Topological Superconductors from a Materials Perspective

Abstract

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Figure 1

Classifications of gapped topological phases of matter and the TSC topological classes. (a) The TSC family in a zoo of topological materials families. At a mean-field level, TSCs can be considered as one type of noninteracting SPT phase. (b) Four subclasses of BdG family topological materials with inherent particle-hole symmetry. The most common TSC is the class D, and a related DIII is a TRS-preserved version which can be considered as a direct product of two copies class-D TSCs with opposite chirality. Subfigure b adapted from ref (19). TRS: Time-reversal symmetry. PHS: Particle-hole symmetry. TI: Topological insulator. FQHE: Fractional quantum Hall effect. SLS: Sublattice symmetry.

Figure 2

Schematic illustration of TSCs and Majorana-based topological quantum computing. (a) 1D topological superconductor (Kitaev chain), where each conventional Fermion is a combination of two Majorana Fermions. When “intra-site” pairing between the two Majorana Fermions is stronger than the “inter-site” pairing (upper), a topologically trivial SC is obtained. When intersite interaction is stronger (lower), a 1D TSC is obtained, with two unpaired Majorana Fermions (red spheres) with zero energy at two ends. (b) 2D p + ip superconductor. (top) Just like the 1D TSC can have 0D boundary modes at two ends, the 2D TSC has 1D chiral Majorana edge modes. (middle) If we pierce one hole to create a region without superconductivity, half-integer excitation spectra are created. (bottom) If we add one magnetic flux quantum Φ to the hole to create a superconducting vortex, the energy spectra become integers and a Majorana zero mode is generated. (c) Scheme for topological quantum computation. With 2N superconducting vortices, the ground states will have a 2^N degeneracy. The unitary transform of U, which can be used as a quantum gate, can be realized by exchanging different pairs of Majorana zero modes within the ground states.

Figure 3

An example of the superconductor bandstructure. The gray lines indicate the energy band ϵ(k), −ϵ(−k) while the red and blue lines are the bandstructure after tuning on the interaction potential. Note that since Δ is momentum-dependent, the perturbation of band crossing can result in either the nodal or gap structure.

Figure 4

Scanning tunneling spectroscopy for TSC studies. (a) By varying bias voltage, the differential tunneling current becomes a measure of local density states for electrons. (b) A zero-bias conductance map under 2.0 T is shown on a sample surface FeSe_0.45Te_0.55. dI/dV spectrum measured at the center of the vortex core. (c) A line-cut intensity plot from the vortex shows a stable MZM across the vortex core. (d) An overlapping plot of dI/dV spectra under different tunnel coupling values. Figures reproduced from ref (109). (e) Zero bias mapping of a vortex at 0.1 T with the spin nonpolarized tip on the topological superconductor Bi₂Te₃/NbSe₂. (f) dI/dV away from the center of a vortex measured with a fully spin-polarized tip, where the tunneling is found to be independent of the spin polarization. Figures reproduced from (119). (g) STM image of a monolayer-thick CrBr₃ island grown on NbSe₂. (h) Experimental dI/dV spectroscopy on the NbSe₂ substrate (blue), the middle of the CrBr₃ island (red), and the edge of the CrBr₃ island (green). Figures reproduced from (129).

Figure 5

ARPES studies on TSCs. (a) Schematic diagram of ultrathin Bi₂Se₃ films epitaxially grown on the (001) surface of s-wave superconductor 2H-NbSe₂ (top). High-resolution ARPES dispersion map of Bi₂Se₃ film on NbSe₂ where the white circle and cross schematically show the measured direction of the spin texture on the top surface of the Bi₂Se₃ film (bottom). Figure reproduced from ref (142). (b) Band dispersion of FeTe_0.5Se_0.5 (top). The momentum distribution curvature plot shows the Dirac-cone type band. The Dirac-cone type band (blue lines) is the topological surface band, and the parabolic band (white curve) is the bulk valence band. In the low-temperature (2.4 K) data, the spectral features are narrower. The extracted bands overlap well with the curvature intensity plot, confirming the existence of the parabolic bulk band and the Dirac-cone-type surface band (bottom). Figure reproduced from ref (104). (c) Photoemission spectra intensity plots of the band dispersions in the superconducting (top left) and normal (top right) states show clear superconducting gaps from both the TSS (red dashed lines) and bulk state (BS) (blue dashed lines) in 2M-WS₂. Temperature dependence of the band dispersions of the TSS and BS shows the clear superconducting gap below T_c (bottom). Figure reproduced from ref (75).

Figure 6

Signature of TSCs from μSR. (a) The symmetric diagram of positron emission and the muon spin direction. (b) Time evolution of the spin polarization of muons above and below superconducting transition temperature under zero-field (ZF) conditions indicates the TRS breaking for Sr₂RuO₄. (c) ZF muon relaxation rate for the initial muon spin polarization for Sr₂RuO₄. Figures reproduced from ref (176). Time evolution of the muon spin polarization in ZF conditions suggests broken TRS for (d) SrPtAs (Figure reproduced from ref (61)) and (e) 4Hb-TaS₂ (Figure reproduced from ref (32)).