Clearing the Way for Floquet-Bloch States

Estimated reading time: 6 minutes

In 2013, MIT physicists showed for the first time that shining powerful mid-infrared laser light on solid bismuth selenide produces Floquet-Bloch states, which are characterized by replicas of electronic energy states inside a solid with gaps opening up at crossing points of replica states. The same external light also interacts with free electron states immediately outside the solid producing a competing state, called the Volkov state, which is gapless.

Now, researchers led by Nuh Gedik, the Lawrence C. (1944) and Sarah W. Biedenharn Career Development Associate Professor of Physics, have shown that changing the light’s polarization eliminates competition from Volkov states, yielding pure Floquet-Bloch states.

MIT graduate student Fahad Mahmood and postdoc Ching Kit (Chris) Chan, demonstrate experimental proof and offer a mathematical framework for understanding interference between these competing states as a function of electron momentum. The results are published online in Nature Physics.

“Fahad figured out a clever way of quantifying the interference of these two states with each other, and then from this interference, we can deduce selectively, this part is coming from the outside, this part is coming from inside,” says Gedik, who is senior author on the new work. “I think this is a big step because if you eventually want to realize a new state of matter based on periodic excitation, you really need to be able to isolate just the contribution of the electrons inside the solid.”

MIT co-authors of the study are Zhanybek Alpichshev, a postdoc in Gedik’s group; recent physics alumnus Dillon R. Gardner PhD ’15; Professor Young S. Lee; and William and Emma Rogers Professor of Physics Patrick A. Lee.

Proportional bandgap

Floquet-Bloch states, occurring on incredibly fast time scales, are observed using an experimental technique called time-and-angle-resolved photoemission spectroscopy (Tr-ARPES). This consists of using a mid-IR laser pulse, with energy below the bulk band gap of the material, to stimulate electrons in the solid. A second laser pulse, at a lesser intensity, overlaps the first and leads to emission of electrons, which are collected in a time-of-flight analyzer that records their angle of emission and energy. “We study the photoemitted electron intensity as a function of the electron energy and momentum,” Gedik says. “If you’re using this technique, it’s super important to be able to selectively, only, probe the photo-excited state inside the solid, and this paper gives you a way,” Gedik explains.

The researchers also show that the value of the artificially induced bandgap is proportional to the square root of the intensity of the light. “That really means it is proportional to the electric field, rather than the intensity, so this is what is actually expected from all this theory work that this gap would actually scale with the electric field of the light,” Gedik says.

The new work yields higher resolution for experimental demonstrations of replica electronic levels, which are also called sidebands, and also offers a theoretical explanation for distinguishing Floquet states from Volkov states. “It was very helpful to have Patrick Lee and his postdoc [Chan] help with the theory. I think it would have been very challenging without their help,” Mahmood says. “That close collaboration helped us a lot because now we can make predictions of exactly how the interference would behave as a function of this electron momentum and you can see that theory and experiment match really well for different directions of electron momentum.”

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