Why topological insulators

Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.

Haldane, F. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the 'parity anomaly'. Murakami, S. Spin-Hall insulator. Kane, C. Z2 topological order and the quantum spin Hall effect. This paper explains the theoretical requirements for a non-magnetic material to be a 2D topological insulator, with a quantum spin Hall effect. Bernevig, B. Quantum spin Hall effect and topological phase transition in HgTe quantum wells.

Science , — Quantum spin Hall insulator state in HgTe quantum wells. This paper reports the first experimental observation of a 2D topological insulator that has a quantum spin Hall effect. Fu, L. Topological insulators in three dimensions. Moore, J. Topological invariants of time-reversal-invariant band structures.

B 75 , R Roy, R. Topological phases and the quantum spin Hall effect in three dimensions. B 79 , Ran, Y. One-dimensional topologically protected modes in topological insulators with lattice dislocations.

Nature Phys. Hsieh, D. A topological Dirac insulator in a quantum spin Hall phase. Nature , — By using ARPES experiments, this study observed a 3D topological insulator, the theoretical predictions for which were made in refs 6 , 7 , 8. Observation of unconventional quantum spin textures in topological insulators. Xia, Y.

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Zhang, H. References 12 and 13 report experiments and theory on next-generation topological insulator materials, which have a large bandgap and a single surface Dirac cone; these are the most promising materials for future experiments. Chen, Y. Experimental realization of a three-dimensional topological insulator, Bi2Te3.

Castro Neto, A. The next step is to uncover more exotic types of anyons, such as Majorana fermions. Two distinct topological states that are closely tied to the spin configurations of a layered compound, here MnBi 2 Te 4 , have been demonstrated. Such control of the topological state should enable new opportunities to realize quantum and spintronic devices.

Research Highlights 20 November Topological insulator band theory usually neglects electron correlations as these are overridden by spin—orbit coupling. Now, two papers strongly confine 1D topological edge states in order to study the effect of correlations. Inducing a topological phase transition by applying pressure is shown to be a successful strategy for improving the performance of thermoelectric materials.

Research Highlights 14 November Two studies published in Phys. Advanced search. Skip to main content Thank you for visiting nature. Atom RSS Feed Topological insulators Definition Topological insulators are materials that are insulating in their interior but can support the flow of electrons on their surface.

Research 09 November Open Access Four-band non-Abelian topological insulator and its experimental realization Non-Abelian topological insulators receive increasing attention due to entangled bulk bandgaps different from Abelian counterparts.

To learn more, read our Privacy Policy. In science, the usual order is that experiments reveal something and then theorists explain it afterward, if at all. A classic example is superconductivity. It was first noticed in , but it took theorists nearly 50 years to come up with an explanation, and even that explanation does not apply to every superconducting material. But once in a while, we theorists hit on things all by ourselves. And once in a long while, that something turns out to be technologically useful.

Now is one of those times. This is the story of a remarkable theory, hatched in the middle of the past decade, that experimentalists have been pursuing ever since. It is particularly sweet because it is linked to a branch of mathematics—topology—that had until now been mostly beyond any hope of practical application.

And the discovery is about as straightforward as it gets: It is possible to produce materials that are insulators on the inside but conductors on the outside. This is heady stuff, for engineers and physicists alike. The mobility, or speed, of the surface electrons in these materials is increasing dramatically every year. Just as important is their intrinsic stability, a quality that suggests they'd be robust enough to work in practical devices, such as extremely high-capacity interconnects and, one day, maybe even practical quantum computers.

Physicists, meanwhile, are deeply intrigued by the possibility of using such materials to simulate new particles and other items of theoretical interest. Topology is the branch of mathematics concerned with aspects of form that can't be fundamentally altered by stretching. A typical example is the hole of a doughnut : Let's say you deform the doughnut into the shape of a coffee cup. What had been the hole in the doughnut is now the "hole" in the cup's handle. Mathematicians call such features topologically invariant.

They can, paradoxically, appear even in a seemingly formless substance such as an electron gas, produced when electrons are confined so that they move in only two dimensions.

In fact, the ability of such a gas to be topologically complex is what led to these new materials. Until recently, electron gases had been found only at the junction of two semiconductors having different electronic properties. These gases are crucial for high electron mobility transistors HEMT s , a form of field-effect transistor used in radar, imaging, and other applications that require high gain at high frequencies.

However, the idea of a 2-D electron gas that exists at the surface of an insulator—and is topologically protected from disorder—was a revelation that emerged from theoretical work done in and Working independently, my group at the University of California Berkeley and Santa Barbara and researchers at the University of Pennsylvania and the University of Illinois predicted the existence of "topological insulators," which have insulating interiors but metallic surfaces.

