Unconventional Meissner screening induced by chiral molecules in a conventional superconductor

The coupling of a superconductor (SC) to a different material often results in a system with unconventional superconducting properties. A conventional SC is a perfect diamagnet expelling magnetic fields out of its volume, a phenomenon known as the Meissner effect. Here, we show that the simple adsorption of a monolayer of chiral molecules (ChMs), which are nonmagnetic in solution, onto the surface of a conventional SC can markedly change its diamagnetic Meissner response. By measuring the internal magnetic field profile in superconducting Nb thin films under an applied transverse field by low-energy muon spin rotation spectroscopy, we demonstrate that the local field profile inside Nb is considerably modified upon molecular adsorption in a way that also depends on the applied field direction. The modification is not limited to the ChMs/Nb interface, but it is long ranged and occurs over a length scale comparable with the superconducting coherence length. Zero-field muon spin spectroscopy measurements in combination with our theoretical analysis show that odd-frequency spin-triplet states induced by the ChMs are responsible for the modification of the Meissner response observed inside Nb. These results indicate that a ChMs/SC system supports odd-frequency spin-triplet pairs due to the molecules acting as a spin-active layer, and therefore, they imply that such a system can be used as a simpler alternative to SC/ferromagnet or SC/topological insulator hybrids for the generation and manipulation of unconventional spin-triplet superconducting states.

Figure 1

Schematic of the low-energy muon spin rotation (LE-μSR) spectroscopy measurement setup. LE-μSR in a transverse-field configuration with the external field $B_{\mathrm{ext}}$ applied parallel to the sample surface and perpendicular to the spin precession plane of the muon. Normalized muon stopping distributions simulated for the ChMs/Nb (65 nm) system are also shown for a few representative energies (black lines).

Figure 2

Magnetic field response in ChMs/Nb and bare Nb probed by low-energy muon spin rotation (LE-μSR spectroscopy). (a) and (b) Average local magnetic field ${\overline{B}}_{\mathrm{loc}}$ and (c) and (d) muon spin depolarization rate $\overline{\sigma }$ as a function of implantation energy Ε (bottom axes) and average muon stopping depth $\overline{z}$ (top axes). The error bars in (a) and (b) are within the size of the symbols. The data are collected for both samples in the normal state at 10 K [hollow symbols; blue for Nb (65 nm) and red for ChMs/Nb (65 nm)] and in the superconducting state at 2.8 K [filled symbols; blue for Nb (65 nm) and red for ChMs/Nb (65 nm)]. The data in (b) and (d) correspond to those in the dashed boxes in (a) and (c).

Figure 3

Magnetic dependence of the unconventional Meissner effect in ChMs/Nb. Shift in the average local magnetic field ${\overline{B}}_{\mathrm{loc}}$ between the superconducting and normal state in a ChMs/Nb (65 nm) sample as a function of muon implantation energy Ε (bottom axis) and average muon stopping depth $\overline{z}$ (top axis) for $B_{\mathrm{ext}}=+300$ Gauss (light blue symbols) and $B_{\mathrm{ext}}=-300$ Gauss (green symbols). The shift in ${\overline{B}}_{\mathrm{loc}}$ is determined as the difference between ${\overline{B}}_{\mathrm{loc}}$ at $T=2.8\mathrm{K}$ and ${\overline{B}}_{\mathrm{loc}}$ at $T=10\mathrm{K}$ normalized to ${\overline{B}}_{\mathrm{loc}}$ at $T=10\mathrm{K}$.

Figure 4

Zero-field (ZF) low-energy muon spin rotation (LE-μSR) spectroscopy in ChMs/Nb and bare Nb. Average muon depolarization rate $\overline{\sigma }$ measured in ZF at $E=3\mathrm{keV}$ across the superconducting transition for a ChMs/Nb (55 nm) sample (red curve) and a bare Nb (55 nm) sample (blue curve). The inset shows the difference in $\overline{\sigma }\left({\overline{\sigma }}_{\mathrm{diff}}\right)$ measured between the two samples as a function of temperature.

