Topological superconductivity in a van der Waals heterostructure

The designer approach has become a new paradigm in accessing novel quantum phases of matter Geim2013 ; Novoselov2016_review ; Cao2018UnconventionalSuperlattices ; Gibertini2019 ; Yan2019engineered ; Khajetoorians2019designer ; Lutchyn2018_review . Moreover, the realization of exotic states such as topological insulators, superconductors and quantum spin liquids often poses challenging or even contradictory demands for any single materialNayak2008 ; Sato2017_review ; Lutchyn2018_review . For example, it is presently unclear if topological superconductivity, which has been suggested as a key ingredient for topological quantum computing, exists at all in any naturally occurring material Mourik2012science ; Nadj-Perge2014 ; Menard2017_NatComm ; Kim2018 ; palacio ; Wang2020_Science . This problem can be circumvented by using designer heterostructures combining different materials, where the desired physics emerges from the engineered interactions between the different components. Here, we employ the designer approach to demonstrate two major breakthroughs – the fabrication of van der Waals (vdW) heterostructures combining 2D ferromagnetism with superconductivity and the observation of 2D topological superconductivity. We use molecular-beam epitaxy (MBE) to grow two-dimensional islands of ferromagnetic chromium tribromide (CrBr₃)chen2019direct on superconducting niobium diselenide (NbSe₂) and show the signatures of one-dimensional Majorana edge modes using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). The fabricated two-dimensional vdW heterostructure provides a high-quality controllable platform that can be integrated in device structures harnessing topological superconductivity. Finally, layered heterostructures can be readily accessed by a large variety of external stimuli potentially allowing external control of 2D topological superconductivity through electricalJiang2018 , mechanicalWu2019 , chemicalJiang2018a , or optical meansZhang2019 .

There has been a surge of interest in designer materials that would realize electronic responses not found in naturally occurring materials Geim2013 ; Novoselov2016_review ; Cao2018UnconventionalSuperlattices ; Gibertini2019 ; Yan2019engineered ; Khajetoorians2019designer ; Lutchyn2018_review . Topological superconductors are one of the main targets of these efforts and they are currently attracting intense attention due to their potential as building blocks for Majorana-based qubits for topological quantum computationNayak2008 ; Sato2017_review ; Lutchyn2018_review . Majorana zero-energy modes (MZM) have been reported in several different experimental platforms, with the most prominent examples being semiconductor nanowires with strong spin-orbit coupling and ferromagnetic atomic chains proximitized with an s-wave superconductor Mourik2012science ; Nadj-Perge2014 ; Sato2017_review ; Kim2018 ; Lutchyn2018_review ; Liu2019_review ; Jaeck2019 . It is also possible to realize MZMs in vortex cores on a proximitized topological insulator surfaceFu2008 ; Sun2016 or on FeTe_0.55Se_0.45 superconductor surface Zhang2018_Science ; Wang2018_Science ; Zhu2020_science . In these cases the MZM were spectroscopically identified as zero energy conductance signals that are localized at the ends of the one dimensional (1D) chain or in the vortex core. The evidence of the Majorana states in these various platforms consists of subgap conductance peaks and the features occurring at system boundaries and defects are consistent with their topological origin. Unfortunately, different disorder-induced states are known to mimic the Majorana conductance signals and the status of the observations remains presently inconclusive. The ultimate proof of the existence of Majorana zero modes would be obtained if their non-Abelian exchange statistics or braiding could be demonstratedLutchyn2018_review .

