A Perfect Gain Medium for Lasers

Light emission resulting from a mutual annihilation of electrons and holes is the operating principle of semiconductor lasers. (Source: E. Khavina, MIPT)

Weyl semimetals are a recently discovered class of materials, in which charge carriers behave the way electrons and positrons do in particle acce­lerators. Researchers from the Moscow Institute of Physics and Tech­nology and Ioffe Institute in St. Petersburg have shown that these materials represent perfect gain media for lasers. The 21st-century physics is marked by the search for pheno­mena from the world of funda­mental particles in tabletop materials. In some crystals, electrons move as high-energy particles in acce­lerators. In others, particles even have pro­perties somewhat similar to black hole matter. MIPT physicists have turned this search inside-out, proving that reactions forbidden for elementary particles can also be forbidden in the crystal­line materials known as Weyl semimetals. Specifically, this applies to the forbidden reaction of mutual particle-anti­particle anni­hilation without light emission. This property suggests that a Weyl semimetal could be the perfect gain medium for lasers.

In a semi­conductor laser, radiation results from the mutual anni­hilation of electrons and the positive charge carriers. However, light emission is just one possible outcome of an electron-hole pair collision. Alter­natively, the energy can build up the oscil­lations of atoms nearby or heat the neighboring electrons, the Auger recom­bination. Auger recom­bination limits the effi­ciency of modern lasers in the visible and infrared range, and severely undermines terahertz lasers. It eats up electron-hole pairs that might have otherwise produced radiation. Moreover, this process heats up the device.

For almost a century, researchers have sought a wonder material in which radiative recom­bination dominates over Auger recom­bination. This search was guided by an idea formulated in 1928 by Paul Dirac. He developed a theory that the electron, which had already been discovered, had a posi­tively charged twin particle, the positron. Four years later, the prediction was proved experi­mentally. In Dirac’s calculations, a mutual annihi­lation of an electron and positron always produces light and can not impart energy on other electrons. This is why the quest for a wonder material to be used in lasers was largely seen as a search for analogues of the Dirac electron and positron in semi­conductors.

“In the 1970s, the hopes were largely associated with lead salts, and in the 2000s – with graphene,” says Dmitry Svintsov, the head of the Laboratory of 2D Materials for Opto­electronics at MIPT. “But the particles in these materials exhibited deviations from Dirac’s concept. The graphene case proved quite patho­logical, because confining electrons and holes to two dimensions actually gives rise to Auger recom­bination. In the 2D world, there is little space for particles to avoid colli­sions. Our latest paper shows that Weyl semimetals are the closest we’ve gotten to realizing an analogy with Dirac’s electrons and positrons,” added Svintsov.

Electrons and holes in a semi­conductor do have the same electric charges as Dirac’s particles. But it takes more than that to eliminate Auger recom­bination. Laser engineers seek the kind of particles that would match Dirac’s theory in terms of their dispersion relations. The latter tie particle’s kinetic energy to its momentum. That equation encodes all the information on particle’s motion and the reactions it can undergo. In classical mechanics, objects such as rocks, planets, or spaceships follow a quadratic dispersion equation. That is, doubling of the momentum results in four-fold increase in kinetic energy. In conven­tional semi­conductors – silicon, germanium, or gallium arsenide – the dispersion relation is also quadratic. For photons, the quanta of light, the dispersion relation is linear. One of the conse­quences is that a photon always moves at precisely the speed of light.

The electrons and positrons in Dirac’s theory occupy a middle ground between rocks and photons: at low energies, their dispersion relation is quadratic, but at higher energies it becomes linear. Until recently, though, it took a particle acce­lerator to catapult an electron into the linear section of the dispersion relation. Some newly discovered materials can serve as pocket acce­lerators for charged particles. Among them are the pencil-tip acce­lerator – graphene and its three-dimen­sional analogues, the Weyl semimetals: tantalum arsenide, niobium phosphate, molybdenum telluride. In these materials, electrons obey a linear dispersion relation starting from the lowest energies. That is, the charge carriers behave like electri­cally charged photons. These particles may be viewed as analogous to the Dirac electron and positron, except that their mass approaches zero.

The researchers have shown that despite the zero mass, Auger recom­bination still remains forbidden in Weyl semi­metals. Foreseeing the objection that a dispersion relation in an actual crystal is never strictly linear, the team went on to calculate the probability of residual Auger recom­bination due to deviations from the linear law. This proba­bility, which depends on electron concentration, can reach values some 10,000 times lower than in the currently used semi­conductors. In other words, the calcu­lations suggest that Dirac’s concept is rather faithfully reproduced in Weyl semimetals.

“We were aware of the bitter experience of our prede­cessors who hoped to reproduce Dirac’s dispersion relation in real crystals to the letter,” Svintsov explained. “That is why we did our best to identify every possible loophole for potential Auger recom­bination in Weyl semimetals. For example, in an actual Weyl semimetal, there exist several sorts of electrons, slow and fast ones. While a slower electron and a slower hole may collapse, the faster ones can pick up energy. That said, we calculated that the odds of that happening are low.”

The team gauged the lifetime of an electron-hole pair in a Weyl semimetal to be about 10 nano­seconds. That timespan looks extremely small by everyday standards, but for laser physics, it is huge. In conventional materials used in laser technology of the far infrared range, the lifetimes of electrons and holes are thousands of times shorter. Extending the lifetime of non­equilibrium electrons and holes in novel materials opens up prospects for using them in new types of long-wave­length lasers. (Source: MIPT)

Reference: A. N. Afanasiev et al.: Relativistic suppression of Auger recombination in Weyl semimetals, Phys. Rev. B 99, 115202 (2019); DOI: 10.1103/PhysRevB.99.115202

Link: Laboratory of Nanooptics and Plasmonics, Moscow Institute of Physics and Technology, Dolgoprudny, Russia

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