In-plane ferromagnetism-driven topological nodal-point superconductivity with tilted Weyl cones

TL;DR

This work demonstrates a route to two-dimensional topological superconductivity by coupling a 2D in-plane ferromagnet to a conventional $s$-wave superconductor, as realized in Co monolayers on Nb(110). Through combined DFT structuring, atomistic spin dynamics, low-energy YSR-based modeling, and high-resolution STS, the authors identify a nodal-point superconducting phase characterized by tilted Weyl cones and a gapless spectrum, with a robust in-gap double-peak LDOS that is enhanced at island edges. Real-space tight-binding simulations reproduce the experimental LDOS features and reveal parameter-dependent Weyl tilting and edge localization, supporting the interpretation of a nodal topological phase. The study establishes in-plane ferromagnetism with conventional superconductivity as a viable platform for designing two-dimensional topological quantum phases and opens avenues for exploring type-I and type-II Weyl physics in magnet–superconductor hybrids, including potential van der Waals implementations.

Abstract

The potential application of topological superconductivity in quantum transport and quantum information has fueled an intense investigation of hybrid materials with emergent electronic properties, including magnet-superconductor heterostructures. Here, we report evidence of a topological nodal-point superconducting phase in a one-atom-thick in-plane ferromagnet in direct proximity to a conventional $s$-wave superconductor. Low-temperature scanning tunneling spectroscopy data reveal the presence of a double-peak low-energy feature in the local density of states of the hybrid system, which is rationalized via model calculations to be an emergent topological nodal-point superconducting phase with tilted Weyl cones. Our results further establish the combination of in-plane ferromagnetism and conventional superconductivity as a route to design two-dimensional topological quantum phases.

Figures (9)