In two-dimensional systems, 1D dispersive chiral Majorana fermions are expected to localize near the edge of the system (Fig. 1a). For example, it was proposed that the dispersing Majorana states can be created at the edges of an island of magnetic adatoms on the surface of an s-wave superconductorRoentynen2015 ; Li2016 ; Rachel2017 . Experimentally, promising signatures of such 1D chiral Majorana modes have recently been reported around nanoscale magnetic islands either buried below a single atomic layer of PbMenard2017_NatComm , or adsorbed on a Re substratepalacio , and in domain walls in FeTe_0.55Se_0.45 Wang2020_Science . However, these types of systems can be sensitive to disorder and may require interface engineering through, e.g., the use of an atomically thin separation layer. In addition, it is difficult to incorporate these materials into device structures. These problems can be circumvented in van der Waals (vdW) heterostructures, where the different layers interact only through vdW forcesGeim2013 . VdW heterostructures naturally allow for very high quality interfaces and a multitude of practical devices have been demonstrated. While vdW materials with a wide range of properties have been discovered, ferromagnetism has been notably absent until recent discoveries of atomically thin Cr₂Ge₂Te₆Gong2017_Cr2Ge2Te6 , CrI₃Huang2017_CrI3 and CrBr₃Ghazaryan2018 ; Zhang2019 . The first reports relied on mechanical exfoliation for the sample preparation, but CrBr₃chen2019direct and Fe₃GeTe₂Liu2017_Fe3Gete2 have also been grown using molecular-beam epitaxy (MBE) in ultra-high vacuum (UHV). This is essential for realizing clean edges and interfaces.

The recently discovered monolayer ferromagnet transition metal trihalides combined with transition metal dichalcogenide (TMD) superconductors form an ideal platform for realizing 2D topological superconductivity (Fig. 1a). Here, we use MBE to grow high-quality monolayer ferromagnet CrBr₃ on a NbSe₂ superconducting substrate. The mirror symmetry is broken at the interface between the different materials and this lifts the spin degeneracy due to the Rashba effect. Therefore, we have all the necessary ingredients – magnetism, superconductivity and Rashba spin-orbit coupling – required to realize a designer topological superconductor Sato2009_PRB ; Sau2010_PRL . The use of a van der Waals heterostructure has significant advantages: They can potentially be manufactured by simple mechanical exfoliation, the interfaces are naturally very uniform and of high quality, and the structures can be straightforwardly integrated in device structures. Finally, layered heterostructures can be readily accessed by a large variety of external stimuli making external control of 2D topological superconductivity potentially possible by electricalJiang2018 , mechanicalWu2019 , chemicalJiang2018a , and optical approachesZhang2019 .

Pioneering theoretical works Sato2009_PRB ; Sau2010_PRL demonstrated that topological superconductivity may arise from a combination of out-of-plane ferromagnetism, superconductivity and Rashba-type spin-orbit coupling, as illustrated in Fig. 1b,c. In this scheme, the Rashba coupling lifts the spin-degeneracy of the conduction band while Zeeman splitting due to proximity magnetization lifts the remaining Kramers degeneracy. Adding superconductivity creates a particle-hole symmetric band structure and the superconducting pairing opens gaps at the Fermi energy. In our theoretical model for magnetically covered NbSe₂, a similar picture arises for the real band structure around any of the high symmetry points of the hexagonal Brillouin zone ($\Gamma$, $\mathrm{K}$, or $\mathrm{M}$) where Rashba coupling vanishes. Depending on the magnitude of the magnetization induced gap $M$ and the position of the Fermi energy $\mu$, the system enters a topological phase when $|\epsilon(\vec{k_{0}})-\mu|\leq M$, where $\epsilon(\vec{k_{0}})$ is the energy of the band crossing at the high symmetry point in the absence of magnetization. This is due to the created effective $p$-wave pairing symmetry.

In Fig. 1d, we show a constant-current scanning tunneling microscopy (STM) image of the CrBr₃ island grown on a freshly cleaved bulk NbSe₂ substrate by MBE (see Methods for details). The CrBr₃ islands show a well-ordered moiré superstructure with 6.3 nm periodicity arising from the lattice mismatch between the CrBr₃ and the NbSe₂ layers. Fig. 1e shows an atomically resolved STM image of the CrBr₃ monolayer, revealing periodically spaced triangular protrusions. These features are formed by the three neighbouring Br atoms as highlighted in the Fig. 1f (red triangle) showing the fully relaxed geometry of CrBr₃/NbSe₂ heterostructure obtained through density functional theory (DFT) calculations (see Methods for details). The measured in-plane lattice constant is 6.5 Å, consistent with the recent experimental value (6.3 Å) of monolayer CrBr₃ grown on graphite chen2019direct and our DFT calculations. DFT calculations further confirm that the CrBr₃ monolayer retains its ferromagnetic ordering with a magnetocrystalline anisotropy favouring an out-of-plane spin orientation as shown in Fig. 1f. We confirmed the ferromagnetism of the CrBr₃ islands on NbSe₂ experimentally with magneto-optical Kerr effect measurements. The magnetization density (Fig. 1f) shows that the magnetism arises from the partially filled $d$ orbitals of the Cr³⁺ ion. While the largest magnetization density is found close to the Cr atoms, there is also significant proximity induced magnetization on the Nb atoms in the underlying NbSe₂ layer.

