Fortune teller fermions in two-dimensional materials

Abstract

Dirac-like electronic states are the main engines powering the tremendous advances in research of graphene, topological insulators and other materials with these states. Zero effective mass, high carrier mobility and numerous applications are some consequences of linear dispersion that distinguishes Dirac states. Here we report a new class of linear electronic bands in two-dimensional materials with zero effective mass and sharp band edges never seen in solid state matter before, and predict stable materials with such electronic structure utilizing symmetry group analysis and ab initio approach. We make a full classification of completely linear bands in two-dimensional materials and find that only two classes exist: Dirac fermions on one hand and pyramidal-like and cootie catcher-like states on the other hand. The new class supports zero effective mass and hence high carrier mobility similar to that of graphene, anisotropic electronic properties like that of phosphorene, and robustness of states with respect to electronic correlations.

Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials

“…Γ 2DP V denotes 2D polar-vector representation that acts in 2D reciprocal space, Γ 1 is the unit representation, while [Γ ⊗n 2DP V ] is the symmetrised n-th power of Γ 2DP V . It turned out that four-component Hamiltonians, that do not correspond to fortune teller (FT) dispersion [38,39], do not support MNLs. Since gray layer single and double groups have multidimensional little group correps of dimensions two and four, our method exhausts all possibilities.…”

“…Finally, guided by the result described in the previous paragraph, we have included groups that host FT states, described in [38] and [39] for non-SOC and SOC cases, respectively, and also experimentally observed [40]. Among conclusions of previous paragraph is that FT states cannot be the only features at the Fermi level.…”

Two-dimensional topological semimetals*

“…Ref. [62] listed three layer groups that host such points, and a hypothetical phosphorous 2D structure was proposed, which hosts the point near the Fermi level.…”

Fully linear band crossings at high symmetry points in layers: classification and role of spin-orbit coupling and time reversal

“…For completeness, a brief overview of all types of dispersions (of linearity rank 2) are given, despite some of them have been already studied [11,19,20,24,25]. For each model (row of the Tables I and II) the Hamiltonian matrix is formed according to ( 5) or ( 6) with non-vanishing v p i and v p ij ; it is expressed in terms of independent coefficients c 1 , .…”

“…The raising interest in exploring bands topology, including its symmetry based aspects, points out the necessity to systematize numerous particular studies, and fill in existing gaps. In particular, layer groups have been intensively used to predict Dirac and beyond-Dirac topological semimetals [11,14,[18][19][20][21][22][23][24][25][26], but still there is no complete overview of such symmetry-enforced band structures of layered materials. This thorough and systematic presentation will facilitate both numerical or experimental search for the materials with preferred symmetry and desirable band topology.…”