Weyl semimetal

Last updated

Weyl semimetals are semimetals or metals whose quasiparticle excitation is the Weyl fermion, a particle that played a crucial role in quantum field theory but has not been observed as a fundamental particle in vacuum. [1] In these materials, electrons have a linear dispersion relation, making them a solid-state analogue of relativistic massless particles. [2]

Contents

Theoretical predictions

Weyl fermions are massless chiral fermions embodying the mathematical concept of a Weyl spinor. Weyl spinors in turn play an important role in quantum field theory and the Standard Model, where they are a building block for fermions in quantum field theory. Weyl spinors are a solution to the Dirac equation derived by Hermann Weyl, called the Weyl equation. [3] For example, one-half of a charged Dirac fermion of a definite chirality is a Weyl fermion. [4]

Weyl fermions may be realized as emergent quasiparticles in a low-energy condensed matter system. This prediction was first proposed by Conyers Herring in 1937, in the context of electronic band structures of solid state systems such as electronic crystals. [5] [6] Topological materials in the vicinity of band inversion transition became a primary target in search of topologically protected bulk electronic band crossings. [7]

The first (non-electronic) liquid state which is suggested, has similarly emergent but neutral excitation and theoretically interpreted superfluid's chiral anomaly as observation of Fermi points is in Helium-3 A superfluid phase. [8] [ non-primary source needed ] Crystalline tantalum arsenide (TaAs) is the first discovered topological Weyl fermion semimetal which exhibits topological surface Fermi arcs where Weyl fermion is electrically charged along the line of original suggestion by Herring. [6] [9] An electronic Weyl fermion is not only charged but stable at room temperature where there is no such superfluid or liquid state known.[ citation needed ]

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. Weyl Balents.png
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.

Experimental observation

A Weyl semimetal is a solid state crystal whose low energy excitations are Weyl fermions that carry electrical charge even at room temperatures. [11] [12] [13] A Weyl semimetal enables realization of Weyl fermions in electronic systems. [9] It is a topologically nontrivial phase of matter, together with Helium-3 A superfluid phase, that broadens the topological classification beyond topological insulators. [14] The Weyl fermions at zero energy correspond to points of bulk band degeneracy, the Weyl nodes (or Fermi points) 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 (Fermi points) 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. [11] Comparable 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. [9] [11] 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 2012 theoretical investigation of superfluid Helium-3 [15] suggested Fermi arcs in neutral superfluids.

A detector image (top) signals the existence of Weyl fermion nodes and the Fermi arcs. 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) CartoonvWeyl.jpg
A detector image (top) signals the existence of Weyl fermion nodes and the Fermi arcs. 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 16 July 2015 the first experimental observations of Weyl fermion semimetal and topological Fermi arcs in an inversion symmetry-breaking single crystal material tantalum arsenide (TaAs) were made. [9] Both Weyl fermions and Fermi arc surface states were observed using direct electronic imaging using ARPES, which established its topological character for the first time. [9] This discovery was built upon previous theoretical predictions proposed in November 2014 by a team led by Bangladeshi scientist M Zahid Hasan. [16] [17]

Weyl points (Fermi points) were also observed in non-electronic systems such as photonic crystals, in fact even before their experimental observation in electronic systems [18] [19] [20] and Helium-3 superfluid quasiparticle spectrum (neutral fermions). [21] Note that while these systems are different from electronic condensed matter systems, the basic physics is very similar.

Crystal growth, structure and morphology

TaAs is the first discovered Weyl semimetal (conductor). Large-size (~1 cm), high-quality TaAs single crystals [22] can be obtained by chemical vapor transport method using iodine as the transport agent.

TaAs crystallizes in a body-centered tetragonal unit cell with lattice constants a = 3.44 Å and c = 11.64 Å and space group I41md (No. 109). Ta and As atoms are six coordinated to each other. This structure lacks a horizontal mirror plane and thus inversion symmetry, which is essential to realize Weyl semimetal.

