Spying on Topology

Topological insulators are quantum materials, which, due to their exotic electronic structure, on surfaces and edges conduct electric current like metal, while acting as an insulator in bulk. Scientists from the Max Born Institute for Nonlinear Optics and Short Pulse Spectro­scopy MBI have demonstrated for the first time how to tell apart topo­logical materials from their regular – trivial – counter­parts within a millionth of a billionth of a second by probing it with ultra-fast laser light. Their method could open the way for such materials to be used as logic elements in light-controlled electronics able to process infor­mation tens of thousands times faster as currently possible.

The direction of rotation of the light maps the topological phase diagram of the system, distinguishing between its trivial phase and its topological phase. (Source: MBI)

The most common illus­tration of the topology concept involves an elastic pretzel, which can be stretched, bent, or twisted in any way; no matter the deformation, it is impossible to make a bagel out of a pretzel or add holes to it, without tearing it apart. The number of holes in a pretzel is thus invariant and provides topo­logical information about the pretzel shape. In a solid material, quantum-mechanical laws restrict which energies electrons can have, leading to the formation of bands with either allowed or forbidden energies. Using the concept of topology, physicists can describe complex shapes of allowed energy bands and assign them a specific topo­logical number. A special topology of the band structure in a material system manifests itself in exotic pro­perties that can be observed – such as the surface conduc­tivity in topo­logical insulators.

“The most remarkable aspect of topology is its robustness: properties induced by topology are protected by it,” explains Álvaro Jiménez-Galán from MBI. In the same way that we cannot change the number of holes in a pretzel without breaking it, impurities and other pertur­bations that usually disrupt the ability of the material to conduct electricity do not affect high electron mobility on the surface of topo­logical insu­lators. The immunity to impurities is the reason why topo­logical materials strongly appeal to electronic industries.

Although the topology of the system is deeply linked to the behavior of electrons in it, the imprint of topo­logical properties on electron dynamics at the time scale of a millionth of a billionth of a second has not been discovered up to now. By using numerical simu­lations and theo­retical analysis, the group from MBI has proved that information about system topology is indeed encoded in this extremely fast electron dynamics and can be retrieved by looking at light emitted by electrons as they are excited with laser light. “If we imagine the electrons in a solid moving within energy bands as runners on the racing track, then our method allows to learn about the topo­logy of this racing track, by simply measuring the acce­leration of the runners,” clarifies Olga Smirnova, head of a MBI Theory group. The ultra-short laser pulses excite electrons of the system, making them hop from one energy band to a higher one, acce­lerating them on the new track. The accelerated electrons then emit light and quickly fall back to the lower position.  This process lasts merely an infini­tesimal part of a second but is enough for an electron to “feel” the fine difference between the energy structures of trivial and topo­logical insulators and “encode” this information into the emitted light.

The current work demons­trates how to distinguish between trivial and topological insulators at an ultra-fast rate, in other words, to read out the topological information of the system using laser spectro­scopy. For the next step, the MBI researchers plan to use this knowledge to convert a trivial insulator into a topo­logical and vice versa with laser light – that is to write the topological infor­mation into material at the similar rate. The theoretical proof of this effect could bring forward the imple­mentation of topological materials in optically-controlled elec­tronics, where only the speed of electronic response to light defines the limit for the speed of information processing. (Source: MBI)

Reference: R. E. F. Silva et al.: Topological strong-field physics on sub-laser-cycle timescale, Nat. Phot., online 23. September 2019; DOI: 10.1038/s41566-019-0516-1

Link: Fundamentals of Extreme Photonics, Max-Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Berlin, Germany

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