Topological invariants of time-reversal-invariant band structures

Moore, Joel E.; Balents, Leon

doi:10.1103/physrevb.75.121306

Cited by 2,301 publications

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“…This proximity effect has been proposed as a powerful resource for practical applications in optoelectronics 3 and has been predicted to produce the elusive Majorana fermion 4 by combining a superconductor with a topological insulator (TI) [5][6][7][8][9][10] . These goals have been pursued actively, including the recent demonstrations of novel semiconductor light sources 11 and induced superconductivity in TIs [12][13][14][15][16] such as Bi 2 Se 3 and Bi 2 Te 3 , which have been shown to have topologically protected surface states [17][18][19] .…”

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Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3

et al. 2012

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Interest in the superconducting proximity effect has been reinvigorated recently by novel optoelectronic applications as well as by the possible emergence of the elusive majorana fermion at the interface between topological insulators and superconductors. Here we produce high-temperature superconductivity in Bi 2 se 3 and Bi 2 Te 3 via proximity to Bi 2 sr 2 CaCu 2 o 8 + δ , to access higher temperature and energy scales for this phenomenon. This was achieved by a new mechanical bonding technique that we developed, enabling the fabrication of highquality junctions between materials, unobtainable by conventional approaches. We observe proximity-induced superconductivity in Bi 2 se 3 and Bi 2 Te 3 persisting up to at least 80 K-a temperature an order of magnitude higher than any previous observations. moreover, the induced superconducting gap in our devices reaches values of 10 mV, significantly enhancing the relevant energy scales. our results open new directions for fundamental studies in condensed matter physics and enable a wide range of applications in spintronics and quantum computing.

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Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3

et al. 2012

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“…T he helical Dirac fermions that exist on the surface of topological insulators (TIs) are condensed matter analogues of relativistic fermions extensively studied in high-energy physics [1][2][3][4][5][6] . Many theoretical scenarios in high-energy physics such as Majorana fermions and axion electrodynamics are also anticipated to manifest experimental signatures in TIs 2, 7-9 .…”

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Ripple-modulated electronic structure of a 3D topological insulator

et al. 2012

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3D topological insulators, similar to the Dirac material graphene, host linearly dispersing states with unique properties and a strong potential for applications. A key, missing element in realizing some of the more exotic states in topological insulators is the ability to manipulate local electronic properties. Analogy with graphene suggests a possible avenue via a topographic route by the formation of superlattice structures such as a moiré patterns or ripples, which can induce controlled potential variations. However, while the charge and lattice degrees of freedom are intimately coupled in graphene, it is not clear a priori how a physical buckling or ripples might influence the electronic structure of topological insulators. Here we use Fourier transform scanning tunneling spectroscopy to determine the effects of a one-dimensional periodic buckling on the electronic properties of Bi 2 Te 3. By tracking the spatial variations of the scattering vector of the interference patterns as well as features associated with bulk density of states, we show that the buckling creates a periodic potential modulation, which in turn modulates the surface and the bulk states. The strong correlation between the topographic ripples and electronic structure indicates that while doping alone is insufficient to create predetermined potential landscapes, creating ripples provides a path to controlling the potential seen by the Dirac electrons on a local scale. Such rippled features may be engineered by strain in thin films and may find use in future applications of topological insulators.

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“…Until the mid-2000s, the quantum Hall effect and other topological effects had been seen only in the presence of strong magnetic fields. But Kane and his colleagues 3 , and separately another team 4 , realized that some insulators made from heavy elements could provide their own magnetic fields through internal interactions between electrons and atomic nuclei. This gave electrons on the surface of the material robust, 'topologically protected' states, which allowed them to flow with next to no resistance.…”

Section: Physics With a Twistmentioning

confidence: 99%

The strange topology that is reshaping physics

Castelvecchi¹

2017

Nature

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Charles Kane never thought he would be cavorting with topologists. "I don't think like a mathematician, " admits Kane, a theoretical physicist who has tended to focus on tangible problems about solid materials. He is not alone. Physicists have typically paid little attention to topology -the mathematical study of shapes and their arrangement in space. But now Kane and other physicists are flocking to the field.In the past decade, they have found that topology provides unique insight into the physics of materials, such as how some insulators can sneakily conduct electricity along a single-atom layer on their surfaces.Some of these topological effects were uncovered in the 1980s, but only in the past few years have researchers begun to realize that they could be much more prevalent and bizarre than anyone expected. Topological materials have been "sitting in plain sight, and people didn't think to look for them", says Kane, who is at the University of Pennsylvania in Philadelphia.Now, topological physics is truly exploding: it seems increasingly rare to see a paper on solid-state physics that doesn't have the word topology in the title. And experimentalists are about to get even busier. A study on page 298 of this week's Nature unveils an atlas of materials that might host topological effects 1 , giving physicists many more places to go looking for bizarre states of matter such as Weyl fermions or quantum-spin liquids.Scientists hope that topological materials could eventually find applications in faster, more efficient computer chips, or even in fanciful quantum computers. And the materials are already being used as virtual laboratories to test predictions about exotic and undiscovered elementary particles and the laws of physics. Many researchers say that the real reward of topological physics will be a deeper understanding of the nature of matter itself. "Emergent phenomena in topological physics are probably all around us -even in a piece of rock, " says Zahid Hasan, a physicist at Princeton University in New Jersey.Some of the most fundamental properties of subatomic particles are, at their heart, topological. Take the spin of the electron, for example, which can point up or down. Flip an electron from up to down, and then up again, and you might think that this 360° rotation would return the THE SHAPE OF THINGS TO COME Strange topological effects might be hiding inside perfectly ordinary materials. Finding them could reveal new particles, deliver superfast transistors and even bolster quantum computing.

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Topological invariants of time-reversal-invariant band structures

Cited by 2,301 publications

References 19 publications

Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3

Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3

Ripple-modulated electronic structure of a 3D topological insulator

The strange topology that is reshaping physics

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