TaAs single crystals have shiny facets, which can be divided into three groups: the two truncated surfaces are {001}, the trapezoid or isosceles triangular surfaces are {101}, and the rectangular ones {112}. TaAs belongs to point group 4mm, the equivalent {101} and {112} planes should form a ditetragonal appearance. The observed morphology can be vary of degenerated cases of the ideal form. Beside the initial discovery of TaAs as Weyl semimetal, many other materials such as Co2TiGe, MoTe2, WTe2, LaAlGe and PrAlGe have been identified to exhibit Weyl semimetallic behavior. [23] [24]

Applications

The Weyl fermions in the bulk and the Fermi arcs on the surfaces of Weyl semimetals are of interest in physics and materials technology. [3] [25] The high mobility of charged Weyl fermions may find use in electronics and computing.

In 2017, [26] a research team from Vienna University of Technology carrying out experimental work to develop new materials, and a team at Rice University carrying out theoretical work, have produced material which they term Weyl–Kondo semimetals. [27]

A group of international researchers led by a team from Boston College discovered in 2019 that the Weyl semimetal Tantalum Arsenide delivers the largest intrinsic conversion of light to electricity of any material, more than ten times larger than previously achieved. [28]

2D Weyl semimetals are spin-polarized analogues of graphene that promise access to topological properties of Weyl fermions in (2+1)-dim spacetime. In 2024, an intrinsic 2D Weyl semimetal with spin-polarized Weyl cones and topological Fermi string edge states was discovered in epitaxial monolayer bismuthene by a team from University of Missouri, National Cheng Kung University, and Oak Ridge National Laboratory. [29]

Further reading

See also

Related Research Articles

<span class="mw-page-title-main">Fermion</span> Type of subatomic particle

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Fermions have a half-odd-integer spin and obey the Pauli exclusion principle. These particles include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.

<span class="mw-page-title-main">Kondo effect</span> Physical phenomenon due to impurities

In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature. The cause of the effect was first explained by Jun Kondo, who applied third-order perturbation theory to the problem to account for scattering of s-orbital conduction electrons off d-orbital electrons localized at impurities. Kondo's calculation predicted that the scattering rate and the resulting part of the resistivity should increase logarithmically as the temperature approaches 0 K. Extended to a lattice of magnetic impurities, the Kondo effect likely explains the formation of heavy fermions and Kondo insulators in intermetallic compounds, especially those involving rare earth elements such as cerium, praseodymium, and ytterbium, and actinide elements such as uranium. The Kondo effect has also been observed in quantum dot systems.

<span class="mw-page-title-main">Cadmium arsenide</span> Chemical compound

Cadmium arsenide (Cd3As2) is an inorganic semimetal in the II-V family. It exhibits the Nernst effect.

<span class="mw-page-title-main">Topological order</span> Type of order at absolute zero

In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.

<span class="mw-page-title-main">Pseudogap</span> State at which a Fermi surface has a partial energy gap in condensed matter physics

In condensed matter physics, a pseudogap describes a state where the Fermi surface of a material possesses a partial energy gap, for example, a band structure state where the Fermi surface is gapped only at certain points.

<span class="mw-page-title-main">Majorana fermion</span> Fermion that is its own antiparticle

A Majorana fermion, also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles.

<span class="mw-page-title-main">Tungsten ditelluride</span> Chemical compound

Tungsten ditelluride (WTe2) is an inorganic semimetallic chemical compound. In October 2014, tungsten ditelluride was discovered to exhibit an extremely large magnetoresistance: 13 million percent resistance increase in a magnetic field of 60 tesla at 0.5 kelvin. The resistance is proportional to the square of the magnetic field and shows no saturation. This may be due to the material being the first example of a compensated semimetal, in which the number of mobile holes is the same as the number of electrons. Tungsten ditelluride has layered structure, similar to many other transition metal dichalcogenides, but its layers are so distorted that the honeycomb lattice many of them have in common is in WTe2 hard to recognize. The tungsten atoms instead form zigzag chains, which are thought to behave as one-dimensional conductors. Unlike electrons in other two-dimensional semiconductors, the electrons in WTe2 can easily move between the layers.

The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, and that does not require the application of a large magnetic field. The quantum spin Hall state does not break charge conservation symmetry and spin- conservation symmetry.

<span class="mw-page-title-main">Topological insulator</span> State of matter with insulating bulk but conductive boundary

A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material.

