Distinct multiple fermionic states in a single topological metal

Abstract

Among the quantum materials that have recently gained interest are the topological insulators, wherein symmetry-protected surface states cross in reciprocal space, and the Dirac nodal-line semimetals, where bulk bands touch along a line in k-space. However, the existence of multiple fermion phases in a single material has not been verified yet. Using angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations, we systematically study the metallic material Hf₂Te₂P and discover properties, which are unique in a single topological quantum material. We experimentally observe weak topological insulator surface states and our calculations suggest additional strong topological insulator surface states. Our first-principles calculations reveal a one-dimensional Dirac crossing-the surface Dirac-node arc-along a high-symmetry direction which is confirmed by our ARPES measurements. This novel state originates from the surface bands of a weak topological insulator and is therefore distinct from the well-known Fermi arcs in semimetals.

Fig. 1

Crystal structure and sample characterization of Hf₂Te₂P. a The rhombohedral tetradymite crystal structure of Hf₂Te₂P, depicted in the conventional (hexagonal) and primitive (rhombohedral) unit cells. The stacking of quintuple layers (QL) is depicted by the blue square. The inversion center is indicated with the red star. b Temperature dependence of the electrical resistivity measured on a single crystal of Hf₂Te₂P in a zero (brown circles) and 9 T (orange triangles) magnetic field applied perpendicular to the current flowing within the basal plane of the crystallographic unit cell. The inset shows a picture of one of the single crystal grown for the present research. c Magnetic field dependencies of the transverse magnetoresistance measured for a range of different temperatures on a single crystal of Hf₂Te₂P with current flowing within the basal plane of the crystallographic unit cell. d 3D bulk Brillouin zone and its projection on the hexagonal surface Brillouin zone of the Hf₂Te₂P-crystal. High symmetry points are marked in the plot. e Core level spectroscopic measurement of Hf₂Te₂P. Sharp peaks of Te 4d and Hf 4f are observed which indicate good sample quality

Fig. 2

Fermi surface and observation of multiple fermionic states. a Fermi surface maps at various photon energies. Photon energies are marked on the plots. The white dashed lines marking No. 1 and 2 denote the direction of the dispersion maps. b–d Dispersion maps measured along various high-symmetry directions for different photon energies. These data were collected at the SIS-HRPES end station at the SLS, PSI, at a temperature of 18 K

Fig. 3

Experimental observation of the Dirac node arc. a Constant energy contour plots at various binding energies. b Constant energy contour plots closer to the Dirac-node arc. Binding energies are given in the plots. c Dispersion map along the K–M–K direction along the cut directions indicated in the 1000-meV constant energy contour panel of b. All data were collected at the SIS-HRPES end station at the SLS, PSI at a photon energy of 100 eV with a temperature of 18 K

Fig. 4

Calculated multiple fermionic states. a The bulk electronic structure, calculated with spin-orbit coupling, along high-symmetry directions. Blue and red circles indicate the Hf-d and Te-p character of the band states, respectively. Band inversions are highlighted by the green rectangles. b Calculated surface states for the (111) surface with Hf and Te character indicated. The purple rectangle highlights the strong TI surface state stemming from bulk bands B and C whereas the green rectangle highlights the weak TI surface states due to bulk bands A and B. An additional gapless surface state is highlighted with a black box. c, d Calculated Fermi surface and constant energy contour 900 meV below the Fermi level, respectively. At 900 meV below the Fermi level, we observe a symmetry protected surface Dirac-node arc, denoted by the green arrow

Fig. 5

Schematic view of distinct fermionic states. a, b Sketch of electronic surface state dispersion of the n-type topological insulator and p-type topological insulator, respectively. c Dispersion of bulk states in a nodal-line semimetal of ZrSiS-type. d Sketch of electronic dispersions of the 221-material Hf₂Te₂P. This material consists of both n- and p-type topological surface states as well as a surface Dirac-node arc phase. e View of the calculated surface electronic structure of this material that confirms its weak topological nature, also showing the Dirac-node arc starting at M. The Dirac-node arc is purely surface-derived, in contrast to the nodal-line semimetal phase shown in c, which is bulk-derived