We probe the emerging topological superconductor phase with scanning tunneling spectroscopy (STS) measurements at a temperature of $T=350$ mK. Fig. 1g shows experimental d$I$/d$V$ spectra (raw data) taken at different locations indicated in Fig. 1d (marked by filled circles). The d$I$/d$V$ spectrum of bare NbSe₂ has a hard gap with an extended region of zero differential conductance around zero bias, which can be fitted by the McMillan two-band modelNoat2015_nbse2 (see Extended Data Fig. 1a). In contrast, in the spectra taken in the middle of the CrBr₃ island, we observe pairs of conductance onsets at $\pm 0.3$ mV around zero bias (red arrows). The magnetization causes the formation of energy bands (dubbed Shiba bands) that exist inside the superconducting gap of the substrate Sato2009_PRB ; Sato2017_review . Spin-orbit interactions can drive the system into a topological phase with associated closing and reopening of the gap between the Shiba bands.

We observe edge modes consistent with the expected Majorana modes along the edge of the magnetic island that are the hallmark of 2D topological superconductivity Sato2017_review ; Menard2017_NatComm ; palacio . The spectroscopic feature of the Majorana edge mode appears inside the gap defined by the Shiba bands (the topological gap) and is centred around the Fermi level ($E_{\mathrm{F}}$). This is a further indication that the edge states are indeed topological edge modes. A typical spectrum taken at the edge of the CrBr₃ island is shown in Fig. 1g, where a peak localized at $E_{\mathrm{F}}$ is clearly seen together with side features stemming from the Shiba bands (detailed analysis shown in Extended Data Fig. 1c-f).

We develop an effective low-energy model (see Supplementary Information (SI) for details) based on earlier work on individual magnetic impurities on a bulk NbSe₂ substrate Menard2015_NatPhys and DFT calculations. The band structure of the Nb $d$-states derived band used in the effective model is shown in Fig. 2a (direct comparison with DFT is shown in the SI). Topological superconductivity can be generated when magnetization is sufficiently strong to push one of the spin-degenerate bands at a high-symmetry point above the Fermi energy. We identify the observed topological phase as a state arising from the gap-closing transition at M point with a Chern number $C=3$. While the M-point is at $\sim 270$ meV below the Fermi level in our TB model (calculated phase diagram shown in Fig. 2b), it is estimated to be $\sim 100$ meV below Fermi level in bulk NbSe₂ PhysRevLett.102.166402 ; Ugeda2016NatPhys . This implies that for a reasonable magnetization of $M\lesssim 100$ meV, we need slight doping to bring the experimental system into the $C=3$ state. This is precisely what we observe by following the Nb d-bands from bare NbSe₂ onto a CrBr₃ island. There is an upward shift of the NbSe₂ bands of $\sim 80$ meV under CrBr₃ (Extended Data Fig. 2). The two other nontrivial phases that originate from gap closings at the $\Gamma$ point and $K$ points give rise to topological phases with $C=-1$ and $C=-2$. Realization of either of these phases would require notably larger shifts in chemical potential ($\sim 0.6$ eV), making them improbable for the experimental observations. The absolute values of the nontrivial Chern numbers can be understood by a three-fold rotational symmetry (see SI).