<span class="mw-page-title-main">Piers Coleman</span> British-American physicist

Piers Coleman is a British-born theoretical physicist, working in the field of theoretical condensed matter physics. Coleman is professor of physics at Rutgers University in New Jersey and at Royal Holloway, University of London.

Bismuth selenide is a gray compound of bismuth and selenium also known as bismuth(III) selenide.

In the field of unconventional superconductivity, a Fermi arc is a phenomenon visible in the pseudogap state of a superconductor. Seen in momentum space, part of the space exhibits a gap in the density of states, like in a superconductor. This starts at the antinodal points, and spreads through momentum space when lowering the temperature until everywhere is gapped and the sample is superconducting. The area in momentum space that remains ungapped is called the Fermi arc.

<span class="mw-page-title-main">Chiral magnetic effect</span>

Chiral magnetic effect (CME) is the generation of electric current along an external magnetic field induced by chirality imbalance. Fermions are said to be chiral if they keep a definite projection of spin quantum number on momentum. The CME is a macroscopic quantum phenomenon present in systems with charged chiral fermions, such as the quark–gluon plasma, or Dirac and Weyl semimetals. The CME is a consequence of chiral anomaly in quantum field theory; unlike conventional superconductivity or superfluidity, it does not require a spontaneous symmetry breaking. The chiral magnetic current is non-dissipative, because it is topologically protected: the imbalance between the densities of left-handed and right-handed chiral fermions is linked to the topology of fields in gauge theory by the Atiyah-Singer index theorem.

<span class="mw-page-title-main">Dirac cone</span> Quantum effect in some non-metals

In physics, Dirac cones are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators. In these materials, at energies near the Fermi level, the valence band and conduction band take the shape of the upper and lower halves of a conical surface, meeting at what are called Dirac points.

The term Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation itself was formulated for fermions, the quasi-particles present within Dirac matter can be of any statistics. As a consequence, Dirac matter can be distinguished in fermionic, bosonic or anyonic Dirac matter. Prominent examples of Dirac matter are graphene and other Dirac semimetals, topological insulators, Weyl semimetals, various high-temperature superconductors with -wave pairing and liquid helium-3. The effective theory of such systems is classified by a specific choice of the Dirac mass, the Dirac velocity, the gamma matrices and the space-time curvature. The universal treatment of the class of Dirac matter in terms of an effective theory leads to a common features with respect to the density of states, the heat capacity and impurity scattering.

In solid-state physics, the kagome metal or kagome magnet is a type of ferromagnetic quantum material. The atomic lattice in a kagome magnet has layered overlapping triangles and large hexagonal voids, akin to the kagome pattern in traditional Japanese basket-weaving. This geometry induces a flat electronic band structure with Dirac crossings, in which the low-energy electron dynamics correlate strongly.

Magnetic topological insulators are three dimensional magnetic materials with a non-trivial topological index protected by a symmetry other than time-reversal. In contrast with a non-magnetic topological insulator, a magnetic topological insulator can have naturally gapped surface states as long as the quantizing symmetry is broken at the surface. These gapped surfaces exhibit a topologically protected half-quantized surface anomalous Hall conductivity perpendicular to the surface. The sign of the half-quantized surface anomalous Hall conductivity depends on the specific surface termination.

Maia Garcia Vergniory is a Spanish computational physicist who is a group leader at the Max Planck Institute for Chemical Physics of Solids. Her work in topological quantum chemistry investigates the phases of topological materials. She was elected Fellow of the American Physical Society in 2022.

Shuyun Zhou is a Chinese physicist and a tenured professor of physics at Tsinghua University. She is the distinguished Professor of the 2017 "Cheung Kong Scholars" of the Ministry of Education of the People's Republic of China, and won the 13th "China Young Women Scientists Award".

