Abstract
We present a comprehensive theoretical study of the static spin response in HgTe quantum wells, revealing distinctive behavior for the topologically nontrivial inverted structure. Most strikingly, the (long-wavelength) spin susceptibility of the undoped topological-insulator system is constant and equal to the value found for the gapless Dirac-like structure, whereas the same quantity shows the typical decrease with increasing band gap in the normal-insulator regime. We discuss ramifications for the ordering of localized magnetic moments present in the quantum well, both in the insulating and electron-doped situations. The spin response of edge states is also considered, and we extract effective Landé factors for the bulk and edge electrons. The variety of counterintuitive spin-response properties revealed in our study arises from the system’s versatility in accessing situations where the charge-carrier dynamics can be governed by ordinary Schrödinger-type physics; it mimics the behavior of chiral Dirac fermions or reflects the material’s symmetry-protected topological order.
1 More- Received 29 June 2015
DOI:https://doi.org/10.1103/PhysRevX.6.021010
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Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Ordinary materials are classified as either metals, semiconductors, or insulators. But a recently discovered new materials class called topological insulators intriguingly combines aspects of all three: They have metallic surfaces and are insulating in the bulk, and the most paradigmatic realizations of such systems occur in semiconductor nanostructures. Topological insulators are known to exhibit very unusual electric properties. Here, we reveal their magnetism to be of an exotic type as well, opening up avenues for creating novel types of magnets.
In addition to carrying electric charge, electrons also have an internal magnetic degree of freedom called spin that causes them to behave like tiny permanent magnets. Like compass needles, the spins of electrons tend to align with an applied magnetic field and also with each other. These effects give rise to paramagnetism and ferromagnetism, two well-understood spin-related phenomena exhibited by electrons in ordinary materials. Investigating the analogous magnetic properties of topological insulators, we find unconventional magnetism originating from a peculiar quantum-physical effect. Hiding under the blanket of the uncertainty principle, electrons can make transitions across the narrow band gap in the topological insulator that would normally be forbidden by energy conservation, and the special character of these virtual transitions in a topological insulator gives rise to the material’s unusual magnetic behavior.
Our findings are obtained from calculating the static spin susceptibility of the paradigmatic topological insulator formed in mercury-telluride quantum wells. Besides describing how electrons in the material will mediate the alignment between deliberately introduced spin-carrying defects, we also characterize paramagnetism of conduction electrons in the doped topological insulator by deriving effective gyromagnetic ratios, revealing opposite trends in their dependence on physical parameters to those seen in ordinary materials.