Interface induced Zeeman-protected superconductivity in ultrathin crystalline lead films

Two dimensional (2D) superconducting systems are of great importance to exploring exotic quantum physics. Recent development of fabrication techniques stimulates the studies of high quality single crystalline 2D superconductors, where intrinsic properties give rise to unprecedented physical phenomena. Here we report the observation of Zeeman-type spin-orbit interaction protected superconductivity (Zeeman-protected superconductivity) in 4 monolayer (ML) to 6 ML crystalline Pb films grown on striped incommensurate (SIC) Pb layers on Si(111) substrates by molecular beam epitaxy (MBE). Anomalous large in-plane critical field far beyond the Pauli limit is detected, which can be attributed to the Zeeman-protected superconductivity due to the in-plane inversion symmetry breaking at the interface. Our work demonstrates that in superconducting heterostructures the interface can induce Zeeman-type spin-orbit interaction (SOI) and modulate the superconductivity.

The experimental data of / versus / can be quantitatively fitted by equation (1). The fitting procedure gives effective Zeeman-type SOI = 3.54 meV and 4.24 meV for 6 ML and 4 ML Pb films. The in-plane critical field increases with reducing film thickness, which yields larger for thinner films.
Since the in-plane inversion symmetry is preserved in both free-standing Pb atomic layers and Si substrate, the Zeeman-type SOI and large parallel critical field observed in our system should originate from the interface between them.
The SIC phase is a special surface reconstruction of Pb on Si (111) substrate with a Pb coverage of 4/3 ML [5]. To be specific, each unit cell of SIC phase consists of four Pb atoms (the purple circles) located on three surface Si (the blue circles) atoms give rise to Zeeman-type SOI, which has been demonstrated by DFT calculation [30] and spin-resolved angular-resolved photoemission spectroscopy (ARPES) Cooper pairs in the out-of-plane orientation and prevents the alignment of the spin to the external in-plane magnetic field when < , and the superconductivity is protected under large parallel magnetic field far beyond the Pauli limit, i.e.
To further confirm and investigate Zeeman-protected superconductivity in ultrathin crystalline lead film, we measured the R sq (B) curves of a 6 ML sample in pulsed parallel magnetic field up to 47 T [ Fig. 4(a)]. The superconductivity survives under a high parallel magnetic field of 40 T at 1.7 K. In Fig. 4(b), the temperature dependence of in-plane critical magnetic field, defined as the field corresponding to 50% R n , is fitted by equation (1) with effective Zeeman-type SOI = 3.01meV (close to the value measured in steady high field for another 6 ML sample, as shown in Fig. 3(d)), suggesting Zeeman-protected superconductivity is the underlying reason for the enhancement of in 6 ML Pb film.
We then discuss other possible origins that may contribute to a high parallel critical field in 2D superconductors, such as spin-triplet pairing, spin-orbit impurity scattering and Rashba-type SOI. In ultrathin crystalline Pb films, the out-of-plane critical field ( ) can be well fitted by WHH theory, indicating conventional s-wave pairing [ Fig. S2]. Thus, the contribution from potential spin-triplet pairing due to SOI can be neglected. The microscopic Klemm-Luther-Beasley (KLB) theory [15] points out that the effect of spin paramagnetism can be reduced by spin-orbit impurity scattering and hence the parallel critical field can be enhanced beyond the Pauli limit.
The KLB formula, however, cannot describe the observed relationship between B c /B p and T/T c (the inset of Fig. 4 where ( ) is the digamma function, and , , is the solution of the following equations: with effective Zeeman-type SOI = /(1 + ℏ ) and mean free time for spin-orbit impurity scattering and mean free time for spin-independent impurity scattering. The fitting curve gives ℏ/ ≈ 0 meV, which is very small compared to the effective Zeeman-type SOI = 3.01 meV . Therefore, the Zeeman-type SOI is the dominating mechanism of the enhanced B c . superconducting systems, the spin orientation is polarized to the out-of-plane direction by Zeeman-type SOI, while Rashba-type SOI weakens the Zeeman-protection mechanism by tilting the spin of the electron to the in-plane direction, which can be more easily affected by the parallel magnetic field. To clarify the influence of Rashba-type SOI, we display a set of theoretical curves with a fixed effective Zeeman-type SOI of 3.16 meV and increasing effective Rashba-type SOI from 0.22 meV to 1.26 meV ( Fig. 4(d)). The Rashba-type SOI bends down the curves at low temperatures and gives rise to a relatively small in-plane critical field, which qualitatively deviates from the quasi-linear temperature dependence of our measured data. Besides, a special case with only large effective Rashba-type SOI is also considered (the olive line, where is far below the experimental data, indicating Rashba-type SOI alone cannot account for the observed large in-plane critical field. As a conclusion, we systematically investigate the transport properties of ultrathin crystalline Pb films at low temperatures and high magnetic fields. Under parallel magnetic field, superconductivity protected by intrinsic Zeeman-type SOI survives at high fields far beyond the Pauli limit. We demonstrate that the interface Here we assume ( ) to be isotropic, which can be justified in the following part.
We introduce an integral kernel function as: Thus, the relation for transition temperature in Eq. (S3) reduces to: We firstly neglect the disorder influence in Eq. (S1), and the bare anomalous Green's function reads: We consider the simplest model with Zeeman-type spin splitting in z-direction and in-plane magnetic field deduced spin splitting in x-direction: here and denotes the real spin and valley index respectively.
Section 3.1 Zeeman-type SOI protected superconductivity with spin-independent scattering.
The spin-independent scattering disorder gives a finite life time Here, ( ) ≡ ∫ ( ) and we only consider spin-independent scattering, and we define the effective Rashba SOI ≡ √ ℏ . for convenience.
Moreover, we assume the angular average can be calculated separately, then we obtain: The Eq. (S27-2) can be simplified using digamma functions after introducing auxiliary quantities: in the supplementary information) takes spin-independent scattering into account and can be used in the dirty limit. In Fig. S6(a), the temperature dependence of the Zeeman-protected superconductivity mechanism (the black line) is similar to that of 2D GL formula (the red line) when > 0.8 , since equation (1) is proportional to 1 − ⁄ near . But the parameters of these two formulas are different. Due to the small thickness of the Pb film, we only consider the theoretical model with Zeeman energy induced by magnetic field and neglect the orbital effect. Furthermore, the in-plane critical field at lower temperatures is important to reveal the difference between the fitting results by these two formulas. In Fig. S6(b)-(d), although the measured in-plane critical field of 4 ML Pb films near T c can be fitted by the GL formula, the high field data in 6 ML Pb film deviates from the GL formula but can be well fitted by the Zeeman-protected superconductivity mechanism in the relatively low temperature region.       (111) substrate. The definition of Pb1, Pb2 and Pb3 is presented in Fig. 3(e). D 13 is the distance between Pb1 and Pb3 and D 12 is the distance between Pb1 and Pb2.The ratio of D 13 /D 12 shows pronounced lattice distortion in SIC and the upper Pb layers.