References

  1. Shuang Jia, Su-Yang Xu & M. Zahid Hasan (2016). "Weyl semimetals, Fermi arcs and chiral anomalies". Nature Materials. 56 (15): 1140–1144. arXiv: 1612.00416 . Bibcode:2016NatMa..15.1140J. doi:10.1038/nmat4787. PMID   27777402. S2CID   1115349.
  2. Pongsangangan, K. (2018). Role of Coulomb Interactions in Weyl Semimetals: Renormalisation and Symmetry Breaking (MSc Physics thesis). Utrecht university.
  3. 1 2 Johnston, Hamish (2015). "Weyl fermions are spotted at long last". Physics World.
  4. Weyl, H. (1929). "Elektron und gravitation. I". Z. Phys. 56 (5–6): 330–352. Bibcode:1929ZPhy...56..330W. doi:10.1007/bf01339504. S2CID   186233130.
  5. Herring, C. (1937). "Accidental Degeneracy in the Energy Bands of Crystals". Phys. Rev. 52 (4): 365–373. Bibcode:1937PhRv...52..365H. doi:10.1103/physrev.52.365.
  6. 1 2 Vishwanath, Ashvin (2015-09-08). "Where the Weyl Things Are". APS Physics. Vol. 8. p. 84. Bibcode:2015PhyOJ...8...84V. doi: 10.1103/Physics.8.84 .
  7. Hasan, M. Zahid; Xu, Su-Yang; Neupane, Madhab (2015), "Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators", Topological Insulators, John Wiley & Sons, Ltd, pp. 55–100, doi:10.1002/9783527681594.ch4, ISBN   978-3-527-68159-4 , retrieved 2020-04-27
  8. Bevan, T. D. C.; Manninen, A. J.; Cook, J. B.; Hook, J. R.; Hall, H. E.; Vachaspati, T.; Volovik, G. E. (1997-04-17). "Momentum creation by vortices in superfluid 3He as a model of primordial baryogenesis". Nature. 386 (6626): 689–692. arXiv: cond-mat/9611164 . Bibcode:1997Natur.386..689B. doi:10.1038/386689a0. S2CID   4315194.
  9. 1 2 3 4 5 6 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 (6248): 613–617. arXiv: 1502.03807 . Bibcode:2015Sci...349..613X. doi:10.1126/science.aaa9297. PMID   26184916. S2CID   206636457.
  10. Balents, L. (2011). "Weyl electrons kiss". Physics. 4: 36. Bibcode:2011PhyOJ...4...36B. doi: 10.1103/physics.4.36 .
  11. 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 (20): 205101. arXiv: 1007.0016 . Bibcode:2011PhRvB..83t5101W. doi:10.1103/physrevb.83.205101. S2CID   119281249.
  12. Burkov, A. A.; Balents, L. (2011). "Weyl Semimetal in a Topological Insulator Multilayer". Phys. Rev. Lett. 107 (12): 127205. arXiv: 1105.5138 . Bibcode:2011PhRvL.107l7205B. doi:10.1103/physrevlett.107.127205. PMID   22026796. S2CID   12954084.
  13. Singh, Bahadur; Sharma, Ashutosh; Lin, H.; Hasan, M. Z.; Prasad, R.; Bansil, A. (2012-09-18). "Topological electronic structure and Weyl semimetal in the TlBiSe${}_{2}$ class of semiconductors". Physical Review B. 86 (11): 115208. arXiv: 1209.5896 . doi:10.1103/PhysRevB.86.115208. S2CID   119109505.
  14. 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 (9): 356. arXiv: 0710.0930 . Bibcode:2007NJPh....9..356M. doi:10.1088/1367-2630/9/9/356. S2CID   13999448.
  15. Silaev, M. A. (2012). "Topological Fermi arcs in superfluid". Physical Review B. 86 (21): 214511. arXiv: 1209.3368 . Bibcode:2012PhRvB..86u4511S. doi:10.1103/PhysRevB.86.214511. S2CID   118352190.
  16. 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 Communications. 6: 7373. Bibcode:2015NatCo...6.7373H. doi:10.1038/ncomms8373. PMC   4490374 . PMID   26067579.