We also predicted that though these surfaces would be atomically thin, they would nevertheless be remarkably impervious to disorder and other effects that would tend to destroy their conductivity. That is, they would resist fundamental change, much as the hole does in a stretching, twisting doughnut. Experimentalists confirmed these predictions in , working with compounds of bismuth.

This success triggered an explosion of experimental and theoretical work that continues to this day. Because of their unique conductive properties, topological insulators will extend the bag of tricks available with electronic devices. There is reason to hope that these topological tricks will transform electronics by making it possible to create robust 2-D electronic gases of arbitrary shape and by allowing the simple manipulation of the spin of an electron.

Electron spin is already a crucial property for magnetic storage in your hard drive; topological insulators may also allow it to be used for logic, replacing the microprocessor in your computer with a more energy-efficient and potentially faster design. First, though, a little background. Okay, a lot of background. Remember, in this case the theory is not an afterthought; it's the main story.

To understand topological insulators, you must first grasp how a conventional semiconductor junction creates a 2-D electron gas. This issue is not merely academic—the same technique it's called modulation doping used to create the best such gases for academic research is also used to create the HEMTs in cellphones and other demanding applications.

A central idea of quantum mechanics is that electrons confined to a small spatial volume take on the properties of electrons confined within atoms or molecules. Confined electrons can have only certain discrete energy levels, or "eigenstates.

Scientists have learned how to confine an electron's motion in one, two, or all three directions, creating what are known as quantum wells, wires, and dots, respectively.

Quantum dots are occasionally referred to as artificial atoms , because the confined electron's energy levels resemble those of an atom. In a quantum well, an electron moves freely in two directions, but in the third one it bumps up against a wall, called a trapping potential; if the trapping potential is strong enough, the electrons will be confined in the lowest-energy eigenstate in this direction.

The electron can't change how it moves in this confined condition unless a shot of energy kicks it to an excited state, something that won't happen if the temperature's low enough.

Consequently, we say that electron motion in the third direction is frozen out, that is, totally fixed; the electrons therefore move in only two directions. In other words, they're perfectly arranged in a plane, which we call a 2-D electron gas.

Semiconductors are good at creating these confined electronic states because they react sensitively to changes in their environment. Despite its name, a pure semiconductor is actually an insulator. To make it conduct first requires doping with an impurity that provides an excess of charge carriers, either electrons or holes.

Properly arranged and packaged, devices consisting of several layers of these semiconductors will conduct well only when you apply an electrical field to one of the layers by means of an external voltage or current. In a 2-D electron gas, the charge carriers concentrate at the interface between two different layers—for example, a layer of gallium arsenide against one of aluminum gallium arsenide. Modulation doping is a way of keeping the doping impurities away from the interface where the electrons travel.

As a result, the charge carriers in the 2-D electron gas can move almost perfectly freely. At low temperature, in a gas contained in AlGaAs-GaAs structures, electrons can travel, on average, several millimeters before colliding with an impurity, a distance many times farther than in a typical metal. The conducting nature of the surface layers of topological insulators has to do with an aspect of the electron's quantum soul: its spin. Spin is the elusive quantum-mechanical property that underlies magnetism.

Cava , a chemist who heads the Solid State Chemistry Research Group at Princeton, is fascinated by the idea that he can make crystals that might demonstrate the existence of fundamental particles known as Majorana fermions that are predicted by theory to exist but that have never been definitively observed in nature.

But the elements that are good at forming topological materials are also ones that are difficult for chemists to work with. Heavy metals such as mercury and thallium are poisonous and thus require more stringent safety procedures when handling, Cava says. Alkali and alkaline earth metals tend to react with air. Making trisodium bismuthide, which has topological properties, entails getting a crystal to grow from molten sodium.

And the topological insulator potassium mercury antimonide? The search for topological materials is becoming more systematic. The theoretical paper published by Bernevig and Felser laid out a method for determining whether a material is topological. If a chemist knows the elements in a material, its crystal structure, and the position of its atoms, their method will tell whether it ought to have topological properties.

The two are in the process of combing through the hundreds of thousands of inorganic compounds that have been described in the literature to see which ones might be worth experimenting on. Beyond its promise for finding specific compounds with interesting properties, the study of topological matter also provides a new way to think about materials and to classify them into a new sort of periodic table.

Materials that were thought of as being different may be more similar when examined through the lens of topology. They may have very different structures. Related: Quantum computing goes beyond hydrogen and helium. That could allow chemists to search materials more systematically for desirable properties. Neil Savage is a freelance writer. Contact the reporter. Submit a Letter to the Editor for publication. Engage with us on Twitter. The power is now in your nitrile gloved hands Sign up for a free account to increase your articles.

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