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Topological matter

Topological matter

Quadrupole topological insulator created in mechanical metamaterial

17 Jan 2018
Illustration of a system with a quadrupole charge distribution
On the corner: illustration of corner charges in a quadrupole system

The first “quadrupole topological insulator” has been created in a mechanical metamaterial by physicists in Switzerland. The experiment confirms a theoretical prediction made in 2017 that the concepts behind traditional dipole topological insulators can be extended to create higher multipole versions. The researchers believe the work could lead to one-way waveguides that are immune to scattering.

Unlike most topological insulators – which involve the conduction of electrical charge – the topological properties of the metamaterial arise from its vibrational modes. Work done recently by two other teams of physicists suggest that quadrupole topological insulators can also be made from systems based on electrons and photons.

In traditional electrical topological insulators, electric dipole moments sit head-to-tail in the bulk of the crystal, effectively cancelling each other. At the surfaces, however, electrical charges can build up, leading to edge modes that conduct charge in one direction with no scattering. In 2017, Taylor Hughes of the University of Illinois at Urbana Champaign and colleagues calculated that, if higher-order charge polarization occurred within a crystal, more complex phenomena could be seen at the edges. For example, if the bulk contained quadrupolar moments, each edge should become a 1D version of a traditional dipole topological insulator, giving rise to “corner modes” where they met.

Mathematical link

Topological insulators analogous to the electrical dipole type have been created in systems where electromagnetic radiation or mechanical oscillations play the role of electrical charge. “The link is really on the mathematical level,” explains Sebastian Huber of ETH Zurich. “The existence or absence of surface states is independent of these degrees of freedom being charged or not.” In the new research, Huber and colleagues produced a mechanical metamaterial that achieves the first experimental demonstration of a quadrupole topological insulator.

The team used the mathematical principles outlined by Hughes’ team to calculate the resonant frequencies of the various modes in a topological mechanical metamaterial made from 5 mm silicon plates connected together by beams. They then fabricated the metamaterial and measured its response to induced vibrations at various frequencies. “There is a whole frequency range where you can’t excite any vibrations in the system either in the bulk or in the edge,” says Huber. “However, at the four corners, right in the middle of this frequency band, you can excite vibrations: these are the four corner states.”

At present, the system is two dimensional, so the corner modes have nowhere to go. However, Huber and colleagues aim to develop a stacked, three-dimensional set-up. It should be possible, says Huber, to develop a cubic architecture in which some corners will only allow propagation in one direction and some will only allow it the opposite way. This, he says, would be “the dream” for producing things like topologically protected, scatter-proof waveguides.

“One of the significant things here is that I think this is the first example in which a concept from topological matter has been realized first in a mechanical system,” says Martin van Hecke of the Institute for Atomic and Molecular Physics in Amsterdam, who was not involved with the research.

Rapid realization

“We were excited to see that our predictions could be realized so quickly,” says Hughes, “It shows that the field of topological metamaterials is a very capable avenue for realizing these interesting topological phases in experiments.”

In pre-prints published recently, Hughes’ team describes an analogous system based on a microwave resonator, whereas Ronny Thomale of the University of Würzburg in Germany and colleagues describe a describe a similar system based on an electrical circuit.

Huber and colleagues described their metamaterial in Nature.

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