Figure 5

Global fit and theoretical model of the local field profile in ChMs/Nb. (a) $B_{\mathrm{loc}}\left(z\right)$ profile from the global fit convoluted by the muon stopping distributions (solid lines) and comparison with single-energy asymmetry data (filled symbols) for bare Nb based on the Ginzburg-Landau model (blue solid curve) and for the ChMs/Nb sample based on the theoretical field profile for unconventional Meissner screening due to spin triplets (red solid curve). (b) Theoretical field profile for unconventional Meissner screening in ChMs/Nb (yellow curve) calculated by solving simultaneously the Usadel and Maxwell equations. This field profile differs from that expected for conventional Meissner screening based on Ginzburg-Landau model (black dashed curve) because of two additional terms, both decaying on a length scale comparable with the Nb coherence length ${\xi }_{\mathrm{S}}$: one term ($B_{\mathrm{spin}}$) related to the generation of odd-frequency spin-triplet pairs, which leads to a magnetization $M$ component adding to the magnetization $M_0$ inside Nb (red area), and a second term related to the suppression of Δ at the ChMs/Nb interface (blue area).

Figure 6

Surface potential of a Nb thin film with selective adsorption of ChMs. Surface potential image in (a) three dimensions (3D) and (b) two dimensions 2D measured by Kelvin probe force microscopy on a 10 × 10 μm area of a Nb (65 nm) thin film with ChMs selectively adsorbed onto its surface. The surface potential in (c) is measured along the blue line in (b). Selective adsorption of ChMs is obtained by defining squares by e-beam lithography into a poly(methyl methacrylate) (PMMA) resist layer and then adsorbing the ChMs onto the patterned area. The PMMA is removed after the adsorption. The presence of the ChMs in the adsorbed area is evidenced by a variation in the surface potential of ∼35 mV.

Figure 7

X-ray photoelectron spectroscopy (XPS) measurements. XPS spectra for (a) N $1s$ and (b) C $1s$ for ChMs/Nb (65 nm; green curves) and Nb (65 nm; red curves) with corresponding analysis of the chemical bonds contributing to the spectra. The XPS spectra are collected on the same ChMs/Nb (65 nm) and Nb (65 nm) samples used for the low-energy muon spin spectroscopy (LE-μSR) measurements discussed in this paper, after completion of the LE-μSR study. Quantification of the atomic concentration for Nb, C, N, O on the surface of the same bare (c) Nb (65 nm) and (d) ChMs/Nb (65 nm) sample determined from analysis of XPS spectra acquired on the samples. The existence of the molecules on the surface of the ChMs/Nb sample is verified through the signal contribution from N $1s$ orbitals, which are present in the α-helix polyalanine (AHPA) molecules used in this paper.

Figure 8

Electronic transport properties of a Nb thin film used for low-energy muon spin rotation (LE-μSR) spectroscopy measurements. $R$($T$) normalized to the resistance at 293 K ($R_{293\mathrm{K}}$) and measured in a four-probe configuration on a Nb (65 nm) thin film, with the inset showing a zoom on the same $R\left(T\right)/R_{293\mathrm{K}}$ curve across the superconducting transition. The data show that the thin film has $T_{\mathrm{c}}\sim 9.15\mathrm{K}$ and a residual resistivity ratio (RRR) of ∼ 4.

Figure 9

X-ray reflectometry (XRR) for a Nb (65 nm) thin film sample. XRR data (blue curve) measured on a Nb (65 nm) thin film deposited on a $\mathrm{Si}{\mathrm{O}}_2$ substrate and used for the low-energy muon spin spectroscopy (LE-μSR) measurements done to acquire the results shown in Fig. 2. The fit to the experimental data indicates the presence of a surface native oxide ${\mathrm{Nb}}_2{\mathrm{O}}_5$ layer with thickness of 3.847 ± 0.04 nm, $\mathrm{density}=3.482\pm 0.04\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$, and roughness 0.796 nm ± 0.1 nm on top of a Nb thin film with thickness 64.678 ± 0.05 nm, $\mathrm{density}=8.5\pm 0.04\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$, and roughness of 1.56 ± 0.1 nm. The density and the thickness values obtained from this fit for the ${\mathrm{Nb}}_2{\mathrm{O}}_5$ and Nb layers are given as input to the program TrimSP to simulate the proper muon implantation distributions for the sample.

Figure 10

Low-energy muon spin rotation (LE-μSR) spectroscopy asymmetry data in zero field (ZF). (a) Average muon depolarization rate $\overline{\sigma }$ measured in ZF at $E=8\mathrm{keV}$ across the superconducting transition for a ChMs/Nb (55 nm) sample (red curve) and a bare Nb (55 nm) sample (blue curve). The inset shows the difference in $\overline{\sigma }\left({\overline{\sigma }}_{\mathrm{diff}}\right)$ measured between the two samples as a function of temperature. (b) Asymmetry signal corresponding to the points in (a) measured above $T_{\mathrm{c}}$ at 10 K (black symbols) and below $T_{\mathrm{c}}$ at 2.8 K (blue symbols) with fits to the Kubo-Toyabe model (solid lines with corresponding colors). The variation between the curves is related to an increase in the $\overline{\sigma }$ value of the model, as defined in this paper, and it shows the presence of additional spin activity in the sample with ChMs below $T_{\mathrm{c}}$.

