Weyl semimetal

Weyl fermions are massless chiral fermions that play an important role in quantum field theory and the standard model. They may be thought of as a building block for fermions in quantum field theory, and were predicted from a solution to the Dirac equation derived by Hermann Weyl.[1] For example, one-half of a charged Dirac fermion of a definite chirality is a Weyl fermion.[2] They have not been observed as a fundamental particle in nature. Weyl fermions may be realized as emergent quasiparticles in a low-energy condensed matter system.[3][4]

A schematic of the Weyl semimetal state, which include the Weyl nodes and the Fermi arcs. The Weyl nodes are momentum space monopoles and anti-monopoles. The sketch is adapted from Ref.[5]

Experimental discovery

A Weyl semimetal is a solid state crystal whose low energy excitations are Weyl fermions.[6][7] A Weyl semimetal enables the first-ever realization of Weyl fermions.[8] It is a topologically nontrivial phase of matter that broadens the topological classification beyond topological insulators.[4] The Weyl fermions at zero energy correspond to points of bulk band degeneracy, the Weyl nodes that are separated in momentum space. Weyl fermions have distinct chiralities, either left handed or right handed. In a Weyl semimetal crystal, the chiralities associated with the Weyl nodes can be understood as topological charges, leading to monopoles and anti-monopoles of Berry curvature in momentum space, which (the splitting) serve as the topological invariant of this phase.[6] Comparing to the Dirac fermions in graphene or on the surface of topological insulators, Weyl fermions in a Weyl semimetal are the most robust electrons and do not depend on symmetries except the translation symmetry of the crystal lattice. Hence the Weyl fermion quasiparticles in a Weyl semimetal possess a high degree of mobility. Due to the nontrivial topology, a Weyl semimetal is expected to demonstrate Fermi arc electron states on its surface.[6][8] These arcs are discontinuous or disjoint segments of a two dimensional Fermi contour, which are terminated onto the projections of the Weyl fermion nodes on the surface.

A detector image (top) signals the existence of Weyl fermion nodes and the Fermi arcs.[8] The plus and minus signs note the particle's chirality. A schematic (bottom) shows the way Weyl fermions inside a crystal can be thought as monopole and antimonopole in momentum space. (Image art by Su-Yang Xu and M. Zahid Hasan)

On July 16, 2015 the first experimental observations of Weyl fermion semimetal in an inversion symmetry-breaking single crystal material tantalum arsenide (TaAs) were made.[8] Both Weyl fermions and Fermi arc surface states were observed, which established its topological character.[8] This discovery was built upon previous theoretical predictions proposed in November 2014.[9][10] Weyl points were also observed in a non-fermionic system, a photonic crystal. [11] [12]

Applications

The Weyl fermions in the bulk and the Fermi arcs on the surface are of interest in physics and materials technology.[1][13] Their high mobility may find use in electronics and computing.

Further reading

References

  1. 1 2 Johnston, Hamish (2015). "Weyl fermions are spotted at long last". Physics World.
  2. ↑ Weyl, H. (1929). "Elektron und gravitation". I. Z. Phys. 56: 330–352. doi:10.1007/bf01339504.
  3. ↑ Herring, C. (1937). "Accidental Degeneracy in the Energy Bands of Crystals". Phys. Rev. 52: 365–373. doi:10.1103/physrev.52.365.
  4. 1 2 Murakami, S. (2007). "Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase". New J. Phys. 9: 356. doi:10.1088/1367-2630/9/9/356.
  5. ↑ Balents, L. (2011). "Weyl electrons kiss". Physics 4: 36. doi:10.1103/physics.4.36.
  6. 1 2 3 Wan, X.; Turner, A. M.; Vishwanath, A.; Savrasov, S. Y. (2011). "Topological Semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates". Phys. Rev. B 83: 205101. doi:10.1103/physrevb.83.205101.
  7. ↑ Burkov, A. A.; Balents, L. (2011). "Weyl Semimetal in a Topological Insulator Multilayer". Phys. Rev. Lett. 107: 127205. doi:10.1103/physrevlett.107.127205.
  8. 1 2 3 4 5 Xu, S.-Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Bian, G.; Zhang, C.; Sankar, R.; Chang, G.; Yuan, Z.; Lee, C.-C.; Huang, S.-M.; Zheng, H.; Ma, J.; Sanchez, D. S.; Wang, B. K.; Bansil, A.; Chou, F.-C.; Shibayev, P. P.; Lin, H.; Jia, S.; Hasan, M. Z. (2015). "Discovery of a Weyl Fermion semimetal and topological Fermi arcs". Science 349: 613–617. doi:10.1126/science.aaa9297.
  9. ↑ Huang, S.-M.; Xu, S.-Y.; Belopolski, I.; Lee, C.-C.; Chang, G.; Wang, B. K.; Alidoust, N.; Bian, G.; Neupane, M.; Zhang, C.; Jia, S.; Bansil, A.; Lin, H.; Hasan, M. Z. (2015). "A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class". Nature Commun. 6: 7373. doi:10.1038/ncomms8373.
  10. ↑ Weng, H.; Fang, C.; Fang, Z.; Bernevig, A.; Dai, X. (2015). "Weyl semimetal phase in non-centrosymmetric transition metal monophosphides". Phys. Rev. X 5: 011029. doi:10.1103/PhysRevX.5.011029.
  11. ↑ Lu, L.; Fu, L.; Joannopoulos, J.; Soljačić, M. (2013). "Weyl points and line nodes in gyroid photonic crystals". Nature Photonics 7: 294–299. doi:10.1038/nphoton.2013.42.
  12. ↑ Lu, L.; Wang, Z.; Ye, D.; Fu, L.; Joannopoulos, J.; Soljačić, M. (2015). "Experimental observation of Weyl points". Science 349: 622–624. doi:10.1126/science.aaa9273.
  13. ↑ Shekhar, C.; et al. (2015). "Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP". Nature Physics 11: 645–649. doi:10.1038/nphys3372.
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