The Fermi-Dirac distribution is distributed at three different temperatures, including absolute zero (blue line). Image credit: Lauro B. Braz/Wikimedia Commons. https://commons.wikimedia.org/wiki/File:FermiDist.png
Researchers from Germany and Singapore studied a non-equilibrium state of Fermi liquid, called Floquet Fermi liquid (FFL), which is formed when Fermi liquid is subjected to periodic driving forces and remains in contact with a fermion bath.
Fermi liquids are quantum mechanical systems in which fermions, such as electrons in metals, collectively behave predictably at absolute zero temperatures, equivalent to 0 Kelvin or -273.15°C.
Fermions are one of the two classes of elementary particles in the universe that obey Fermi-Dirac (FD) statistics. This describes their distribution when the system is in thermal equilibrium.
Here we come across an interesting quantum system called Fermi liquid. The term "Fermi liquid" comes from the idea that, similar to how liquids flow freely and can change shape, the fermions in Fermi liquids move relatively freely in the material due to their collective behavior.
In the case of Fermi liquids, the behavior of fermions is characterized by Fermi surfaces. The Fermi surface marks the separation of the energy states of the Fermi liquid, indicating the filled and empty energy states occupied by the fermions.
The motivation of the researchers was to understand what happens to the electrons when a periodic driving force is applied to them, combined with a fermion thermal bath.
The study, published in Physical Review Letters, was conducted by Dr. Li-kun Shi and Dr. Inti Sodemann Villadiego from the University of Leipzig, Germany, and Dr. Oles Matsyshyn and Dr. Justin C. W. Song from Nanyang Technological University, Singapore.
Phys.org spoke with the researchers, and they cite a larger question they hope to answer: Does photocurrent (the current produced to illuminate a material) exist in pure bulk crystals such as metals and semiconductors, even though the material does not absorb light?
This question led them to Floquet's Fermi liquid.
Floquet Fermi liquid
In Fermi liquids, the energy state is continuous, the full energy state is lower than the Fermi energy, and the empty state is higher than the Fermi energy. The Fermi level marks the transition of the probability of finding a fermion state from an energy level close to 100% occupied to one that is close to 0% occupied.
At absolute zero, all states before Fermi energy are filled, while all states above Fermi energy are empty. This energy level effectively defines the Fermi surface in momentum space: a theoretical concept that helps visualize what is happening inside matter.
When we apply a periodic force to a Fermi liquid, its normal energy level is modified to the Floquet band, which is the energy level of the Fermi liquid that changes due to the driving force. Think of it as ripples that form on the surface of the water.
Researchers now want to understand what would happen if this system was far from equilibrium. To do this, the researchers introduced the fermion bath, which is a reservoir or environment made up of fermions.
The researchers found that the resulting Fermi liquid is in a non-homeostatic trivial state, called Floquet Fermi liquid. They found that the resulting liquid did not match typical FD statistics.
FD stairs and nested surfaces
In this case, the FFL state is considered non-trivial because it is the result of periodic driving forces, fermion interactions, and ambient interactions.
The smooth transition of the energy state, similar to the single jump typically observed in the equilibrium FD distribution, the occupation of the energy state shows a staircase-like pattern with multiple jumps.
"Every jump leads to the emergence of a new Fermi (Floquet)," Dr. Shi explains.
"Floquet Fermi surfaces in the FFL state are closed to each other," adds Dr. Matsyshyn.
Think of it as a layered Fermi surface, similar to the matryoshka doll situation in Russia. These floating Fermi surfaces affect the behavior of the entire system, resulting in specific phenomena.
Runout modes in quantum oscillations and controlling electronic behavior
Quantum oscillations are periodic changes in material properties, such as electrical resistance, as a function of external parameters such as magnetic field or pressure.
In the case of FFL, the researchers observed a runout pattern in quantum oscillations under the influence of an external magnetic field.
These patterns are created due to interference between Floquet Fermi surfaces of different sizes, which are nested within each other. The presence of multiple Floquet Fermi surfaces results in constructive and destructive interference effects, resulting in resistive oscillations.
"The runout mode in the quantum oscillation is consistent with the microwave-induced resistance oscillation (MIRO) experiments observed in two-dimensional electronic systems," Dr. Song explained.
They also provide a way to design and customize the electronic behavior of the system.
Dr. Villadiego said: "The presence of multiple Fermi surfaces allows for a better control of the system's electronic characteristics. By adjusting the frequency or intensity of light, we can manipulate the shape and separation of Floquet Fermi surfaces.
This opens up new possibilities for controlling electronic behavior.
Potential applications and insights
One of the most interesting lessons the researchers pointed out is that, as Dr. Shi puts it, homeostasis should not be seen as "a boring, slightly hot version of the equilibrium FD distribution."
"Conversely, the system is close to steady state, with a higher energy density than the equilibrium state, but this excess energy is not stored in some kind of featureless heat, but results in the occupation of a very precise rearranged state, maintaining precise quantum properties," says Dr. Matsyshyn.
The researchers also provide the conditions or criteria to be met for the implementation of FFL through experiments. They also listed several potential avenues for future work, one of which was the original problem of photocurrents in bulk materials.
"Using our Floquet Fermi Liquid, one can rigorously demonstrate that even pure monochromatic light does have the potential to drive a net rectification current, even if its frequency is within the gap," says Dr. Villadiego.
"These ideas may be related to the development of new optoelectronic technologies, such as optical amplifiers, sensors, solar cells, and energy harvesting devices," Dr. Song concluded.
更多信息:Li-kun Shi et al, Floquet Fermi Liquid, Physical Review Letters (2024). DOI: 10.1103/PhysRevLett.132.146402.在arXiv上:DOI: 10.48550/arxiv.2309.03268
Journal Information: Physical Review Letters, arXiv