Symmetry-protected ideal Weyl semimetal in HgTe-class materials

Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of in-plane compressive strain, could be materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to realize ideal Weyl semimetals. Such ideal Weyl semimetals could further provide a unique platform to study emergent phenomena such as the interplay between ideal Weyl fermions and superconductivity in the half-Heusler compound LaPtBi.Comment: Accepted by Nature Communication

Oscillatory crossover from two dimensional to three dimensional topological insulators

We investigate the crossover regime from three dimensional topological insulators $Bi_2Te_3$ and $Bi_2Se_3$ to two dimensional topological insulators with quantum spin Hall effect when the layer thickness is reduced. Using both analytical models and first-principles calculations, we find that the crossover occurs in an oscillatory fashion as a function of the layer thickness, alternating between topologically trivial and non-trivial two dimensional behavior.Comment: 5 pages, 3 figures; 3 added references, an added not

Strain-induced quantum topological phase transitions in Na3Bi

Strain can be used as an effective tool to tune the crystal structure of materials and hence to modify their electronic structures, including topological properties. Here, taking Na3Bi as a paradigmatic example, we demonstrated with first-principles calculations and k$\cdot$p models that the topological phase transitions can be induced by various types of strains. For instance, the Dirac semimetal phase of ambient Na3Bi can be tuned into a topological insulator (TI) phase by uniaxial strain along the h100i axis. Hydrostatic pressure can let the ambient structure transfer into a new thermodynamically stable phase with Fm-3m symmetry, coming with a perfect parabolic semimetal having a single contact point between the conduction and valence bands, exactly at $\Gamma$ point on the Fermi level like $\alpha$-Sn. Furthermore, uniaxial strain in the direction can tune the new parabolic semimetal phase into a Dirac semimetal, while shear strains in both the and directions can take the new parabolic semimetal phase into a TI. k$\cdot$p models are constructed to gain more insights into these quantum topological phase transitions. At last, we calculated surface states of Fm-3m Na3Bi without and with strains to verify these topological transitions.Comment: 10 pages, 9 figures. (Email: [email protected]

Model Hamiltonian for Topological Insulators

In this paper we give the full microscopic derivation of the model Hamiltonian for the three dimensional topological insulators in the $Bi_2Se_3$ family of materials ($Bi_2Se_3$, $Bi_2Te_3$ and $Sb_2Te_3$). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang {\it et al} [\onlinecite{zhang2009}] based both on symmetry principles and the ${\bf k}\cdot{\bf p}$ perturbation theory. Two different types of $k^3$ terms, which break the in-plane full rotation symmetry down to three fold rotation symmetry, are taken into account. Effective Hamiltonian is derived for the topological surface states. Both the bulk and the surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For more quantitative fitting to the first principle calculations, we also present a new model Hamiltonian including eight energy bands.Comment: 18 pages, 9 figures, 5 table