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, 4 (4), eaao4793

Strong Coupling Superconductivity in a Quasiperiodic Host-Guest Structure


Strong Coupling Superconductivity in a Quasiperiodic Host-Guest Structure

Philip Brown et al. Sci Adv.


We examine the low-temperature states supported by the quasiperiodic host-guest structure of elemental bismuth at high pressure, Bi-III. Our electronic transport and magnetization experiments establish Bi-III as a rare example of type II superconductivity in an element, with a record upper critical field of ~ 2.5 T, unusually strong electron-phonon coupling, and an anomalously large, linear temperature dependence of the electrical resistivity in the normal state. These properties may be attributed to the peculiar phonon spectrum of incommensurate host-guest structures, which exhibit additional quasi-acoustic sliding modes, suggesting a pathway toward strong coupling superconductivity with the potential for enhanced transition temperatures and high critical fields.


Fig. 1
Fig. 1. Evolution of the temperature dependence of the resistivity ρ(T) of bismuth with pressure p.
As p approaches 25 kbar, ρ rises rapidly at low T, indicating a reduction in the carrier concentration. Over a narrow range in p and T above 25 kbar, Bi is known to assume the Bi-II structure (blue line), which goes along with a drastic decrease in ρ(300 K). At higher pressures still, Bi orders in the incommensurate Bi-III structure (red line). (Inset) Crystal structure of Bi-I and schematic p-T phase diagram of Bi.
Fig. 2
Fig. 2. ρ(T) for bismuth at 27 kbar (Bi-III), showing a nearly linear T dependence at low T above a superconducting transition at Tc ≃ 7.05 K.
Moderate magnetic fields (1, 2, and 3 T) suppress Tc, but the critical field ≃ 2.5 T is much higher than that of Pb, which has a similar Tc ≃ 7.2 K but a far weaker T dependence of ρ(T) (black line). Left inset: Crystal structure of Bi-III, showing the commensurate arrangement within the ab plane of guest (purple) and host atoms (gray). Along the c axis (right inset), the discrepancy between the lattice constants of guest and host atoms becomes apparent.
Fig. 3
Fig. 3. Low T resistivity of bismuth at 31.4 kbar in 0.5 T field increments from 0 to 3 T.
Inset: Upper critical field Bc2 for Bi-III at 31.4 kbar (full symbols) and 27 kbar (empty symbols), extracted from the mid-point of the resistive transition. The measured data deviate strongly from the weak coupling clean limit Werthamer-Helfand-Hohenberg (WHH) form (18) (black line), suggesting a strong coupling description (19) (red line for λ = 2.9).
Fig. 4
Fig. 4. Magnetic and phonon properties of Bi-III.
Left: Magnetization M over applied field H (both in SI units) in Bi at 29 kbar as a function of temperature for μ0H = 0.002 T, on warming zero-field cooling (zfc) and field cooling (fc). Right: Phonon dispersion computed for wave vectors q perpendicular to c indicated by open circles, interpolated in between. We identify not only three acoustic modes (dotted lines) and a spaghetti of optical modes but also two further modes at very low energy, which have low dispersion (dashed lines). These correspond to the zero-frequency phason modes expected in the incommensurate structure of Bi-III.

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Cited by 4 PubMed Central articles


    1. T. Janssen, G. Chapuis, M. de Boissieu, Aperiodic Crystals: From Modulated Phases to Quasicrystals (Oxford Univ. Press, 2007).
    1. Hofstadter D. R., Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976).
    1. Frenkel J., Kontorowa T., On the theory of plastic deformation and twinning. Phys. Z. Sowjetunion 13, 1–10 (1938).
    1. Axe J. D., Bak P., Long-wavelength excitations in incommensurate intergrowth compounds with application to Hg3–δ As F6 . Phys. Rev. B 26, 4963–4973 (1982).
    1. Hastings J. M., Pouget J. P., Shirane G., Heeger A. J., Miro N. D., MacDiarmid A. G., One-dimensional phonons and “phase-ordering” phase transition in Hg3–δ As F6 . Phys. Rev. Lett. 39, 1484–1487 (1977).

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