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The analogues of elementary particles have been extensively searched for in condensed matter systems because of both scientific interests and technological applications. Recently massless Dirac fermions were found to emerge as low energy excitations in the materials named Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry $mathcal{T}$ and inversion symmetry $mathcal{P}$. Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where $mathcal{T}$ and $mathcal{P}$ are broken but their combination $mathcal{PT}$ is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points with symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by emph{ab initio} calculations. Our results give a new route towards the realization of Dirac materials, and provide a possible platform to study the interplay of Dirac fermion physics and magnetism.
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We proposed that BaHgSn is a Dirac semimetal (DSM) which can host hourglass-like surface states (HSSs) as protected by nonsymmorphic glide symmetry. Compared to KHgSb, an isostructural topological crystalline insulator with the same HSSs, BaHgSn has an additional band inversion at $Gamma$ point. This band inversion is induced by the stronger interlayer coupling among Hg-Sn honeycomb layers than that among Hg-Sb-layers in KHgSb, which leads to bulk Dirac nodes in BaHgSn along the layer stacking direction $Gamma$-$A$. In addition, the mirror Chern number $C_{i}$ protected by the mirror plane $overline{M}_{z}$ ($k_z$=0) changes from 2 in KHgSb to 3 in BaHgSn. Therefore, when a compressive uniaxial strain is applied along the $y$ axis to break the rotation symmetry protecting the DSM state, BaHgSn becomes a strong topological insulator with $Z_{2}$ indices of $(1;000)$ and the topological surface Dirac cone co-exists with HSSs on the (010) surface. The Wilson-loop spectra have been calculated to verify these topological features. The calculated surface states, the Fermi surfaces and their quasiparticle interference patterns are ready to be compared with experimental measurements.
Materials with triply-degenerate nodal points in their low-energy electronic spectrum produce crystalline-symmetry-enforced three-fold fermions, which conceptually lie between the two-fold Weyl and four-fold Dirac fermions. Here we show how a silver-based Dirac semimetal BaAgAs realizes three-fold fermions through our first-principles calculations combined with a low-energy effective $mathbf{k.p}$ model Hamiltonian analysis. BaAgAs is shown to harbor triply-degenerate nodal points, which lie on its $C_{3}$ rotation axis, and are protected by the $C_{6v}$($C_2otimes C_{3v}$) point-group symmetry in the absence of spin-orbit coupling (SOC) effects. When the SOC is turned on, BaAgAs transitions into a nearly-ideal Dirac semimetal state with a pair of Dirac nodes lying on the $C_{3}$ rotation axis. We show that breaking inversion symmetry in the BaAgAs$_{1-x}$P$_x$ alloy yields a clean and tunable three-fold fermion semimetal. Systematic relaxation of other symmetries in BaAgAs generates a series of other topological phases. BaAgAs materials thus provide an ideal platform for exploring tunable topological properties associated with a variety of different fermionic excitations.
We use determinant quantum Monte Carlo (DQMC) simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $pi$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-ranged AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)d Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in birefringent Dirac fermion system. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions, and may be observed using ultracold atoms in an optical lattice.
Band-crossings occurring on a mirror plane are compelled to form a nodal loop in the momentum space without spin-orbit coupling (SOC). In the presence of other equivalent mirror planes, multiple such nodal loops can combine to form interesting nodal-link structures. Here, based on first-principles calculations and an effective $mathbf{k.p}$ model analysis, we show that CaAuAs hosts a unique starfruit-like nodal-link structure in the bulk electronic dispersion in the absence of SOC. This nodal-link is comprised of three nodal loops, which cross each other at the time-reversal-invariant momentum point $A$. When the SOC is turned on, the nodal loops are gapped out, resulting in a stable Dirac semimetal state with a pair of Dirac points along the $mathrm{Gamma-A}$ direction in the Brillouin zone. The Dirac points are protected by the combination of time reversal, inversion, and $C_3$ rotation symmetries. We show how a systematic elimination of the symmetry constraints yields a Weyl semimetal and eventually a topological insulator state.
Graphene nanoribbons are widely regarded as promising building blocks for next-generation carbon-based devices. A critical issue to their prospective applications is whether and to what degree their electronic structure can be externally controlled. Here, we combine simple model Hamiltonians with extensive first-principles calculations to investigate the response of armchair graphene nanoribbons to transverse electric fields. Such fields can be achieved either upon laterally gating the nanoribbon or incorporating ambipolar chemical co-dopants along the edges. We reveal that the field induces a semiconductor-to-semimetal transition, with the semimetallic phase featuring zero-energy Dirac fermions that propagate along the armchair edges. The transition occurs at critical fields that scale inversely with the width of the nanoribbons. These findings are universal to group-IV honeycomb lattices, including silicene and germanene nanoribbons, irrespective of the type of edge termination. Overall, our results create new opportunities to electrically engineer Dirac fermions in otherwise semiconducting graphene-like nanoribbons.
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