• Figure 1: Structural characterization of Co monolayer islands on the Nb(110) surface. a Constant-current STM image of a typical sample, where about $50\%$ of a Co monolayer is deposited on a clean and unreconstructed Nb(110) surface. A stripe-like pattern along the $[1\overline{1}0]$ crystallographic direction indicates the presence of a uniaxial reconstruction in the Co islands. b A zoom-in on the Co island showing the stripe-like reconstruction. c A different appearance of the structural reconstruction in the Co monolayer obtained for different tunneling parameters, where the red dotted rectangle indicates the structural unit cell. d Constant-current STM image showing the atomic corrugation of the Nb(110) surface, with the structural unit cell indicated by the cyan dotted rectangle. e Constant-current STM image showing the atomic corrugation of the Co/Nb(110) surface, with its structural unit cell, indicated by the red dotted rectangle, compared with the unit cell of the Nb(110) surface underneath, indicated by the cyan dotted rectangle. f Side-view schematic of the $(3\times1)$ reconstruction, with 4 Co atoms sitting on top of 3 Nb atoms along the [001] crystallographic direction. g LEED pattern acquired from the Co/Nb(110) sample with an electron beam energy of 70 eV, showing the primary spots of the Nb(110) surface (highlighted with cyan dotted circles) and the additional spots (highlighted with red dotted circles) due to the $(3\times1)$ reconstruction along the [001] crystallographic direction of the Co monolayer. The remaining gray dotted circles indicate other expected LEED spots due to the $(3\times1)$ reconstruction which were not clearly visible in the LEED pattern. Scanning parameters: aI=0.5 nA, V=50 mV; bI=5 nA, V=20 mV; cI=20 nA, V=20 mV; dI=5 nA, V=2 mV; eI=20 nA, V=2 mV. T=4.2 K.
• Figure 2: Structural and magnetic model from first-principles calculations. a Relaxed atomic structure for the Co monolayer on the Nb(110) surface. The structural unit cell is indicated by the red dotted rectangle, which is in agreement with the atomic configuration observed experimentally; see Fig. \ref{['fig1']}c. The inset shows a simulated constant-current STM image of the calculated Co/Nb(110) atomic arrangement, which reproduces closely the experimentally acquired image shown in Fig. \ref{['fig1']}e. b In-plane ferromagnetic ground state of the Co monolayer obtained from first-principles-parametrized spin-model simulations, with the magnetic easy axis x and perpendicular axis y along the $[001]$ and $[1\overline{1}0]$ crystallographic directions, respectively.
• Figure 3: Formation of type I and II Weyl cones with non-vanishing winding number in the low-energy theory. a Schematics for in-plane magnetization. b Schematics for out-of-plane magnetization. c Energy difference between upper and lower band $\delta E=E_{+}-E_{-}$, plotted in the hexagonal BZ with the magnetization direction (black arrow) along the $x$ direction ($[001]$). The intersection of the nodal lines of the $d_y$ (light yellow) and $d_z$ (red) components of the effective Hamiltonian in Eq. (\ref{['eq:GiannisEffHam']}) coincide with the vanishing of the band gap (dark green on the colormap). d Energy bands plotted in a linecut along the $q_y$ direction, which shows the appearance of a pair of tilted type I Weyl cones (gray inset) for an in-plane magnetization, $\zeta=\pi/2$. e Same as in $\textbf{d}$ but for the out-of-plane case, $\zeta=0$. f Winding of $\boldsymbol{d}/|\boldsymbol{d}|$ around the Weyl point shown in d, indicating the topological charge. g Appearance of type II Weyl nodes for larger spin-orbit coupling than in d. In all plots, we use a next-nearest-neighbor model, and the parameters are fixed at $m=10\hbar^2 l^{-2}/\Delta$, $\mu=10\Delta$, $a=0.5l\cdot\Delta$, $J=4\upsilon_\mathrm{F}l^{-2}/\left(k_\mathrm{F+}+k_\mathrm{F-}\right)$ (to ensure that $\epsilon_{\pm}\rightarrow0$), except for panel g where $a=7 l\cdot\Delta$ is used.
• Figure 4: Scanning tunneling spectroscopy at Co monolayer islands on the Nb(110) surface. a Constant-current STM image of the Co islands labeled $1$ to $5$ on the Nb(110) surface (scanning parameters: I=200 pA, V=10 mV). The dark patches visible on the Nb(110) terraces are oxygen contamination aggregates remaining after the cleaning process. b-c As-measured dI/dV spectra on Co islands acquired in the middle of the islands b and on the edge of the islands c. Spectra are color-coded to specific islands whose positions are shown in panel a. In all plots, the brown graphs mark the substrate spectrum for reference. The value of $\Delta\textsubscript{tip}$ is marked by an orange dashed line, while the green dashed line shows the value of $\Delta\textsubscript{tip}+\Delta\textsubscript{Nb(110)}.$d-f LDOS obtained via deconvolution of dI/dV shown in panels b and c. d Data averaged over all islands for the middle of the islands (in black) and the edges (in gray). In panels e and f spectra for the middle and the edge of each island are shown, respectively. In panels b,c, e, and f the curves are offset by 0.15 arb. u. for clarity. Stabilization parameters: I$_{\textrm{stab}}$=1 nA; V$_{\textrm{stab}}$=4 mV; $\Delta{V}$=16 $\mu$V. dI/dV spectra acquired with a superconducting tip with $\Delta\textsubscript{tip}$=1.43 meV at a measurement temperature T=300 mK.
• Figure 5: Spatially resolved local density of states of a Co monolayer island on the Nb(110) surface. a Constant-current STM image of a Co island on the Nb(110) surface. b Waterfall plot of the LDOS obtained by deconvolution of differential tunneling conductance spectra acquired over the edge of a Co island marked by a red arrow in panel a. Stabilization parameters: I= 1 nA; V= 4 mV; $\Delta{V}$=16 $\mu$V. c Differential tunneling conductance maps of the same Co island in panel a acquired at different bias voltages V. Stabilization parameters: I$_{\textrm{stab}}$=1 nA; V$_{\textrm{stab}}$=-4 mV; $\Delta{V}$=40 $\mu$V. dI/dV maps and spectra are acquired with a superconducting tip with $\Delta\textsubscript{tip}$=1.43 meV. Scanning parameters: I= 200 pA, V= -10 mV.