Type-III Dirac fermions in Hf x Zr 1-x Te 2 topological semimetal candidate

Topological semimetals host interesting new types of low-energy quasiparticles such as type-I and type-II Dirac and Weyl fermions. Type-III topological semimetals can emerge exactly at the border between type-I and II, characterized by a line-like Fermi surface and a flat energy dispersion near the topological band crossing. Here, we theoretically predict that 1T-HfTe 2 and 1T-ZrTe 2 transition metal dichalcogenides are type-I and type-II DSMs, respectively. By alloying the two materials, a new Hf x Zr 1-x Te 2 alloy with type-III Dirac cone emerges at x=0.2, in combination with 1% in-plane compressive strain. By imaging the electronic energy bands with in situ angle-resolved photoemission spectroscopy of this random alloy with the desired composition, grown by molecular beam epitaxy on InAs(111) substrates, we provide experimental evidence that the tοp of type-III Dirac cone lies at -or very close to- the Fermi level.

motivated by the spectacular predictions, 2,3 that type-III DSMs (i.e. black phosphorous, 11 Zn2In2S5 12 ) could be the solid state (or fermionic) analogue of the black hole event horizon potentially generating "Hawking radiation" at relatively high "Hawking temperature" 2 showing promise for new exotic physics and applications. Although a type-III Dirac crossing was only a theoretical possibility up to now, experimental evidence has been recently obtained in strained epitaxial SnTe, 13 between its two uppermost valence bands, 1.83 eV below the Fermi level using synchrotron ARPES and also in artificial photonic orbital graphene lattices. 14 Prototypical topological Dirac semimetals are 3D crystal structures and are typically grown as bulk crystals, 15,16 usually suffering from heteroepitaxial defects which yield discontinuous films with poor crystalline quality. Discovering and engineering topological semimetals from the family of two-dimensional transition metal dichalcogenides (TMDs) could open the way for exploitation of their topological properties by fabricating thin epitaxial films and devices on suitable substrates via van der Waals epitaxy. Previous report from our team 17,18 provide the first experimental evidence by angle-resolved photoemission spectroscopy (ARPES) that few layer 1Τ-HfTe2 17 and 1T-ZrTe2 18 epitaxially grown by molecular beam epitaxy (MBE) are 3D DSMs. More specifically, we observed that linearly dispersing bands along ΓK and ΓM directions in the plane of the film cross at the Fermi level indicating the existence of Dirac Fermions even down to the ultimate 2D limit of 1 ML with the DP located at -or very close to-Fermi level, which is notably different than theory which predicts the DP well above it.
In order to reveal the topological nature of the Dirac cones in these materials, we present ab initio calculations of electronic structure and perform symmetry analysis. The first-principles calculations were performed using the Vienna Ab-initio Simulation Package 34,35 (VASP). The generalized-gradient approximation with Perdew-Burke-Ernzerhof 36 (PBE) parameterization was used as exchange-correlation functional. Our study of the electronic band structure is based on the experimental lattice constants of Refs. 17 and 18, measured by synchrotron x-ray diffraction, instead of the equilibrium ones from DFT calculations. The kinetic energy cutoff was set at 500 eV and the reciprocal space was sampled using the Monkhorst-Pack scheme 37 employing a 11 × 11 × 11 k-point mesh. Spin-orbit coupling (SOC) was included for the band structure calculations. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0038799
We used Hf d orbitals, Zr d orbitals, and Te p orbitals to construct Wannier functions using the which touch at the DP, indicating that ZrTe2 is type-II DSM.
It should be mentioned, that unlike Weyl semimetals, Dirac semimetals do not possess Berry phase or Berry curvature since the three-dimensional Dirac nodes are not chiral, since they are the sum This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.   Fig. 6(b) shows a 500 × 500 nm 2 area scan of the sample. It can be inferred that Hf0.2Zr0.8Te2 is grown in the form of two-dimensional islands, with an average surface roughness of ~3.5 Å, which is consistent with the InAs atomic step previously observed in epitaxial ZrTe2 18 and MoTe2 54 .
The band structure of 17 layers Hf0.2Zr0.8Te2 is imaged along the ΓΜ direction of the BZ [Fig. 7].
The valence band exhibits a Dirac-like cone dispersion, with the cone tip touching the Fermi level which is similar to what has been observed in epitaxial HfTe2 17 and ZrTe2. 18 On the other hand these observations are notably different than the theoretical predictions that the DP is located around 0.63 eV above the EF. This is also in contrast to what is observed in the band structure of HfTe2 and ZrTe2 bulk single crystals imaged by synchrotron ARPES. [19][20][21][22] This difference may be

FIG. 2.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0038799