The key quantity characterizing robustness of the nontrivial phase is the topological energy gap $\Delta_{t}$. This scale should be much larger than temperature for the state to be observable in experiment. In the simple parabolic band model this quantity can be estimated by $\Delta_{t}=\alpha k_{F}/[(\alpha k_{F})^{2}+M^{2}]^{1/2}$, where $\alpha$ is the Rashba coupling and $k_{F}$ the Fermi wavelength Alicea2010_PRB . The calculated gap based on our more realistic tight-binding (TB) model is shown in Fig. 2c. Based on the experimental results shown in Fig. 1g, the topological gap is $\Delta_{t}\approx 0.3\Delta$. The calculated band structure in a strip geometry corresponding to the experimental gap is shown in Fig. 2d, where we see the Majorana edge modes crossing the topological gap. The edge modes are seen to coexist with the bulk states in a finite subgap energy window in agreement with experimental observations.

We have carried out spatially resolved d$I$/d$V$ spectroscopy across the edge of the CrBr₃ island (Fig. 3a). The energy dependence of the main feature of the edge mode LDOS is such that it splits off from the top edge of the topological gap inside the CrBr₃ island, smoothly crosses the topological gap and merges with its lower edge outside the CrBr₃ island. We have recorded grid d$I$/d$V$ spectroscopy maps (Fig. 3b-g) to probe the spatial evolution of the edge modes. At $E_{\mathrm{F}}$, the edge modes are confined within $\sim 2.4$ nm of the edge of the island (see Extended Data Fig. 3). In addition to the edge mode signature close to the Fermi level, there is also enhanced LDOS at the energies above the topological gap (Fig. 3e,f) where we also see significant excitations inside the magnetic island. This implies that the edge modes coexist with Shiba bands at energies higher than the topological gap. The theoretically computed LDOS (Fig. 3h-n, see SI for details) reproduces the essential features of the experimental results. In addition to the universal signatures of topological superconductivity, our theoretical model reproduces a number of experimentally observed system-specific characteristics including 1) the correct edge mode penetration depth which is orders of magnitude smaller than simple estimates (similar to the case of 1D Fe wires on Pb Nadj-Perge2014 ; peng2015 ), 2) the specific form of the subgap local density of states, which depends on system-specific dispersion of the topological edge modes, and 3) a non-generic coexistence of the topological edge modes and bulk states in a substantial energy window. Finally, we confirm the experimental finding that the distribution of the spectral weight of the edge mode along the edge is non-uniform. This stems from the geometric irregularities of the island boundary with characteristic length scale that is comparable to the edge mode penetration depth. However, the edge modes are not discontinuous along the edge, interference effects near edge irregularities suppress the visibility of the edge mode due to finite experimental resolution.

The experimentally observed edge modes could possess a topologically trivial origin. However, in addition to the near quantitative match with the theoretical results incorporating the main ingredients of the experimental system, the edge mode signature is experimentally very robust. We consistently observe it in our hybrid vdW heterostructures on all CrBr₃ islands, irrespective of their specific size and shape (Extended Data Fig. 4). Based on theoretical considerations, to observe the modes for all subgap energies, the linear dimension of the islands should be much larger than the edge mode penetration depth. This condition is clearly fulfilled in our experimental results. To prove the observed edge modes of the hybrid heterostructures are strongly linked to the superconductivity of the NbSe₂ substrate, we have carried out experiments in magnetic fields up to 4 T, suppressing superconductivity in the NbSe₂ substrate. All features associated with the gap at the centre of the island and the edge modes disappear in the absence of superconductivity in NbSe₂ (Extended Data Fig. 5). This rules out trivial edge modes as the cause of the observed results. Another non-topological reason for resonances close to the Fermi energy, the Kondo effect, should also be present in the normal state and can hence be ruled out as well.

In conclusion, our work constitutes two breakthroughs in designer quantum materials. By fabricating vdW heterostructures with 2D ferromagnet epitaxially coupled to superconducting NbSe₂, we obtained a near ideal designer structure exhibiting two competing electronic orders. The induced magnetization and spin-orbit coupling renders the superconductor topologically nontrivial, supporting Majorana edge channels which we characterized by STM and STS measurements. The demonstrated heterostructure provides a high-quality platform for electrical devices employing topological superconductivity. This is an essential step towards practical devices employing topological superconductivity and the demonstrated system would in principle allow electrical control of the topological phase through electrostatic tuning of the chemical potential.