  17. Weng, H.; Fang, C.; Fang, Z.; Bernevig, A.; Dai, X. (2015). "Weyl semimetal phase in non-centrosymmetric transition metal monophosphides". Phys. Rev. X. 5 (1): 011029. arXiv: 1501.00060 . Bibcode:2015PhRvX...5a1029W. doi:10.1103/PhysRevX.5.011029. S2CID   15298985.
  18. Lu, L.; Fu, L.; Joannopoulos, J.; Soljačić, M. (2013). "Weyl points and line nodes in gyroid photonic crystals". Nature Photonics. 7 (4): 294–299. arXiv: 1207.0478 . Bibcode:2013NaPho...7..294L. doi:10.1038/nphoton.2013.42. S2CID   5144108.
  19. Lu, L.; Wang, Z.; Ye, D.; Fu, L.; Joannopoulos, J.; Soljačić, M. (2015). "Experimental observation of Weyl points". Science. 349 (6248): 622–624. arXiv: 1502.03438 . Bibcode:2015Sci...349..622L. doi:10.1126/science.aaa9273. PMID   26184914. S2CID   11725179.
  20. Noh, Jiho; Huang, Sheng; Leykam, Daniel; Chong, Yidong; Chen, Kevin; Rechtsman, Mikael (2017). "Experimental observation of optical Weyl points and Fermi arc-like surface states". Nature Physics. 13 (6): 611–617. arXiv: 1610.01033 . Bibcode:2017NatPh..13..611N. doi:10.1038/nphys4072. S2CID   45026039.
  21. Volovik, G. E. (2009). The universe in a helium droplet. Oxford: Oxford University Press. ISBN   978-0-19-956484-2. OCLC   519697958.
  22. Li, Zhilin; Chen, Hongxiang; Jin, Shifeng; Gan, Di; Wang, Wenjun; Guo, Liwei; Chen, Xiaolong (2016). "Weyl Semimetal TaAs: Crystal Growth, Morphology, and Thermodynamics". Cryst. Growth Des. 16 (3): 1172–1175. doi:10.1021/acs.cgd.5b01758.
  23. Dulal, Rajendra P.; Dahal, Bishnu; Forbes, Andrew; Bhattarai, Niraj (2019). "Weak localization and small anomalous Hall conductivity in ferromagnetic Weyl semimetal Co2TiGe". Scientific Reports. 9 (1): 3342. Bibcode:2019NatSR...9.3342D. doi: 10.1038/s41598-019-39037-0 . PMC   6399263 . PMID   30833580.
  24. Bhattarai, Niraj (2020). "Transport characteristics of type II Weyl semimetal MoTe2 thin films grown by chemical vapor deposition". Journal of Materials Research. 35 (5): 454–461. arXiv: 2001.01703 . Bibcode:2020JMatR..35..454B. doi:10.1557/jmr.2019.320. S2CID   209862800.
  25. Shekhar, C.; et al. (2015). "Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP". Nature Physics. 11 (8): 645–649. arXiv: 1502.04361 . Bibcode:2015NatPh..11..645S. doi:10.1038/nphys3372. S2CID   119282987.
  26. Lai, Hsin-Hua; Grefe, Sarah E.; Paschen, Silke; Si, Qimiao (18 December 2017). "Weyl–Kondo semimetal in heavy-fermion systems". Proceedings of the National Academy of Sciences. 115 (1): 93–97. Bibcode:2018PNAS..115...93L. doi: 10.1073/pnas.1715851115 . ISSN   0027-8424. PMC   5776817 . PMID   29255021.
  27. Josh Gabbatiss (21 Dec 2017). "Scientists discover entirely new material that cannot be explained by classical physics". The Independent. Retrieved 22 May 2019.
  28. Boston College (4 Mar 2019). "Chirality yields colossal photocurrent". phys.org. Retrieved 22 May 2019.
  29. Lu, Qiangsheng; Sreenivasa Reddy, P. V.; Jeon, Hoyeon; Mazza, Alessandro R.; Brahlek, Matthew; Wu, Weikang; Yang, Shengyuan A.; Cook, Jacob; Conner, Clayton; Zhang, Xiaoqian; Chakraborty, Amarnath; Yao, Yueh-Ting; Tien, Hung-Ju; Tseng, Chun-Han; Yang, Po-Yuan; Lien, Shang-Wei; Lin, Hsin; Chiang, Tai-Chang; Vignale, Giovanni; Li, An-Ping; Chang, Tay-Rong; Moore, Rob G.; Bian, Guang (17 July 2024). "Realization of a two-dimensional Weyl semimetal and topological Fermi strings". Nature Communications. 15: 6001. arXiv: 2303.02971 . doi: 10.1038/s41467-024-50329-6 .