Blocking infinity in a topological insulator

February 8, 2013 by Paul Preuss, Lawrence Berkeley National Laboratory
Blocking infinity in a topological insulator
The hybrid band structure of the compound topological insulator bismuth telluride, thinly layered with pure bismuth, as drawn by ARPES: the relative intensity of the bands changes with increasing energy of x-ray photons from the Advanced Light Source (left to right). The unmoving vertical line that connects the apex of bismuth telluride’s surface valence band (below) with the apex of the hybrid band (above) is a sign of surface many-body interactions.

(—In bulk, topological insulators (TIs) are good insulators, but on their surface they act as metals, with a twist: the spin and direction of electrons moving across the surface of a TI are locked together. TIs offer unique opportunities to control electric currents and magnetism, and new research by a team of scientists from China and the U.S., working with Berkeley Lab's Alexei Fedorov at beamline 12.0 at the Advanced Light Source, points to ways to manipulate their surface states.

Graphene, a single layer of , shares an intriguing property with TIs. In both, their band structures – the energies at which electrons flow freely in a or are bound to atoms in a – are quite unlike the overlapping bands of metals, the widely separated bands of insulators, or a semiconductor's narrow between bands. In graphene and TIs, conduction and valence bands form cones that meet at a point, the Dirac point.

Here their resemblance ends. Graphene's perfect cones give only a sketchy view of the real band structure: a deviation from perfectly straight lines shows up when all possible interactions of electrons on their way across the carbon-atom lattice are included – a process called "renormalization." Renormalizing the near the Dirac point (in other words, drawing the tips of the cones) requires understanding the of numerous electrons and positively charged holes (absences of electrons, also known as quasiparticles).

Renormalization has been observed in graphene, but not in TIs – until now, and doing it took a trick. The researchers studied different TI compounds using angle-resolved photoemission spectroscopy (ARPES) at 12.0, which has the unique ability to image electronic band structures directly. They took spectra of two promising topological insulators, bismuth telluride and bismuth selenide.

TIs have two sets of band structures, echoing the difference between their bulk and surface properties, and when ARPES imaged the sample compounds "naked," the bulk bands obscured the surface cones and Dirac points. But after layering films of pure bismuth, which is also a TI, onto the compounds, the pesky bulk bands vanished.

In one layered compound, bismuth on bismuth telluride, ARPES dramatically revealed the Dirac point—in fact two of them. Two sets of converging lines showed up, one meeting at the apex of bismuth telluride's surface valence band and the other at a higher energy. A bright vertical line connected the tips of the two cones.

If the cones were really separated, the charged particles between them would have infinite velocity. But after analysis, the researchers determined that the ARPES spectrum was a hybrid, and that the tell-tale vertical line originated from many-body interactions that were the sign of the infinity-blocking renormalization they were seeking.

What makes many-body interactions difficult to detect in TIs is that, unlike graphene, their surface band structures are spin polarized, or "helical." By hybridizing two especially well matched TIs and skewing their Dirac cones, the hidden renormalization has been found – in at least one TI structure.

Explore further: Beyond the high-speed hard drive: Topological insulators open a path to room-temperature spintronics

More information: … /1218104110.abstract

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1 / 5 (2) Feb 08, 2013
Looks like it's related to the Flux Capacitor of the Delorean Time Machine in 'Back to the Future'.
1 / 5 (2) Feb 09, 2013
It's not so difficult to imagine it. The topological insulator is behaving with respect to movable electrons like the hydrophobic sponge with respect to mercury: the electrons are expelled from its pores and they collect at its surface, when they form a conductive layer. Because of it the electrons are mutually compressed each other and their repulsive forces are compensated in certain points, so that the electrons transfer their charge freely there in similar way, like the electrons within superconductors or at the surface of graphene. The renormalization is mathematical procedure used in quantum field theories for reconciliation of mutually inconsistent extrinsic perspective of quantum mechanics and intrinsic perspective of general relativity. At the case of topological insulators the renormalization means that the electrons are moving so chaotically that their collective behavior from intrinsic perspective becomes blurred with their behavior from extrinsic perspective.
1 / 5 (2) Feb 09, 2013
The phase transition of electrons compressed at the surface of the topological insulator can be simulated easily both physically, both at the computer with array of particles which are mutually repulsing at the large distance (so-called plasma crystal). When the mutual compression of particles will exceed certain limit, then the particles will form a chaotic fluid, which will exhibit a foamy density fluctuations (in similar way, like the virtual particles inside of vacuum in accordance to dense aether model). So instead of clusters of electrons with positive curvature we suddenly have the foamy density fluctuations of the opposite curvature - a topological inversion of system happens there and the low-dimensional formal solutions of system from both sides will become singular.
1 / 5 (2) Feb 09, 2013
One the option how to solve such a situation numerically is to use the hyperdimensional model, which suffers with high number of hidden parameters and low stability. The renormalization procedure just helps to cross this "critical point" without resorting to poorly conditioned hyperdimensional models. It's based on the fact, that whereas the function describing the behavior of system from both sides of singularity diverge, their higher derivations limit to singular point more smoothly - so they can be used for finding of common averaged solution. The wild behavior of physical model at the singular point will get blurred and smoothed in this way. The renormalized solution is sorta unphysical in this way, but it helps to apply the low-dimensional models to the high-dimensional systems smoothly.
1 / 5 (2) Feb 09, 2013
Note that at the above simulation the particles tend to form a hexagonal mesh. The distribution of electrons at the surface of topological insulator therefore follows a hexagonal Mott lattice around singular points, which is easier to imagine in 3D. The existence of hexagonal distribution of electrons at the surface can be therefore analyzed with polarized light shinning at it under low angle (ARPES method), which will release the photoelectrons just at the moment, when the plane of polarization of light will become collinear with the orientation of Mott lattice.
1 / 5 (1) Feb 10, 2013
"The wild behavior of physical model at the singular point will get blurred and smoothed in this way. The renormalized solution is sorta unphysical in this way". As is the Infinite Improbability Drive from The Hitchhiker's Guide to the Galaxy.
1 / 5 (2) Feb 10, 2013
Best example of what renormalization does and cannot do is the reconciliation of relativity and quantum mechanics. These theories are describing abstract four-dimensional multiverses, which are separated with many dimensions each other. You should be able to derive the trees, bees, grass and human beings with renormalization, which of course isn't possible, until you working in four-dimensional space-time.

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