| Fermi arc | |
|---|---|
| Name | Fermi arc |
| Field | Condensed matter physics |
| Discovered | 2010s |
| Related | Weyl semimetal, Fermi surface |
Fermi arc
A Fermi arc is a discontinuous segment of electronic states at the Fermi energy that appears on the surface of certain crystalline solids, rather than forming a closed Fermi surface. Fermi arcs are significant in Quantum Physics because they provide direct evidence of nontrivial bulk topology and of exotic quasiparticles such as Weyl fermions in solid-state systems, with consequences for surface transport and electromagnetic response.
A Fermi arc is defined as a locus of gapless surface states at the Fermi level forming an open curve in the surface Brillouin zone, terminating at projections of bulk band crossings such as Weyl points or nodal points. Unlike conventional Fermi surfaces that are closed contours, Fermi arcs reflect a bulk–boundary correspondence between topological invariants in the bulk and protected surface modes. They are central to the classification of topological phases in topological matter and are tied to chiral anomalies and anomalous Hall responses in systems with broken time-reversal symmetry or inversion symmetry.
Fermi arcs occur in several classes of materials studied in condensed matter physics, most prominently in Weyl semimetals such as TaAs, NbAs, TaP, and NbP. They are also predicted or observed in some Dirac semimetals like Na3Bi and Cd3As2 under symmetry-breaking perturbations, in certain cuprate phases as truncated Fermi surfaces, and in engineered systems including photonic crystals and cold-atom lattices. Experimental realizations have been reported by groups at institutions such as Stanford University, Princeton University, Max Planck Institutes, and Los Alamos National Laboratory.
Topologically, Fermi arcs reflect the presence of bulk band degeneracies characterized by integer-valued invariants: the net chirality of Weyl points is a Chern number that enforces surface states connecting points of opposite chirality. In Weyl semimetals the bulk Fermi surface reduces to isolated Weyl nodes, and the surface projection yields open arcs. For Dirac semimetals, which host fourfold degenerate Dirac points protected by crystal symmetries, splitting into Weyl nodes via symmetry breaking produces arcs. The connection is formalized by the bulk–boundary correspondence and by topological band theory developed using Berry phase and Berry curvature concepts. Theoretical classification employs K-theory and symmetry indicators used in topological materials databases.
Fermi arcs have been observed using surface-sensitive probes. Angle-resolved photoemission spectroscopy (ARPES) is the primary technique, providing momentum-resolved maps of electronic dispersion; pioneering ARPES studies on TaAs and related compounds identified arc-like features. Other approaches include scanning tunneling microscopy (STM) and quasiparticle interference (QPI) imaging, which detect surface-state interference patterns, and magnetotransport measurements that infer surface conduction channels via quantum oscillations (e.g., Shubnikov–de Haas effect). Synchrotron facilities and beamlines at Advanced Light Source, European Synchrotron Radiation Facility, and SPring-8 have enabled high-resolution ARPES. Complementary probes include infrared spectroscopy and angle-dependent magnetoresistance experiments.
Microscopic descriptions of Fermi arcs derive from tight-binding Hamiltonians and continuum low-energy models containing linear band crossings, such as the Weyl Hamiltonian H(k)=±v k·σ. Lattice models like the Haldane model analogs on three-dimensional lattices, and inversion- or time-reversal-breaking perturbations, generate separated Weyl nodes whose surface projections connect via Fermi arcs. First-principles density functional theory (DFT) calculations combined with surface Green's function methods predict arc dispersion for candidate materials; codes such as VASP and Quantum ESPRESSO are commonly used. Analytical treatments invoke Berry curvature monopoles at nodes and the analytic continuation of bulk band eigenstates to derive surface spectral weight.
Fermi arcs give rise to unusual surface transport phenomena. They contribute to anisotropic surface conductivity, can mediate low-dissipation channels, and interact with bulk states to produce phenomena such as the chiral anomaly-induced negative magnetoresistance. In confined geometries, closed cyclotron orbits combining surface arcs and bulk states produce anomalous quantum oscillations measurable in magnetotransport. Fermi-arc-mediated quasiparticles may affect superconducting proximity effects and magneto-optical responses, and they are relevant to device proposals exploiting topologically protected conduction for spintronics and quantum technology.
Open questions include the detailed role of interactions and correlations on Fermi-arc stability, the nature of arcs in strongly correlated materials such as the cuprate superconductors, and how disorder and surface reconstruction modify arc signatures. The interplay between Fermi arcs and emergent orders (e.g., charge density waves, magnetism) remains active, as do efforts to engineer arcs in synthetic platforms like cold atoms and photonic crystals. Future directions emphasize material discovery via high-throughput searches, improved ARPES and STM resolution, theoretical frameworks beyond DFT including many-body techniques, and potential applications in topological electronics and metrology.
Category:Condensed matter physics Category:Topological phases of matter Category:Quantum mechanics