A Materials Perspective on Topological Insulators and Related Electronic Materials
Written by Arthur L. Robinson
For his MRS Medal Award presentation, Robert J. Cava covered three topics: geometrically frustrated magnets, topological insulators, and magnetoresistive materials that collectively show the kinds of challenges faced by crystal growers trying to synthesize novel materials with specific properties, often at the request of their colleagues. Cava illustrated the challenges by retracing the routes that resulted in success, that is, quality crystals with the properties sought.
To illustrate geometrical frustration, Cava first considered the problem of placing magnetic moments that want the nearest neighbors to align antiferromagnetically on a two-dimensional triangular lattice. There is no solution to the problem, and the magnetic moments have to compromise with some ferromagnetic alignment, a situation called geometric frustration. A three-dimensional lattice of tetrahedrons has the same issue. The most complicated lattice based on triangles is called a kagome lattice, and the three-dimensional analog is the pyrochlore lattice, which can be visualized as kagome planes formed by tetrahedron bases separated by planes comprising tetrahedron vertices.
Rare-earth kagome compounds are well-known frustrated magnets, but no rare-earth kagome compounds had been found until recently. The trick was to create a pyrochlore with alternately magnetic and nonmagnetic kagome planes. A comparison of the magnetic properties of a Nd2(ScNb)O7 pyrochlore and the Nd3Sb2Mg2O14 kagome compound showed no gross difference in behavior. However the magnetic ordering temperature of around 0.4 K for both materials was too low for materials studies, suggesting the use of divalent 3d transition elements rather than the f-electron rare earths. This strategy also called for using fluorine to help with the charge balance. After a brave student found a way to make HF gas (a neurotoxin) for the synthesis process, several crystals were made based on cobalt and nickel (e.g., NaCaCo2F7, NaSrCo2F7, NaCaNi2F7), all with magnetic interactions larger than 100 K.
Cava then moved to topological insulators. Normal insulators have roughly parabolic (E ~ k2) conduction and valence bands near the Fermi level. In two- and three-dimensional topological insulators, there are additional metallic edge and surface states with linear dispersion (E ~ k) within the bulk bandgap that arise when the bulk bands would overlap in energy but are separated by strong spin-orbit coupling. Where the surface-state bands cross is called the Dirac point. Symmetry protects these states because their wave vector and spin are coupled, so that backscattering cannot occur without forbidden spin flipping and is thus prevented.
The first three-dimensional topological insulator was Bi0.9Sb0.1. However, the material was difficult for materials physicists to study, owing to a complicated surface-state Fermi surface. Looking for materials with a heavy metal, small bandgap, and the same two-dimensional symmetry as bismuth led to Bi2Se3, which was a topological insulator, but the bulk was too conductive to allow detailed study of the surface states. Cava then began a seven-year search for the perfect bulk-crystal topological insulator based on four primary materials requirements: Very high bulk resistivity so that the transport of charge is dominated by surface states, the surface Dirac point energy is isolated from the bulk energies so that there is no interference from bulk electrons, the surface states “show up” in transport measurements, and the crystals are controllable and reproducible to grow. These requirements led to the Bi2Te3‑xSex series of which Bi2Te2Se turned out to be a very good topological insulator, but still the Dirac point energy was in the valence band. Additional substitutions solved the problem with BiSbTe2S, which Cava said has met all the requirements to be the ideal bulk-crystal topological insulator.
Cava finished with a discussion of magnetoresistance, the phenomenon in which an applied magnetic field changes a material’s resistivity at a fixed temperature. There are several ways in which this can happen, depending on the materials. Giant magnetoresistance (GMR) in thin-film structures composed of alternating ferromagnetic and nonmagnetic conductive layers, for example, is used in read sensor heads for magnetic storage devices. While looking at WTe2 during topical insulator studies, a member of Cava’s laboratory found that this material exhibited a very large magnetoresistance. In high fields up to 60 Tesla, the magnetoresistance did not saturate, reaching a value of 13 million percent, but the mechanism remains a mystery. With improved purity, nearly defect-free crystals exhibited improved magnetoresistance (1.8 million percent at 2 K and 9 Tesla).
The MRS Medal, endowed by Toh-Ming Lu and Gwo-Ching Wang, is awarded for a specific outstanding recent discovery or advancement that has a major impact on the progress of a materials-related field. Robert J. Cava is being honored “for pioneering contributions in the discovery of new classes of 3D Topological Insulators.”