Research on Weyl physics is really taking off with no less than three reports by independent research groups in this week’s Science. The first group, led by Zahid Hasan of Princeton University in the US, says it has observed novel topological Weyl fermion “line” and “drumhead” surface states in a room temperature magnet – made of cobalt, manganese and gallium (Co2MnGa) – for the first time. The second and third groups, led by Yulin Chen at the University of Oxford in the UK and Haim Beidenkopf of the Weizmann Institute of Science in Israel, are reporting on the existence of a time-reversal symmetry-broken (that is, magnetic) Weyl semimetal in a crystal containing cobalt, tin and sulphur (Co3Sn2S2), also through measurements of its band structure using spectroscopic techniques. The findings are an important step forward in the quest for materials in which magnetism and topology could be exploited for future technology applications as well as for fundamental studies in physics.
Topological materials can be insulating in the bulk but can conduct electricity extremely well on their edge via special, topologically protected, electronic states. Topological states are protected from fluctuations in their environment and electrons in them do not backscatter. Since backscattering is the main dissipating process in electronics, this means that these materials might be used to make highly energy-efficient electronic devices in the future.
A Weyl semimetal is a recently discovered class of topological material in which electronic excitations behave as massless, Weyl, fermions. These particles, which were first predicted in 1929 by the theoretical physicist Herman Weyl as a solution of the Dirac equation, behave quite differently to electrons in ordinary metals or semiconductors in that they show the chiral magnetic effect. This occurs when a Weyl metal is placed in a magnetic field, which generates a current of positive and negative Weyl particles that move parallel and antiparallel to the field.
Weyl nodes and Fermi arcs
Fermions that can be described by Weyl’s theory can appear as quasiparticles in solids that have linear electron energy bands crossing at so-called (Weyl) “nodes”. The existence of Weyl nodes in the bulk band structure is necessarily accompanied by the formation of “Fermi arcs” on the surface band structure that connect pairs of Weyl nodes of opposite chirality.
Hasan and colleagues studied an exotic crystal made of cobalt, manganese and gallium (Co2MnGa), which is a room temperature magnet with a transition temperature near 690 K. Chen’s and Beidenkopf’s groups focused on crystal containing cobalt, tin and sulphur (Co3Sn2S2), which becomes a ferromagnet at temperatures below 175 K.
Chen and co-workers used a technique called angle-resolved photoemission spectroscopy (ARPES) to study the electronic structure of their material and identified the Weyl band structure inside the ferromagnetic phase. In ARPES, high-intensity light shone on the sample forces electrons to emit from the surface. These emitted electrons can be measured and provide information about their behaviour when they were in the bulk of the sample.
This technique to pin down the role of topological effects by observing the differences in the behaviour of electrons on the surface of the material compared to those in the bulk was pioneered by Hasan and colleagues in 2015 and used to detect Weyl fermions.
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Quasiparticle interference
Beidenkopf’s group identified the same Weyl band structure in Co3Sn2S2 using another approach – scanning tunnelling spectroscopy – to measure electron states in the material with atomic-scale resolution.
“We rely on the quantum particle-wave duality of the surface electrons in the material to image, in a scanning tunnelling microscope, the interference patterns the electrons embed in the surface density states as they scatter,” explains Beidenkopf. “This technique is called quasiparticle interference. From these patterns, we can trace the band dispersion and by comparing these patterns to predictions from band-structure calculations, we can identify the Fermi arc bands among the various bands that exist on the surface of the material.
“The existence of these Fermi-arc bands on the surface is synonymous to the classification of the bulk band structure as a Weyl semimetal – because there is simply no other way to create such surface states,” he tells Physics World.
And that is not all: the researchers also found that the arcs connected different Weyl points depending on the chemical composition of the topmost surface of the material. This means that topological currents in circuits containing Co3Sn2S2 might be manipulated by varying this composition.
“This varying connectivity would alter the magneto-transport response of these materials since it involves electronic orbits that pass through both surface Fermi arcs and bulk Weyl states,” explains Beidenkopf. “Rewiring the surface connectivity would thus lead to distinct electronic paths. This approach also demonstrates a new tool to manipulate the electronic structure of Weyl semimetals and it would be interesting to study exactly how the Fermi arc connectivity changes across an interface and whether new states bind to it.”
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New “drumhead” surface electronic state
Weyl states are also possible in related materials, such as Co2MnGa, as Hasan’s team’s new results attest. In this room-temperature ferromagnet, the bulk node is stretched into a nodal Weyl “line” with a corresponding new kind of “drumhead” surface electronic state, say the researchers. This surface state, which they predicted in 2017, has never been seen before in magnets and is the tell-tale fingerprint of a topological magnet. Again, using ARPES (at the dedicated photoemission spectroscopy beamline recently built at the Stanford Synchrotron Radiation Laboratory) and band structure numerical calculations, they identified this Weyl structure inside the ferromagnetic phase of Co2MnGa.
ARPES is an extremely powerful experimental technique, which in this case allowed us to directly observe that the electrons in Co2MnGa behave as if they are massless Weyl fermions, says team member Daniel Sanchez. By studying these fermions in more detail, the researchers say they realized that the material hosted an infinite series of distinct massless electrons that take the form of a line loop, with some electrons mimicking the properties of particles and some of antiparticles.
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This collective quantum behaviour has been dubbed a magnetic topological Weyl fermion loop – a truly exotic and novel system, says team member and study co-first author Guoqing Chang.
Having been able to identify broken time-reversal symmetry Weyl states could allow researchers to now study even more exotic phenomena, comments Eduardo da Silva Neto in a related Perspectives article in Science. These include the quantum anomalous Hall state (in which a Hall voltage is generated without an external magnetic field), which could allow for dissipationless edge currents for future electronic and spintronics technologies.
“The electrodynamics of axions, hypothetical elementary particles that could resolve symmetry problems in quantum chromodynamics, also finds its analogue in certain magnetic topological materials that could be used as part of the search for axion dark matter,” he writes.
Full details of the three research groups’ results (in the order that they appear in the journal Science) are here: Hasan’s group, Chen’s group and Beidenkopf’s group.
