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One key challenge in the field of topological superconductivity (Tsc) has been the rareness of material realization. This is true not only for the first-order Tsc featuring Majorana surface modes, but also for the higher-order Tsc, which host Majorana hinge and corner modes. Here, we propose a four-step strategy that mathematically derives comprehensive guiding principles for the search and design for materials of general higher-order Tsc phases. Specifically, such recipes consist of conditions on the normal state and pairing symmetry that can lead to a given higher-order Tsc state. We demonstrate this strategy by obtaining recipes for achieving three-dimensional higher-order Tsc phases protected by the inversion symmetry. Following our recipe, we predict that the observed superconductivity in centrosymmetric MoTe₂is a hyrbid-order Tsc candidate, which features both surface and corner modes. Our proposed strategy enables systematic materials search and design for higher-order Tsc, which can mobilize the experimental efforts and accelerate the material discovery for higher-order Tsc phases.

 

Magnetic impurities at surfaces of superconductors can induce bound states referred to as Yu–Shiba–Rusinov states (i.e. Shiba states) within superconducting (SC) gaps. For superconductors with strong spin–orbit coupling (SOC), Shiba states arising from even single magnetic adatoms are too complex to be fully understood using effective models alone because SOC cannot be treated perturbatively and multiple orbitals are strongly mixed with spin projections. Here we investigate Shiba states of single magnetic adatoms at the surface of strongly spin-orbit coupled SC Pb, by solving the fully relativistic Dirac–Bogoliubov–de Gennes equations using multiple scattering Green’s function methods. For Fe and Co adatoms on Pb(110), we show that the Shiba states are better characterized by total angular momentum,J, and its projections on thezaxis,m_J. As a hallmark of the SOC effect, the Shiba states show a strong dependence of the orientation of the adatom moment. As the orientation of the Fe/Co moment changes, the deepest Shiba states merge at zero energy. This zero-energy state disappears with an additional non-magnetic adatom next to the magnetic adatom, although the other Shiba states unchange. For a Mn adatom on Pb, our Shiba states overall agree with experiments. The characteristics of our Shiba states are also observed with the similar energies and characters in the experiments. The deepest Shiba states that we compute, however, do not appear as close to the Fermi level as the experimental data. It would be interesting to compute the Shiba states with continuously varying vertical distances of the Mn adatom from the surface or with varying the charge state of the adatom, and to calculate the spatial dependence of the spectral density. Our findings will be also useful for understanding of Shiba states for dimers and longer spin chains on the Pb surface considering noncollinear magnetic structures in them.

 

Hydrogen, the smallest and most abundant element in nature, can be efficiently incorporated within a solid and drastically modify its electronic and structural state. In most semiconductors interstitial hydrogen binds to defects and is known to be amphoteric, namely it can act either as a donor (H⁺) or an acceptor (H⁻) of charge, nearly always counteracting the prevailing conductivity type. Here we demonstrate that hydrogenation resolves an outstanding challenge in chalcogenide classes of three-dimensional (3D) topological insulators and magnets — the control of intrinsic bulk conduction that denies access to quantum surface transport, imposing severe thickness limits on the bulk. With electrons donated by a reversible binding of H⁺ions to Te(Se) chalcogens, carrier densities are reduced by over 10²⁰cm⁻³, allowing tuning the Fermi level into the bulk bandgap to enter surface/edge current channels without altering carrier mobility or the bandstructure. The hydrogen-tuned topological nanostructures are stable at room temperature and tunable disregarding bulk size, opening a breadth of device platforms for harnessing emergent topological states.

 

Abstract MnBi 2 Te 4 /(Bi 2 Te 3 ) n materials system has recently generated strong interest as a natural platform for the realization of the quantum anomalous Hall (QAH) state. The system is magnetically much better ordered than substitutionally doped materials, however, the detrimental effects of certain disorders are becoming increasingly acknowledged. Here, from compiling structural, compositional, and magnetic metrics of disorder in ferromagnetic (FM) MnBi 2 Te 4 /(Bi 2 Te 3 ) n it is found that migration of Mn between MnBi 2 Te 4 septuple layers (SLs) and otherwise non-magnetic Bi 2 Te 3 quintuple layers (QLs) has systemic consequences—it induces FM coupling of Mn-depleted SLs with Mn-doped QLs, seen in ferromagnetic resonance as an acoustic and optical resonance mode of the two coupled spin subsystems. Even for a large SL separation ( n ≳ 4 QLs) the structure cannot be considered as a stack of uncoupled two-dimensional layers. Angle-resolved photoemission spectroscopy and density functional theory studies show that Mn disorder within an SL causes delocalization of electron wave functions and a change of the surface band structure as compared to the ideal MnBi 2 Te 4 /(Bi 2 Te 3 ) n . These findings highlight the critical importance of inter- and intra-SL disorder towards achieving new QAH platforms as well as exploring novel axion physics in intrinsic topological magnets.