Upper critical field of the noncentrosymmetric superconductor BiPd

The superconducting parameters and upper critical field of the noncentrosymmetric superconductor BiPd have proven contentious. This material is of particular interest because it is a rare example of a $4f$-electron-free noncentrosymmetric superconductor of which crystals may be grown and cleaved, enabling surface-sensitive spectroscopies. Here, using bulk probes augmented by tunneling data on defects, we establish that the lower of the previously reported upper critical fields corresponds to the bulk transition. The material behaves as a nearly weak-coupled BCS $s$-wave superconductor, and we report its superconducting parameters as drawn from the bulk upper critical field. Possible reasons behind the order-of-magnitude discrepancy in the reported upper critical fields are discussed.

Figure 1

Superconductivity in BiPd. (a) Zero-field-cooled magnetization curves in a field $H\parallel \left[010\right]$ of 0.1 mT, then every 2.5 mT from 2.5 to 60.0 mT. (b) Magnetization curves in $H=5\mathrm{mT}$ for three field orientations, (c) $M-H$ loops at 1.8 K for the three field orientations, and (d) zero-field resistivity—the inset shows the effect of adding fields $H\parallel \left[010\right]$ in steps of 5 mT.

Figure 2

Specific heat of BiPd. (a) $c_P\left(T\right)/T$ vs $T$ for several fields, showing the bulk superconducting transition and its suppression by field. The weak-coupling $s$-wave BCS form [23] and the BCS form recalculated using the STM gap [12] are included for comparison. There is no transition visible above 0.4 K in fields $H\ge 0.06\mathrm{T}$. (b) The electronic contribution $c_{el}\left(T\right)/T$ vs $T$. (c) The low-temperature region is fit better by the recalculated form based on the STM gap. (d) All data in fields of 70 mT and above and all data taken above the obvious (field-dependent) bulk transition in all fields. There is no evidence to suggest an additional phase transition. The glitches near $4{\mathrm{K}}^2$ were not reproduced in later measurements.

Figure 3

$H-T$ phase diagram constructed from the transitions in the resistivity, magnetization, and specific heat. A point corresponding to the closing of the gap as observed by STM [12] is included.

Figure 4

Tunneling spectroscopy of individual defects. (a) Topographic image of defects on an atomically flat BiPd surface (settings: $V=50\mathrm{mV},I=0.1\mathrm{nA}$). (b) Spectra taken on two different defects as well as the clean [010] surface as marked in (a) with color-coded $\times$ signs (defect 1 is dark). Spectra in panel (b) were obtained at 2 K using a superconducting tip with a BiPd cluster at its apex, resulting in coherence peaks at $\pm 2\mathrm{\Delta }$. The small peak at zero bias occurs at the difference between the tip and the sample gaps due to the finite measurement temperature. An in-gap state would have produced an additional feature between the coherence peaks, which is not observed. The spectra on the defects show no obvious difference compared to the clean surface ($V=3.9\mathrm{mV},I=2\mathrm{nA},V_{\mathrm{rms}}=70\mu \mathrm{V}$).