Dirac SemimetalsEdit
Dirac semimetals are a phase of matter in which the electronic structure hosts isolated, fourfold-degenerate band crossings in three-dimensional momentum space. Near these crossing points, the energy varies linearly with momentum in all directions, and the low-energy excitations behave like massless Dirac fermions described by the three-dimensional Dirac equation. These materials occupy an important position in the landscape of quantum materials, sitting between conventional semimetals and topological phases. When both time-reversal symmetry Time-reversal symmetry and inversion symmetry Inversion symmetry are preserved, Dirac points are protected by crystal symmetries and the crossing is robust. If one of these symmetries is broken, a Dirac point can split into a pair of Weyl nodes with definite chirality, giving rise to a Weyl semimetal Weyl semimetal.
Dirac semimetals are not merely theoretical curiosities; they have been realized in real compounds and studied through a combination of spectroscopic and transport techniques. Canonical examples include materials such as Cd3As2 and Na3Bi, where experiments have observed linear dispersions and low-energy excitations consistent with three-dimensional Dirac fermions. The field continues to explore a broader class of candidates and to understand how crystal symmetry, spin-orbit coupling, and crystalline anisotropy shape the Dirac spectrum. The Dirac semimetal state is connected to broader concepts in topology and condensed matter, including the relation to graphene-like physics in higher dimensions and the role of topology in protecting gapless excitations Graphene.
Crystal structure and electronic structure
Dirac points occur at isolated momenta in the Brillouin zone where conduction and valence bands touch with a linear dispersion. In three dimensions, a fourfold degeneracy typically arises from the combination of twofold spin degeneracy and twofold orbital or sublattice degeneracy. The symmetry protection that preserves this crossing usually involves a combination of time-reversal symmetry Time-reversal symmetry, inversion symmetry Inversion symmetry, and certain crystal symmetries such as rotational or mirror symmetries in the lattice. When these symmetries are intact, the crossing remains gapless; breaking them can shift the crossing, open a gap, or split the Dirac point into Weyl nodes with chiral charge Berry phase.
From a band-structure perspective, Dirac semimetals exhibit linear dispersion in all directions around the Dirac point, yielding a low-energy Hamiltonian that resembles the Dirac equation in three spatial dimensions. This leads to an effective relativistic description of quasiparticles, with notable consequences for transport and optical responses. The material’s crystal structure dictates where in momentum space the Dirac points can reside and determine the anisotropy of the Dirac cones. For instance, materials like Cd3As2 crystallize in structures where the necessary symmetries are embedded in the lattice, enabling protected crossings along high-symmetry directions Crystal structure.
Realizations and materials
The experimental realization of Dirac semimetals has focused on a few well-characterized compounds, with ongoing efforts to identify new candidates. Two canonical members of this family are Cd3As2 and Na3Bi, both of which exhibit robust Dirac-like dispersions near the Fermi level and have been studied extensively by angle-resolved photoemission spectroscopy (ARPES), magnetotransport, and quantum oscillations. In these materials, the Dirac points occur along certain high-symmetry lines in the Brillouin zone and are protected by the crystal's symmetry operations as well as time-reversal and inversion symmetry Topological semimetal.
Other proposed or studied candidates include materials predicted to host Dirac points due to symmetry-enforced degeneracies or band inversions, sometimes relying on strong spin-orbit coupling to realize the desired band structure. The identification of Dirac semimetals often involves careful synthesis to obtain clean, high-mobility crystals and cross-validation with multiple experimental probes to distinguish true massless Dirac behavior from near-degenerate or nearly linear dispersions. The ongoing search is aided by theoretical classifications that catalog which space groups and symmetry combinations can stabilize Dirac points, as well as by first-principles calculations that guide experimental efforts First-principles calculation.
Experimental probes and signatures
Multiple experimental techniques have established the Dirac semimetal picture in candidate materials. Angle-resolved photoemission spectroscopy (ARPES) directly maps the electronic band structure and can reveal linear dispersions near the Dirac point as well as the location of Dirac nodes in momentum space ARPES. Quantum oscillations in magnetotransport measurements—such as Shubnikov–de Haas or de Haas–van Alphen effects—provide complementary information about the Fermi surface and the effective mass of carriers, consistent with massless or nearly massless Dirac fermions in three dimensions Quantum oscillations.
Other signatures include anomalous transport behavior under magnetic fields, high carrier mobility, and characteristic Landau level spectra that reflect the relativistic-like dispersion. Surface-sensitive probes can reveal whether surface states are present and how they relate to the bulk Dirac nodes; in some Dirac semimetal systems, surface states join the bulk in ways that reflect the underlying symmetry protections or potential symmetry breaking at the surface Surface states.
Theoretical perspectives and controversies
The Dirac semimetal framework rests on symmetry protections that stabilize three-dimensional Dirac points. Theoretically, these points can be understood as points of band crossing that resemble the relativistic Dirac equation at low energies. However, the precise interpretation and robustness of these crossings can be subtle in real materials. Debates in the literature often focus on questions such as:
How robust are Dirac nodes to perturbations like strain, disorder, or substrate interactions? In practice, real crystals deviate from idealized models, and small symmetry breaking or coupling to the environment can move, gap, or split Dirac points in ways that must be carefully disentangled from experimental artifacts Disorder in semimetals.
To what extent do observed spectral features reflect intrinsic bulk Dirac physics versus quasi-Dirac or near-degeneracy effects? Some reported observations may be explained by nearly linear dispersions or by surface-derived states that mimic bulk Dirac signatures under certain conditions, necessitating cross-checks with multiple probes Berry phase.
How should the DSM/Weyl classification be interpreted when certain symmetries are weakly broken or when materials host multiple Dirac points with differing protection mechanisms? The boundary between a true Dirac semimetal and a closely related topological phase can be nuanced, and theoretical frameworks continue to evolve Topological semimetal.
The role of interactions and many-body effects: strong correlations could, in principle, modify the simple single-particle picture, opening gaps or driving instabilities. The extent to which interaction effects alter the Dirac spectrum remains an active area of research in a subset of materials Many-body physics.
These discussions are part of the broader effort to understand how topology, symmetry, and materials science intersect. While the core DSM idea remains compelling and experimentally supported in canonical systems like Cd3As2 and Na3Bi, ongoing work seeks to refine the criteria for robust Dirac physics and to map the full landscape of candidate materials Topological semimetal.