Observation of unusual topological surface states in half-Heusler compounds LnPtBi (Ln=Lu, Y)

Abstract

Topological quantum materials represent a new class of matter with both exotic physical phenomena and novel application potentials. Many Heusler compounds, which exhibit rich emergent properties such as unusual magnetism, superconductivity and heavy fermion behaviour, have been predicted to host non-trivial topological electronic structures. The coexistence of topological order and other unusual properties makes Heusler materials ideal platform to search for new topological quantum phases (such as quantum anomalous Hall insulator and topological superconductor). By carrying out angle-resolved photoemission spectroscopy and ab initio calculations on rare-earth half-Heusler compounds LnPtBi (Ln=Lu, Y), we directly observe the unusual topological surface states on these materials, establishing them as first members with non-trivial topological electronic structure in this class of materials. Moreover, as LnPtBi compounds are non-centrosymmetric superconductors, our discovery further highlights them as promising candidates of topological superconductors.

Figure 1. Crystal structure of LnPtBi and cleavage surface measured by ARPES.

(a) Crystal structure of half-Heusler alloy LnPtBi crystal shows a composite of zinc-blend and rocksalt lattices. (b) Unit cell of LnPtBi at the (111) cleavage surface shows the stacking of triangular Ln, Pt and Bi layers. a₀ is the in-plane lattice constant of the (111) surface unit cell. (c) Bulk BZ of LnPtBi with high symmetry points labelled. Arrows and shaded surfaces indicate the projection to [100], [010] and [001] directions. (d) Surface BZ in the [111] direction with the high symmetry points labelled. (e) Core level photoemission spectrum on LuPtBi (111) and (001) surfaces clearly shows the characteristic Lu 4f and Bi 5d doublets. These spectra are measured with 75 and 215 eV photons, respectively. (f) Broad FS map of LuPtBi covering five BZs, confirming the shape and size of the surface BZ (overlaid yellow hexagons) on the (111) cleave plane. The uneven intensity of the FS at different BZs results from the matrix element effect.

Figure 2. General electronic structure of LuPtBi (111) surface.

(a) FS maps of Bi-terminated LuPtBi (111) surface. Blue lines denote the surface BZ with high symmetry points labelled. The data has been symmetrized according to the crystal symmetry. (b,c) Zoom-in plot of FS map around the point (b) and around the and points (c). (d,e) Plot of 3D electronic structure around the point (d) and around the and points (e). All data were taken with 65 eV photons.

Figure 3. Observation of the metallic surface state and TSS on LuPtBi (111) surface.

(a,b) Calculated band structures of Bi-terminated LuPtBi (111) surface. (a) Result from a slab model calculation, in which the size of filled circles represent the projection to the Bi-terminated surface. Both topologically non-trivial surface state and metallic surface states are captured. (b) Results from a semi-infinite surface that is terminated by Bi. Only topologically non-trivial surface state is revealed by the calculation. (c,d) Photoemission intensity plot (c) and its second-derivative plot (d) along the high symmetry –– directions. (e,f) Photoemission intensity plot (e) and its second-derivative plot (f) along the high symmetry – directions. SS, topologically trivial metallic surface state due to the dangling bonds on sample surface. TSS, topologically non-trivial surface state. All data were taken with 65 eV photons.

Figure 4. Photon energy dependence and Dirac-fermion behaviour of the TSS.

(a) Photoemission intensity plots along the high symmetry –– direction with photon energies from 50 to 75 eV. Two red dotted lines marked the energy where individual MDC is taken to generate the plots in b,c. (b,c) Intensity plot of the MDCs taken at E_F (b) and E_F—0.65 eV (c) at different photon energies. The MDC peak positions of all the observed bands are labelled (SS1–SS3 and TSS). (d) Zoom-in intensity plots of the TSS along the – direction and the – direction. Dirac points of the TSS are labelled. Data are taken with 60 eV photons. (e–g) Measured electronic structure of (111) surface of YPtBi. (e) The FS mapping of (111) surface of YPtBi with the hexagonal BZ (overlaid blue lines). The data has been symmetrized according to the crystal symmetry. (f,g) Photoemission intensity (f) and its second-derivative plot (g) along the high symmetry –– direction. Data in e–g are taken with 70 eV photons at T=20 K. SS, topologically trivial metallic surface state due to the dangling bonds on sample surface. TSS, topologically non-trivial surface state.

Figure 5. Circular dichroism of the metallic and TSS on LuPtBi (111) surface.

(a) Photoemission intensity around along – directions with the right and left circularly polarized (CR and CL) photons, showing clear asymmetry in the difference spectrum CR–CL. Dotted lines on the CR–CL spectrum represent the positions of the MDCs being analysed. Coloured marks label the position of the peaks fitted from the MDC curves in c. Red/Blue solid/dotted curves are the same as in b. (b) Red (Blue) solid curves give eye guides to the branch of bands which is enhanced with the CR (CL) photons, while blue (red) dotted curves give eye guides to the branch of bands which is suppressed with the CR (CL) photons. In the difference CR–CL spectrum both branches of SS3 and TSS could be seen. (c) MDCs analysis at the marked energy positions in a. Each fitted peak curve is drawn in colour, with the peak positions labelled with marks of same colour.