Figure 11

Theoretical model. Schematic of the theoretical model used to determine the field profile in ChMs/Nb.

Figure 12

Theoretical field profile calculated based on our model. Depth dependence of $B_{\mathrm{loc}}\left(z\right)/B_{\mathrm{ext}}$ computed from our theoretical model (red curve) for a ChMs/Nb system with $B_{\mathrm{ext}}=302.6$ Gauss as during the collection of low-energy muon spin rotation (LE-μSR) spectroscopy data in Fig. 2. The profile is simulated assuming a Nb thickness $d_{\mathrm{s}}=4{\xi }_{\mathrm{s}}$. A profile derived from the Ginzburg-Landau model (black curve) for $B_{\mathrm{loc}}\left(z\right)/B_{\mathrm{ext}}$ in the case of conventional Meissner screening is also shown for comparison. We note that $z=0$ corresponds to the ChMs/S interface in our model, with the ChMs being modeled as the equivalent of a spin-active insulator. At the interface between the surface of the spin-active insulator and vacuum (not shown here), the local field in our model coincides with $B_{\mathrm{ext}}$.

Figure 13

Asymmetry signal and corresponding fits. Examples of raw data (symbols with error bars) and theoretical fits (solid lines) for the asymmetry signal $A_{\mathrm{S}}\left(t\right)$ measured for (a) a ChMs/Nb (65 nm) sample and (b) a Nb (65 nm) sample. The top panels in (a) and (b) show the raw $A_{\mathrm{S}}\left(t\right)$ data and corresponding fits obtained for both samples below $T_{\mathrm{c}}$ at $T=2.8\mathrm{K}$ and $E=3\mathrm{keV}$ (black symbols and lines) or $E=7.5\mathrm{keV}$ (green symbols and lines). The bottom panels in (a) and (b) show the raw $A_{\mathrm{S}}\left(t\right)$ data and corresponding fits obtained for both samples above $T_{\mathrm{c}}$ at $T=10\mathrm{K}$ and $E=3\mathrm{keV}$ (red symbols and lines) or $E=7.5\mathrm{keV}$ (blue symbols and lines).

Figure 14

Magnetic field response in ChMs/Nb (55 nm). Average local magnetic field ${\overline{B}}_{\mathrm{loc}}$ as a function of muon implantation energy Ε (bottom axis) and average muon stopping depth $\overline{z}$ (top axis) determined by transverse-field low-energy muon spin rotation (LE-μSR) spectroscopy measurements in the superconducting state ($T_{\mathrm{c}}\sim 8.7\mathrm{K}$) at $T=2.8\mathrm{K}$ (red symbols) and in the normal state at $T=10\mathrm{K}$ (black hollow symbols). The ${\overline{B}}_{\mathrm{loc}}$ profile at $T=2.8\mathrm{K}$ shows an unconventional Meissner screening consistent with that measured for the two other ChMs/Nb (65 nm) samples shown in Figs. 2 and 3.

Figure 15

Simulated normalized stopping profiles and fraction of implanted muons at different energies. (a) Normalized muon stopping profile distributions $p$($z,E$) for Nb (65 nm) thin film with a top 4-nm-thick ${\mathrm{Nb}}_2{\mathrm{O}}_5$ native oxide layer simulated for different implantation energy $E$ values and (b) fraction of implanted muons stopping in ${\mathrm{Nb}}_2{\mathrm{O}}_5$ (magenta curve), Nb (blue curve), in the $\mathrm{Si}{\mathrm{O}}_2$ substrate (green curve), and of backscattered muons (gray curve). The thicknesses for the ${\mathrm{Nb}}_2{\mathrm{O}}_5$ and Nb layers are obtained from x-ray reflectometry (Fig. 9) done on the same samples used for the low-energy muon spin rotation (LE-μSR) spectroscopy measurements. The layer of ChMs is not included in the simulations due its negligible (monolayer) thickness and low stopping power (due to its low density) for the implanted muons.