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Surface state band inversions generate Weyl-like states in NbGeSb

There has been an intense worldwide search over the last decade to realise symmetry- and topologically-protected band crossings in materials, mediated by driving an energetic inversion of their bulk states. In the classic example of a Ztopological insulator, such a bulk band inversion stabilises gapless spin-polarised Dirac surface states, whose presence is a signature of the non-trivial topology in the bulk. At the intersection between topologically trivial and non-trivial bulk phases, or when protected crossing points are formed from a bulk band inversion in the presence of certain crystalline symmetries, a gappless bulk Dirac cone can be realised, somewhat akin to a three-dimensional analogue of graphene.
If time-reversal or inversion symmetry is broken, this Dirac cone can split into non-degenerate pairs of spin-polarised Weyl states; a massless chiral fermion that is a solid state analogue of Weyl fermions in the standard model of particle physics. There has been a significant effort placed in searching for such solid state realisations of this, and similar, symmetry-protected phases in materials. To this end, systems are sought where orbital energy levels are inverted as compared to the atomic insulator. Combined with specific crystalline symmetries, the resulting bulk band inversions then leads to the formation of the bulk Dirac and Weyl states. Realising this in practice, however, can be a major challenge, and new strategies are required to advance the materials design of topological and symmetry-protected states in materials.
In this work, rather than searching for band inversions of the bulk states, a new approach was applied to create band inversions between different manifolds of surface states. The compound studied was NbGeSb (Fig. 1(a)). This is an example of a system where particular, so-called nonsymmorphic, crystalline symmetries in fact already protect Dirac-like crossings of electronic states in the bulk. At the surface, however, a breaking of these relevant symmetries means that new surface states “break away” from the bulk manifolds. These have previously been investigated in the sister compound ZrSiS [Topp et al., Phys. Rev. X 7, 041073 (2017)], where two such sets of surface states have been observed. 
Angle-resolved photoemission measurements (ARPES) performed at the CASSIOPEE beamline of the SOLEIL synchrotron (Fig. 1(b)) indicated how analogues of these two sets of surface states are driven to intersect each other in NbGeSb. This is due to the aliovalent substitution of Nb for Zr and Sb for S. These states also each exhibit a pronounced splitting, leading to an intriguing crossing structure along the Brillouin zone boundary. To investigate this further, spin- and angle-resolved photoemission spectroscopy (SARPES) measurements were carried out at the Advanced Photoelectric Effect (APE) experiments beamline of Elettra, as well as at BL-9B of the HISOR synchrotron. 
As shown in Fig. 1(c), the splitting of the surface states is in fact a splitting of oppositely spin-polarised states. This arises from a strong spin-orbit coupling of Nb and Sb which, together with a loss of inversion symmetry at the surface, leads to spin splitting via a Rasbha-type effect. This leaves a rich crossing structure in the low-energy electronic structure, with pairs of like spin-polarised states crossing to form analogues of bulk Weyl cones in the surface electronic structure. Additional calculations (Fig. 1(d)) indicate how the orbital angular momentum exhibits a chiral texture around these Weyl-like cones. In fact, the orbital and spin texture is central to stabilising a rich hierarchy of protected and gapped crossings in the surface electronic structure here.
The study thus points to a new route to generating analogues of bulk symmetry-protected electronic states in solids by engineering band inversions of their surface states. Excitingly, the surface electronic structure should be more susceptible to dynamic tuning than that of the bulk, for example via electrostatic gating or via controlled surface deposition approaches. The understanding of surface band inversions found here may thus generate new routes to stabilize exotic and much-sought features in the electronic structure of materials, including possibilities to turn these on and off at will.
 

Figure 1 (a) Crystal structure and Brillouin zone of NbGeSb. (b) Measured ARPES dispersions along high-symmetry lines of the surface Brillouin zone. Two surface state pairs are indicated along the XM line. (c) Spin-resolved momentum- (up) and energy-distribution curves (right) along the indicated lines in the XM dispersion show SS and SS' to be spin-split surface states. (d) Model dispersion from tight-binding calculations of the protected Weyl-like cones that form at the indicated crossings between same-spin branches of the surface states. The inset shows the orbital-angular momentum calculated along the indicated loop above the crossing point.

 

 

This research was conducted by the following research team:

I. Marković1, C. A. Hooley1, O. J. Clark1, F. Mazzola1, M. D. Watson1, J. M. Riley1, K. Volckaert1, K. Underwood1, P. D. C. King1, M. S. Dyer2, P. A. E. Murgatroyd2, K. J. Murphy2, J. Alaria2, P. Le Fèvre3, F. Bertran3, J. Fujii4, I. Vobornik4, S. Wu5, T. Okuda6
 

School of Physics and Astronomy, University of St Andrews, St Andrews, United Kingdom
Departments of Physics and Chemistry, University of Liverpool, Liverpool United Kingdom
Synchrotron SOLEIL, CNRS-CEA, France
Istituto Officina dei Materiali (IOM)-CNR, Laboratorio TASC, Trieste, Italy
Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan
Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima, Japan


Contact persons:

Ivana Vobornik, email: ivana.vobornik@elettra.eu
 

Reference

I. Marković, C.A. Hooley, O. J. Clark, F. Mazzola, M. D. Watson, J.M. Riley, K. Volckaert, K. Underwood, M.S. Dyer, P.A.E. Murgatroyd, K.J. Murphy, P. Le Fèvre, F. Bertran, J. Fujii, I. Vobornik, S. Wu, T. Okuda, J. Alaria, and P.D.C. King, "Weyl-like points from band inversions of spin-polarised surface states in NbGeSb", Nature Communications 10, 5485 (2019), DOI: 10.1038/s41467-019-13464-z.

 
Last Updated on Tuesday, 28 January 2020 11:22