# Topological properties controlled by light

When electrons flow through arrays of atoms in certain solids, they behave as quantum-mechanical particles that have extremely high speeds. Graphene — an atomically thin sheet of carbon — is an example of a material in which such behaviour occurs in two dimensions^{1}. In the past decade, there have been worldwide efforts to study solids called Weyl semimetals, which exhibit similar intriguing properties of electrons in three dimensions^{2}. In Weyl semimetals, electrons form structures that have peculiar topological properties, resulting in many fascinating characteristics of matter^{2}. On-demand control of the electronic properties of a Weyl semimetal would therefore enable ultrafast manipulation of the material’s properties. Writing in *Nature*, Sie *et al.*^{3} report that terahertz-frequency light can provide such control in a particular Weyl semimetal.

In the late 1920s, the physicist Paul Dirac discovered an equation that governs the behaviour of relativistic (high-speed) particles, and that combines quantum mechanics and Einstein’s special theory of relativity^{4}. Following this monumental work, the mathematician and theoretical physicist Hermann Weyl suggested a simplified version of Dirac’s equation^{5}, describing massless particles — known as Weyl fermions — that have a chirality (handedness) of −1 or +1. In a Weyl semimetal, the dynamics of low-energy electrons are governed by Weyl’s equation.

The quantum state of an electron is characterized by the particle’s energy, momentum and spin (intrinsic angular momentum). In a solid, these quantum states are dictated by symmetries of the material’s atomic lattice. Under time-reversal symmetry, the physical properties of a material are unchanged when the direction of time is reversed. Under inversion symmetry, the physical properties are retained when the spatial coordinates are flipped. If both of these symmetries are preserved, there are always two quantum states of electrons that have the same energy and momentum.

However, if one of these symmetries is broken, it is still possible to have quantum states of equal energy and momentum at particular points in phase space — the space of all possible energy and momentum values^{2}^{,}^{6}. In the vicinity of these points, electrons are described by Weyl’s equation. As a result, the elementary excitations of electrons in such solids behave as Weyl fermions, and the associated chiralities can be assigned to states near the points. By analogy with particles of opposite electric charge, states of opposite chirality can be produced in pairs, and annihilate each other when they meet.

Among the handful of Weyl semimetals that have been discovered, molybdenum ditelluride and tungsten ditelluride (MoTe_{2} and WTe_{2}, respectively) are of particular scientific interest^{2}^{,}^{7}. These compounds contain 2D structures that stack through a weak attractive force — the van der Waals interaction — to form layered 3D crystals. Depending on the stacking geometry, different crystal symmetries can be realized.

It has been known for more than four decades that, as temperature increases, MoTe_{2} changes from one crystal structure (orthorhombic) to another (monoclinic), whereas WTe_{2} does not^{8}. Inversion symmetry is broken in the orthorhombic structure, so that the associated compounds can exhibit the Weyl-semimetal phase^{2}^{,}^{7} (Fig. 1). By contrast, inversion symmetry is preserved in the monoclinic structure, and the states of opposite chirality can annihilate each other. The two crystal structures have almost the same atomic lattice, except that the monoclinic one is tilted by about 4° with respect to the out-of-plane direction of the orthorhombic one.

Owing to the weak attractive force between the layers of the MoTe_{2} and WTe_{2} compounds, each layer can slide easily, unlike in ordinary materials. As a result, shear forces — pairs of equal and opposite forces that act on the top and bottom layers — can deform the orthorhombic structure into the monoclinic structure, and therefore the Weyl-semimetal phase into a normal phase. Applying such forces in a mechanical way might either permanently alter the atomic lattices or be impossible. A theoretical study suggested that the crystal symmetries of these structures could instead be switched using charge doping, whereby electrons are added to or subtracted from a material^{9}. The study indicated that this method might provide a controllable way to switch between the different topological phases.

Sie and colleagues’ work is probably the first to demonstrate a dynamic transition between two crystal structures that have distinct topological phases. Previous studies have reported similar topological transitions, but these studies used static mechanical controls that cannot easily switch between the different phases^{10}^{,}^{11}. Sie *et al.* found that light pulses at terahertz (THz) frequencies could cause the orthorhombic structure to become unstable by exciting electrons. This could induce the structural transition of WTe_{2} from orthorhombic to monoclinic, as if charge doping had been applied to the sample. The authors analysed the crystal structures using a technique known as relativistic ultrafast electron diffraction. They corroborated their measurements using a method called time-resolved second-harmonic generation, which is quite sensitive to the inversion symmetry of crystals.

All the authors’ measurements clearly indicate that the crystal structure of WTe_{2} has inversion symmetry after the light pulses have been applied, and the switching between structures occurs at THz frequencies — although recovery of the original structure takes much longer. Because the absence of inversion symmetry is a key characteristic of the Weyl-semimetal phase in orthorhombic WTe_{2}, the observation of this switch of symmetries provides strong indirect evidence of the topological transition. Sie and colleagues have therefore discovered a dynamical way to control the topological properties of Weyl semimetals that could open up many applications, because the existence of Weyl fermions can substantially alter the behaviour of these materials^{2}.

Further studies are needed to realize the full potential of the authors’ switching mechanism. Because the structural transitions in MoTe_{2} and WTe_{2} are closely related to topological changes^{9}, combined electrical and optical measurements would not only conclusively determine the topological transitions, but also provide a way to study topology-related transport phenomena in these solids^{2}. The microscopic description of how THz-frequency light pulses affect the electronic and structural properties of WTe_{2} is also required to understand the observed dynamic transitions. These endeavours and others will surely accelerate a fruitful era of topological materials and the control of these materials for applications.

Nature **565**, 32-33 (2019)

## References

- 1.
Geim, A. K. & Kim, P.

*Sci. Am.***298**, 90–97 (2008). - 2.
Armitage, N. P., Mele, E. J. & Vishwanath, A.

*Rev. Mod. Phys.***90**, 015001 (2018). - 3.
Sie, E. J.

*et al.**Nature***565**, 61–66 (2019). - 4.
Dirac, P. A. M.

*Proc. R. Soc. Lond. A***117**, 610–624 (1928). - 5.
Weyl, H.

*Z. Phys*.**56**, 330–352 (1929). - 6.
Herring, C.

*Phys. Rev.***52**, 365–373 (1937). - 7.
Soluyanov, A. A.

*et al.**Nature***527**, 495–498 (2015). - 8.
Clarke, R., Marseglia, E. & Hughes, H. P.

*Phil. Mag.***38**, 121–126 (1978). - 9.
Kim, H.-J., Kang, S.-H., Hamada, I. & Son, Y.-W.

*Phys. Rev. B***95**, 180101(R) (2017). - 10.
Zeljkovic, I.

*et al.**Nature Nanotechnol.***10**, 849–853 (2015). - 11.
Liu, Y.

*et al.**Nature Phys.***10**, 294–299 (2014).