From smartphones to particle accelerators, so much of today's technology owes itself to the development and discovery of new materials with unique properties. Semiconductors underpin the modern computer and nearly every computerized gadget we have. Superconductors also enable MRI machines and particle accelerators like the Large Hadron Collider in Switzerland.

Like with semiconductors and superconductors in the 20th century, we've entered another era of discovery, says M. Zahid Hasan, a physicist at Princeton University, scientist affiliate of Lawrence Berkeley National Laboratory and Moore Foundation grantee. This time, physicists like Hasan are discovering new quantum particles and exploring novel phenomena in topological materials. The theory behind these materials has been the subject of the 2016 Nobel Prize in physics. These materials boast unusual properties that highlight the exotic behaviors of quantum physics and could lead to unforeseen technology.

One characteristic of topological materials is that their surface can have different properties from their bulk — even if they're made from the same compound. For example, the inside of a topological insulator doesn’t conduct electricity. But the surface of this material does, where electrons move like slowed-down light forming a type of particle called helical Dirac fermions. Such topological behavior was first observed in 3D crystals by a Hasan-led team in 2007.

This kind of unusual property emerges from special types of interactions among the electrons. Electrons behave according to mathematical abstractions called wavefunctions, which live in a mathematical, abstract, higher-dimensional space called Hilbert space. The geometry of this abstract space can be described using topology, the mathematical study of shapes and spaces, and how they're twisted, stretched and squished. It’s the topology of this wavefunction-spaces that gives rise to the surprising quantum properties of certain materials.

“We had to re-design our spectrometers and develop new measurement tools and schemes to probe the topology of this quantum wavefunction-space,” says Hasan, whose experiments are supported by an Emergent Phenomena in Quantum Systems Investigator grant.

Since 2008, for example, Hasan has been studying the magnetic properties of topological materials. In a breakthrough published in *Nature* in 2018, his team discovered that the electrons in a topological magnet made of tin and iron interact unusually strongly. Normally, he explains, the electrons in many topological materials collectively behave like a weakly interacting gas, wandering around without caring much about one another. But in this tin-iron alloy, where the electrons interact strongly, they behaved more like a viscous fluid.

The electron interactions were so strong they acquired their own symmetry. In typical materials, the distribution of electronic charge density mirrors the symmetry of the underlying crystal lattice. In this case, the material’s structure has six-fold symmetry. The electrons’ quantum behaviors, however, feature two-fold symmetry.

The key discovery was that by applying and adjusting a magnetic field, the researchers could rotate this symmetric arrangement of electrons. “That is the first time anybody has seen such a quantum control of magnetic behavior in any topological material,” he says. Such control at the quantum level could mean applications, such as devices that measure weak magnetic fields.

Working along that line, more recent work published in *Nature Physics* in 2019, Hasan’s team found that in certain types of materials called topological kagome magnets the electrons behave collectively, like an almost infinitely massive electron that is strangely magnetic, rather than like individual particles. His team also showed that placing the kagome magnet in a high magnetic field causes the direction of magnetism to reverse. This negative magnetism is akin to having a compass that points south instead of north, or a refrigerator magnet that suddenly refuses to stick.

**Hasan and his team have also studied non-magnetic topological materials that have the property of left or right-handedness, or chirality.** Magnetic systems are chiral; a magnetic field propels a charged particle to move in a spiral path with the same orientation as a curled right hand with the thumb pointing forward, making such a phenomenon right-handed. But the researchers wanted to explore topological materials that were not magnetic but with chirality built into its crystal structure (the double-helix of DNA, for example, has structural chirality).

The team of researchers utilizes their expertise of combining theory and experiment to advance the field. From their calculations, published in *Nature Materials* in 2018, the researchers discovered that all chiral, non-magnetic topological materials would contain particle-like objects called Kramers-Weyl fermions. These are quasiparticles and a type of Weyl fermions, which were first predicted in 1929 by Princeton mathematician and physicist Hermann Weyl, but not identified until Hasan’s group found them in several non-magnetic semimetals, after calculating their topological and spectral properties — a discovery that *Physics World* deemed one of the top ten of 2015. Weyl fermions are massless, and can move unimpeded, among other novel properties, potentially enabling efficient devices with nearly-free-flowing electricity.

The team followed up their calculations with experiments on real materials, reporting their results again in *Nature*. They found that non-magnetic chiral topological materials (dubbed “Topological Chiral Crystals” ) occur naturally, in, for instance rhodium silicide family of materials. “We're finding all these bizarre and subtle quantum effects in these materials that were never seen before as reported in this paper,” Hasan says. “More importantly, it is indeed immensely satisfying when you predict something exotic and it also appears in the laboratory experiments” Hasan said.

In addition to possessing Kramer-Weyl fermions, this class of material can boast other bizarre — and potentially useful — properties. For example, they are predicted to exhibit the quantized photogalvanic effect, in which light can induce a quantized current—one that exists in discrete quantities. No other kind of material has this ability, Hasan says, which can be useful for optics, photonic devices, and spintronics, which is technology that exploits the spins of particles rather than their electric charge.

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