The Non-collinear Path to Topological Superconductivity

Abstract

Combining spin textures in ultra-thin films with conventional superconductors has emerged as a powerful and versatile platform for designing topologically non-trivial superconducting phases as well as spin-triplet Cooper pairs. As a consequence, two-dimensional magnet-superconductor hybrids (2D MSHs) are promising candidate systems to realize devices for topology-based quantum technologies and superconducting spintronics. So far, studies have focused mostly on systems hosting collinear ferromagnets or antiferromagnets. However, topologically non-trivial phases have been predicted to emerge in MSH systems with non-collinear spin textures as well. In this article, we present the experimental discovery of topological superconductivity in the MSH system Fe/Ta(110) where a magnetic spiral is realized in the Fe monolayer on the surface of the s-wave superconductor Ta. By combining low-temperature spin-polarized scanning tunneling microscopy measurements with theoretical modeling, we are able to conclude that the system is in a topological nodal-point superconducting phase with low-energy edge modes. Due to the non-collinear spin texture in our MSH system, these edge modes exhibit a magnetization direction-dependent dispersion. Furthermore, we identify direct signatures of Rashba spin-orbit coupling in the experimentally measured differential tunneling conductance. The present work realizes a non-collinear spin texture-based path to topological superconductivity.

Figures (5)

• Figure 1: Magnetic characterization of the MSH system.a SP-STM constant-current image of a sample with 0.8 atomic layers of Fe on Ta(110); the pseudomorphic Fe monolayer areas can be identified by their orange color, the stripes originate from the magnetic spin spiral state. b Closer view of a SP-STM constant-current measurement of the spin spiral in the Fe monolayer. c Expected SP-STM signal due to the TMR effect for a spin spiral. d Sketch of a homogeneous spin spiral; red and blue indicate up and down magnetization directions, respectively. e Expected signal for a spin spiral using a non-magnetic tip due to EMR effects. f STM constant-current image obtained using a non-magnetic tip, revealing a periodic pattern with half of the spin spiral period, in agreement with EMR contrast. g Perspective view of the studied MSH system.
• Figure 2: Spectroscopic characterization of the MSH system.a Spin configuration of the magnetic spin spiral and the expected imaging contrast due to the TMR effect. b Spin-resolved d$I$/d$V$ spectroscopy measurements obtained with a spin-polarized tip along the spin spiral propagation direction. c d$I$/d$V$ intensities along the spin spiral averaged over an energy range of $-0.13$ mV to $+0.06$ mV, as indicated by the green lines in b; the solid line represents a cosine function with the spin spiral period and serves as a guide to the eye. d Spin configuration of the magnetic spin spiral and the expected imaging contrast due to the EMR effect. e spin-averaged d$I$/d$V$ spectroscopy measurements obtained with a superconducting tip along the spin spiral. f d$I$/d$V$ intensities along the spin spiral averaged over an energy range of $+0.80$ mV to $+1.02$ mV, as indicated by the green lines in e; the cosine function with half the spin spiral period serves as a guide to the eye.
• Figure 3: Microscopic origin of the TMR and EMR signal. Line-cut of the out-of-plane magnetization (blue), spin-$\uparrow$ LDOS (orange), spin-averaged LDOS (green) and total Rashba SOC (red) for a sinusoidal spin spiral with a$\alpha = 0$ and b$\alpha = 0.077 \Delta$. For the case shown in b, the energy- and position-dependent c spin-resolved and d spin-averaged LDOS for a line-cut along the spiral direction of propagation, together with the spatial dependence of $m_z$ and the total Rashba SOC, are shown.
• Figure 4: Topological nodal point superconductivity and edge modes in the MSH system.a Spin-averaged in-gap d$I$/d$V$ map at $V=0.1$ mV exhibiting an enhanced contrast along the [001]-edge. b Sketch of the structural and magnetic unit cell. c Electronic structure in the magnetic Brillouin zone exhibiting nodal points with non-zero topological charge. d Theoretical LDOS on the Ta surface (black) and for the Fe/Ta MSH system (red). e Theoretical LDOS at a [001]-edge (blue), [1$\bar{1}$1]-edge (purple) or [1$\bar{1}$0]-edge (green). f Electronic band structure as a function of momentum along the [001]-edges of a ribbon system. The spin spiral terminates with an angle $\theta = 0^{\circ}$ at the ribbon's left and right edges.
• Figure 5: Edge states along [001] direction. Spectral function as a function of momentum along a ribbon with two [001]-edges and termination angle a$\theta =172^{\circ}$ and b$\theta =82^{\circ}$ of the spin spiral. c Low-energy LDOS at an [001]-edge as a function of the termination angle $\theta$. The white dashed and dotted lines represent the $\theta =172^{\circ}$ and $\theta =82^{\circ}$ terminations, respectively. d Experimental spin-averaged zero-bias d$I$/d$V$ map with fast scan direction along [001]-edges of an irregularly shaped Fe island; the inset shows an SP-STM constant-current image of the same area. e Theoretical spin-averaged zero-energy LDOS for a Fe island of the same size and shape as that shown in d. The white line represents the $m_z$-component of the spin spiral along the $[1{\bar{1}}0]$-direction.