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Focus: Nobel Prize—Topological Phases of Matter

Focus: Nobel Prize—Topological Phases of Matter

Hole number. If you’re ignoring a figure and usually counting holes, we can smash and widen a pretzel utterly a bit though changing it. To supplement or subtract a hole takes additional effort. Similarly, topological phases have a robustness that allows their properties to sojourn fast in annoy of impurities or other element details.Hole number. If you’re ignoring a figure and usually counting holes, we can smash and widen a pretzel utterly a bit though changing it. To supplement or subtract a hole takes additional effort. Similarly, topological phases have a robustness that allows their p… Show more
Hole number. If you’re ignoring a figure and usually counting holes, we can smash and widen a pretzel utterly a bit though changing it. To supplement or subtract a hole takes additional effort. Similarly, topological phases have a robustness that allows their properties to sojourn fast in annoy of impurities or other element details. [Credit: iStockphoto.com/buyit]

1]. A spiral is a indicate in a captivating film, for example, around that a captivating spins of a atoms asian in a clockwise instruction (orientation in a counterclockwise instruction is called an antivortex). This intent can be utterly robust. “Once a spiral forms, it can be tough to get absolved of it,” explains precipitated matter idealist Steve Simon from Oxford University, UK.

At high temperature, vortices and antivortices are plentiful, and a spins are disordered. However, Kosterlitz and Thouless showed that during low temperatures, vortices span adult with antivortices, partly canceling out their effect. As a result, a spins via a two-dimensional element are means to align with any other to a certain degree. This fixing is a form of “topological order” that also relates some-more generally to 2D systems of atoms (or electrons) that align an aspect of their quantum states—their quantum automatic phases. As such, a Kosterlitz-Thouless (KT) transition explains a presentation of both superfluidity and superconductivity in dual dimensions.

A decade later, Thouless and colleagues again incited to topological arguments in explaining a quantum Hall outcome (QHE). Discovered in 1980, a QHE is, like a exemplary Hall effect, an prompted voltage in a current-carrying conductor unprotected to a captivating field. In a quantum case, however, a conductor is cramped to dual dimensions. When stream flows longitudinally (north-south, say) by a conductor, a cross (east-west) voltage is measured. Surprisingly, as a captivating margin increases gradually, a ratio of stream to voltage (called a Hall conductance) increases by dissimilar jumps; a values are integer multiples of a elemental conductance unit. This quantization does not count on a form of material, or either it contains any defects or impurities. “You would design that throwing ‘dirt’ into a complement would make a outcome go away, though it doesn’t,” says Marcel basement Nijs from a University of Washington, one of Thouless’s co-authors.

To explain this robustness, Thouless’s organisation deliberate all of a call functions that can report electrons in a 2D element and represented this set of possibilities with a winding surface. The figure of this aspect can be personal by a number, called a topological invariant, that has some stability, like a vortices in a KT transition. A common instance of a topological immutable is a series of holes in an object, like a donut or a pretzel. You can crush a pretzel utterly a bit, though a hole count doesn’t change. With some effort, of course, we can puncture or cut a pretzel to make some-more or fewer holes, though a hole count always jumps by an integer volume (there are no half holes). Thouless and his colleagues showed that their subsequent topological immutable was associated to a integers that conclude a Hall conductance steps. This outcome accounted for a quantization and also explained because a QHE is so robust: tiny changes to a element can impact a set of nucleus call functions, though a topological immutable that describes a set is many harder to change.

The thought that topology could be used to impersonate a proviso of matter was also used by Haldane (currently during Princeton University in New Jersey) in his work on spin chains—one-dimensional systems of joined atoms found in captivating materials. “These works started a trend that is totally widespread now, in that we can systematise matter with a topological immutable and not caring about a excellent details,” Simon says. The many distinguished instance of this trend is a margin of topological insulators—materials that usually control electricity on their surfaces. These aspect currents are pronounced to be “protected” by topology from imperfections along a aspect that would routinely means electrons to scatter. This robustness could make these materials useful as rarely fit nanowires or as a basement for storing fast pieces in a quantum computer, says basement Nijs.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics formed in Lyon, France.

References

  1. J. M. Kosterlitz and D. J. Thouless, “Long Range Order and Metastability in Two Dimensional Solids and Superfluids. (Application of Dislocation Theory),” J. Phys. C 5, L124 (1972); “Ordering, Metastability and Phase Transitions in Two-Dimensional Systems,” 6, 1181 (1973).

More Information


Quantized Hall Conductance in a Two-Dimensional Periodic Potential

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. basement Nijs

Phys. Rev. Lett. 49, 405 (1982)

Published Aug 9, 1982

Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of a One-Dimensional Easy-Axis Néel State

F. D. M. Haldane

Phys. Rev. Lett. 50, 1153 (1983)

Published Apr 11, 1983

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