We propose and characterize a new Z2 class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk onedimensional (1D) Dirac Line Nodes (DLNs) and two-dimensional (2D) nearly-flat surface states, protected by inversion and time-reversal symmetries. We develop the Z2 invariants dictating the presence of DLNs based on parity eigenvalues at the parity-invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in Cu3N near the Fermi energy by doping non-magnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This paper includes a brief discussion of the effects of spin-orbit interactions and symmetry-breaking as well as comments on experimental implications.A recent development in condensed matter physics has been the discovery of semimetallic features in electronic band structures protected by the interplay of symmetry and topology. A tremendous amount of progress has been made in materials with strong spin-orbit interactions, such as the surface states of topological insulators [1,2] and topological crystalline insulators [3], as well as the gapless bulk states of Weyl and Dirac semimetals [4][5][6]. Related topological phenomena can occur in materials with vanishing (or weak) spin-orbit interactions [7]. Indeed, the prototypical topological semimetal is graphene [8], which exhibits Dirac points that are robust to the extent that the spin-orbit interaction in carbon is weak. In the absence of spin-orbit interactions, the Dirac points in graphene are topologically protected by the combination of inversion and time-reversal symmetries.In this paper we study a related phenomenon for three dimensional (3D) materials with weak spin-orbit interaction. We show that the combination of inversion and time-reversal symmetries protects Dirac line nodes (DLNs), for which the conduction band and valence band meet along a line in momentum space, and we predict realistic materials in which they should occur. DLNs have been discussed previously in the context of models that have an additional chiral symmetry, which can arise on a bipartite lattice with only nearest neighbor hopping. In this case, the DLN can be constrained to occur at zero energy. However, chiral symmetry is never expected to be an exact symmetry of a band structure. We will show that despite the absence of chiral symmetry, the line node is protected, though it is not constrained to sit at a constant energy. We will show, however, that in the vicinity of a band inversion transition, a DLN can occur in the form of a small circle, whose energy is approximately flat. The presence of such a Dirac circle has interesting consequences for the surface states, and we show that on the projected interior of the Dirac circle, the surface exhibits a nearly flat band, which must be half-filled when the surface is electrically neutral. Such surface states could be an inte...

The theoretical proposal of chiral fermions in topological semimetals has led to a significant effort towards their experimental realization. In particular, the Fermi surfaces of chiral semimetals carry quantized Chern numbers, making them an attractive platform for the observation of exotic transport and optical phenomena. While the simplest example of a chiral fermion in condensed matter is a conventional |C|=1 Weyl fermion, recent theoretical works have proposed a number of unconventional chiral fermions beyond the standard model which are protected by unique combinations of topology and crystalline symmetries. However, materials candidates for experimentally probing the transport and response signatures of these unconventional fermions have thus far remained elusive. In this Letter, we propose the RhSi family in space group No. 198 as the ideal platform for the experimental examination of unconventional chiral fermions. We find that RhSi is a filling-enforced semimetal that features near its Fermi surface a chiral double sixfold-degenerate spin-1 Weyl node at R and a previously uncharacterized fourfold-degenerate chiral fermion at Γ. Each unconventional fermion displays Chern number ±4 at the Fermi level. We also show that RhSi displays the largest possible momentum separation of compensative chiral fermions, the largest proposed topologically nontrivial energy window, and the longest possible Fermi arcs on its surface. We conclude by proposing signatures of an exotic bulk photogalvanic response in RhSi.

In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials. In particular, monolayers of centrosymmetric β-phase TMDs have been identified as 2D topological insulators, and bulk crystals of noncentrosymmetric γ-phase MoTe2 and WTe2 have been identified as type-II Weyl semimetals. However, ARPES and STM probes of these semimetals have revealed huge, "arc-like" surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this work, we calculate the bulk and surface electronic structure of β-MoTe2, finding that is in fact a Z4-nontrivial higherorder topological insulator (HOTI) driven by double band inversion, and that it exhibits the same surface features as γ-MoTe2 and γ-WTe2. We find that these surface states are not topologically trivial, as previously characterized by the research that differentiated them from the Weyl Fermi arcs, but rather are the characteristic split and gapped fourfold Dirac surface states of a HOTI. In β-MoTe2, this indicates that it would exhibit helical pairs of hinge states if it were bulk-insulating, and in γ-MoTe2 and γ-WTe2, these surface states represent vestiges of HOTI phases without inversion symmetry that are nearby in parameter space and which may be accessible by symmetry-preserving strain or lattice distortion that annihilates the Weyl points. We also show that when the effects of SOC are neglected, β-MoTe2 is a nodal-line semimetal with Z2-nontrivial monopole nodal lines. This finding establishes that monopole nodal lines driven by double band inversion are the weak-SOC limit of HOTIs.Within the past decade, the number of topological phases characterized and identified in real materials has grown immensely. Since the recognition that graphene 1-3 and HgTe gap into Z 2 topological insulators (TI) 4,5 under the introduction of spin-orbit coupling (SOC) 6 , an intrinsic link has emerged between gapped and gapless toplogical phases. As the number of known topological semimetals has increased 7-25 , the number of known topological (crystalline) insulators realized by gapping them with SOC, strain, and interactions has kept pace 26-32 . In one particularly simple example, a topological semimetal with a ring of linearly-dispersing degeneracies, known as a "nodal-line" semimetal (NLSM), can be realized in a weak-SOC crystal with only inversion (I) and timereversal (T ) symmetries [33][34][35] . These nodal lines may be created and annihilated at single, time-reversal-invariant (TRIM) points in the Brillouin zone (BZ) by the inversion of bands with opposite I eigenvalues 33 , such that the total number of nodal lines is given by the same Fu-Kane parity (I) criterion 36,37 that indicates 3D TI phases in strong-SOC crystals. This simple condition has led to the rapid identification of candidate NLSMs, including Ca 3 P 2 38 , Cu 3 (Pd,Zn)N 33,34 , and 3D graphene networks 39 , all of which exhibit characteristic nearly-flatband "drumhead" surface states. ...

We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135, showing that 135 can host an intrinsic double Dirac semimetal -one with no additional degeneracies at the Fermi energy. We consider symmetry-lowering perturbations and show that uniaxial compressive strain in different directions leads to topologically distinct insulating phases. In addition, the double Dirac semimetal can accommodate topological line defects that bind helical modes. Potential materials realizations are discussed.