phys. Rev. Lett. 119, 256601 (2017).
  6. A. Alexandradinata and L. Glazman, Semiclassical theory of landau levels and magnetic breakdown in topological metals, Phys. Rev. B 97, 144422 (2018).
  7. N. L. Nair, M.-E. Boulanger, F. Laliberté, S. Griffin, S. Channa, A. Legros, W. Tabis, C. Proust, J. Neaton, L. Taillefer, and J. G. Analytis, Signatures of possible surface states in TaAs, Phys. Rev. B 102, 075402 (2020).
  8. T. Devakul, Y. H. Kwan, S. L. Sondhi, and S. A. Parameswaran, Quantum Oscillations in the Zeroth Landau Level: Serpentine Landau Fan and the Chiral Anomaly, Phys. Rev. Lett. 127, 116602 (2021).
  9. Y. Zhang, A. V. Maharaj, and S. Kivelson, Disruption of quantum oscillations by an incommensurate charge density wave, Phys. Rev. B 91, 085105 (2015).
  10. S. Spurrier and N. R. Cooper, Theory of quantum oscillations in quasicrystals: Quantizing spiral Fermi surfaces, Phys. Rev. B 100, 081405(R) (2019).
  11. B. S. Tan, Y.-T. Hsu, B. Zeng, M. C. Hatnean, N. Harrison, Z. Zhu, M. Hartstein, M. Kiourlappou, A. Srivastava, M. D. Johannes, T. P. Murphy, J.-H. Park, L. Balicas, G. G. Lonzarich, G. Balakrishnan, and S. E. Sebastian, Unconventional Fermi surface in an insulating state, Science 349, 287 (2015).
  12. J. Knolle and N. R. Cooper, Quantum Oscillations without a Fermi Surface and the Anomalous de Haas–van Alphen Effect, Phys. Rev. Lett. 115, 146401 (2015).
  13. G. Baskaran, Majorana Fermi sea in Insulating SmB6: A proposal and a theory of quantum oscillations in Kondo insulators, arXiv:1507.03477.
  14. O. Erten, P. Ghaemi, and P. Coleman, Kondo Breakdown and Quantum Oscillations in SmB6, Phys. Rev. Lett. 116, 046403 (2016).
  15. L. Zhang, X.-Y. Song, and F. Wang, Quantum Oscillation in Narrow-Gap Topological Insulators, Phys. Rev. Lett. 116, 046404 (2016).
  16. J. Knolle and N. R. Cooper, Anomalous de Haas–van Alphen Effect in InAs/GaSb Quantum Wells, Phys. Rev. Lett. 118, 176801 (2017).
  17. I. Sodemann, D. Chowdhury, and T. Senthil, Quantum oscillations in insulators with neutral Fermi surfaces, Phys. Rev. B 97, 045152 (2018).
  18. M. Hartstein, W. H. Toews, Y.-T. Hsu, B. Zeng, X. Chen, M. C. Hatnean, Q. R. Zhang, S. Nakamura, A. S. Padgett, G. Rodway-Gant, J. Berk, M. K. Kingston, G. H. Zhang, M. K. Chan, S. Yamashita, T. Sakakibara, Y. Takano, J.-H. Park, L. Balicas, N. Harrison et al., Fermi surface in the absence of a Fermi liquid in the Kondo insulator SmB6, Nat. Phys. 14, 166 (2018).
  19. C. W. Hicks, A. S. Gibbs, A. P. Mackenzie, H. Takatsu, Y. Maeno, and E. A. Yelland, Quantum Oscillations and High Carrier Mobility in the Delafossite PdCoO2, Phys. Rev. Lett. 109, 116401 (2012).
  20. F. Arnold, M. Naumann, H. Rosner, N. Kikugawa, D. Graf, L. Balicas, T. Terashima, S. Uji, H. Takatsu, S. Khim, A. P. Mackenzie, and E. Hassinger, Fermi surface of PtCoO2 from quantum oscillations and electronic structure calculations, Phys. Rev. B 101, 195101 (2020).
  21. D. Shoenberg, Magnetic Oscillations in Metals, Cambridge Monographs on Physics (Cambridge University Press, Cambridge, UK, 1984).
  22. J. M. Luttinger, Theory of the de Haas–van Alphen Effect for a System of Interacting Fermions, Phys. Rev. 121, 1251 (1961).
  23. A. Wasserman and M. Springford, The influence of many-body interactions on the de Haas–van Alphen effect, Adv. Phys. 45, 471 (1996).
  24. G. W. Crabtree, Demagnetizing fields in the de Haas–van Alphen effect, Phys. Rev. B 16, 1117 (1977).
  25. T. Champel and V. P. Mineev, de Haas–van Alphen effect in two- and quasi-two-dimensional metals and superconductors, Philos. Mag. B 81, 55 (2001).
  26. P. Grigoriev, The influence of the chemical potential oscillations on the de Haas–van Alphen effect in quasi-two-dimensional compounds, J. Exp. Theor. Phys. 92, 1090 (2001).
  27. P. D. Grigoriev, Theory of the Shubnikov–de Haas effect in quasi-two-dimensional metals, Phys. Rev. B 67, 144401 (2003).
  28. A. S. Alexandrov and A. M. Bratkovsky, de Haas–van Alphen Effect in Canonical and Grand Canonical Multiband Fermi Liquid, Phys. Rev. Lett. 76, 1308 (1996).
  29. M. Nakano, Unexpected de Haas–van Alphen oscillation in 2D multiband systems due to chemical potential oscillation and its relevance to magnetic breakdown systems, J. Phys. Soc. Jpn. 66, 19 (1997).
  30. J.-Y. Fortin and T. Ziman, Frequency Mixing of Magnetic Oscillations: Beyond Falicov-Stachowiak Theory, Phys. Rev. Lett. 80, 3117 (1998).
  31. T. Champel, Origin of combination frequencies in quantum magnetization oscillations of two-dimensional multiband metals, Phys. Rev. B 65, 153403 (2002).
  32. K. Kishigi and Y. Hasegawa, de Haas–van Alphen effect in two-dimensional and quasi-two-dimensional systems, Phys. Rev. B 65, 205405 (2002).
  33. The numerical values of the prefactors of these two terms can vary, depending on the spatial form of the interelectron interactions. The form in (2) arises for the model interactions chosen in (6), of short-range interlayer interactions.
  34. We extract numerical values for μ and t⊥ by fitting the frequencies reported in Ref. [20] to this form.
  35. K. Miyake and C. Varma, Many body effect on oscillatory properties of two-dimensional metals in a magnetic field, Solid State Commun. 85, 335 (1993).
  36. See Supplemental Material at [http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L042009] for calculations of free energies and comparison to magnetic interactions.
  37. Explicitly, we use m*=1.18me, with me the free-electron mass, μ=2.963eV, t⊥=13.98meV, and c-axis lattice constant a⊥=17.808Å.
  38. E. Hassinger (private communication).
  39. As noted in Ref. [21], phase smearing due to inhomogeneity often produces a stronger suppression than a finite quasiparticle lifetime.

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Phys. Rev. Research 3, L042009– Published 28 October, 2021
  • Received 22 March 2021
  • Revised 4 August 2021
  • Accepted 23 September 2021
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