Abstract
Fermi liquid theory forms the basis for our understanding of the majority of metals: their resistivity arises from the scattering of well defined quasiparticles at a rate where, in the low-temperature limit, the inverse of the characteristic time scale is proportional to the square of the temperature. However, various quantum materials1,2,3,4,5,6,7,8,9,10,11,12,13,14,15—notably high-temperature superconductors1,2,3,4,5,6,7,8,9,10—exhibit strange-metallic behaviour with a linear scattering rate in temperature, deviating from this central paradigm. Here we show the unexpected signatures of strange metallicity in a bosonic system for which the quasiparticle concept does not apply. Our nanopatterned YBa2Cu3O7−δ (YBCO) film arrays reveal linear-in-temperature and linear-in-magnetic field resistance over extended temperature and magnetic field ranges. Notably, below the onset temperature at which Cooper pairs form, the low-field magnetoresistance oscillates with a period dictated by the superconducting flux quantum, h/2e (e, electron charge; h, Planck’s constant). Simultaneously, the Hall coefficient drops and vanishes within the measurement resolution with decreasing temperature, indicating that Cooper pairs instead of single electrons dominate the transport process. Moreover, the characteristic time scale τ in this bosonic system follows a scale-invariant relation without an intrinsic energy scale: ħ/τ ≈ a(kBT + γμBB), where ħ is the reduced Planck’s constant, a is of order unity7,8,11,12, kB is Boltzmann’s constant, T is temperature, μB is the Bohr magneton and γ ≈ 2. By extending the reach of strange-metal phenomenology to a bosonic system, our results suggest that there is a fundamental principle governing their transport that transcends particle statistics.
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Data availability
The data that support the plots within this paper are available from the Zenodo data repository, https://doi.org/10.5281/zenodo.5603259. Source data are provided with this paper.
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Acknowledgements
We thank C. M. Varma, H. Yao, A. Lucas and J. M. Kosterlitz for discussions. This work was supported by the National Natural Science Foundation of China (grants 51722204, 51972041, U20A20244, 11888101, 12022407, 11774008 and 12074056), the National Basic Research Program of China (grants 2021YFA0718800, 2017YFA0303300, 2018YFA0305604 and 2017YFA0304600), Beijing Natural Science Foundation (Z180010) and the China National Postdoctoral Program for Innovative Talents (BX2021054).
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J.X. and J.M.V. Jr conceived the study and supervised the project together with Y. Li and Jian Wang. C.Y. and Jiandong Wang fabricated the samples. C.Y., Y. Liu, S.W., D.Q., Y.W., Q.H., X.L., Y.T. and P.L. performed the experimental measurements. C.Y., H.L., J.M.V. Jr and J.X. analysed the data with contributions from Y. Liu, J.W. and Y. Li. X.C.X. participated in discussions. C.Y., J.M.V. Jr, H.L., J.X. and Y. Li wrote the manuscript with comments from J.W. and X.C.X.
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Extended data figures and tables
Extended Data Fig. 1 Scanning electron microscopy image of a nanopatterned YBa2Cu3O7−δ (YBCO) thin film.
The 12-nm-thick nanopatterned YBCO thin film was fabricated by reactive ion etching through an anodic aluminium oxide (AAO) membrane directly placed atop the YBCO. By RIE, the anodized aluminium oxide pattern of a triangular array of holes with ~70-nm diameter and ~103-nm period was duplicated onto the YBCO film.
Extended Data Fig. 2 First derivatives of the R-T curves of nanopatterned YBCO films.
a–f, The first derivatives of resistance as a function of temperature for f2 (a), f3 (b), f4 (c), f7(d) and f8 (e). The table shows the yielded parameters of the statistical analysis (f).
Extended Data Fig. 3 Data residuals after subtracting the linear fit for the R–T curves of nanopatterned YBCO films.
Residuals for the R–T curves of f2 (a), f3 (b), f4 (c), f7(d) and f8 (e). The residual is defined by the resistance subtracting the linear fitting of the R–T curves with the slopes and interceptions shown in f. To delineate the temperature regime for T-linear resistivity, the residual cut-off is set by 50 Ω which is around 0.5% of the normal-state sheet resistance RN. The table shows the temperature regime for T-linear resistivity where the residual is within 50 Ω (f).
Extended Data Fig. 4 Nonlinear fitting for the R-T curves of nanopatterned YBCO films.
a–d, Least-squares nonlinear fitting of the R–T curves for f8 (a), f7 (b), f4 (c) and f2 (d). n is the yielded power from the fitting.
Extended Data Fig. 5 Scale-invariant B-linear resistance in nanopatterned YBCO thin films under perpendicular magnetic field.
a–f, The magnetoresistance for films: f0 (a), f2 (b), f3 (c), f5 (d), f6 (e) and superconducting (SC; f).
Extended Data Fig. 6 First derivatives and nonlinear fitting of the R–B curves of nanopatterned YBCO films.
a, b, The first derivative of resistance as a function of magnetic field for f4 (a) and f2 (b) at various temperatures. c, d, Least-squares nonlinear curve fitting of the R–B curves for f4 (c) and f2 (d).
Extended Data Fig. 7 B–T scaling in nanopatterned YBCO films.
a–c, B–T scaling in nanopatterned YBCO thin films of f2 (a), f3 (b) and f5 (c).
Extended Data Fig. 8 Magnetotransport as a as a function of (kBT + γμBB)/kB) of nanopatterned YBCO films.
a–d, The resistance and magnetoresistance of f1 (a), f2 (b), f3 (c) and f5 (d) as a function of (kBT + γμBB)/kB), where the γ parameter can be estimated by adjusting it when the curves collapse best.
Extended Data Fig. 9 Electrode pattern for the measurement.
a, Illustration of the electrode pattern for standard four-probe measurements. b, Illustration of the electrode pattern for Hall measurements. The current was applied at electrode #1 and #5. The Hall resistance was measured from electrode #3 and #7, the longitudinal resistance is measured from electrode #2 and #3. STO, SrTiO3.
Extended Data Fig. 10 Current voltage (I–V) curves and R–T curves at different current excitations in nanopatterned YBCO film.
a–c, R–T curves for representative films f4 (a), f3 (b) and f2 (c) with different currents. d, Current voltage (I–V) curves for f4.
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Yang, C., Liu, H., Liu, Y. et al. Signatures of a strange metal in a bosonic system. Nature 601, 205–210 (2022). https://doi.org/10.1038/s41586-021-04239-y
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DOI: https://doi.org/10.1038/s41586-021-04239-y
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