Blog

A new study published in Physical examination letters (PRL) explores the potential of quadratic electron-phonon coupling to enhance superconductivity through the formation of quantum bipolarons.

Electron-phonon coupling is the interaction between electrons and vibrations in a lattice called phonons. This interaction is crucial for superconductivity (electrical conduction without resistance) in certain materials because it facilitates the formation of Cooper pairs.

Cooper pairs are pairs of electrons bound together by attractive interactions. When these Cooper pairs condense into a coherent state, we get superconducting properties.

Electron-phonon coupling can be categorized based on its dependence on the phonon shift, meaning how much the lattice vibrates. The most commonly considered case is when the electron density is linearly related to the lattice displacements, resulting in a distortion of the lattice around each electron.

The researchers wanted to investigate whether superconductivity could be enhanced for materials exhibiting quadratic coupling, which is when the interaction energy is proportional to the square of the phonon displacement.

Phys.org spoke with the study’s co-authors, Zhaoyu Han, Ph.D. candidate at Stanford University and Dr. Pavel Volkov, assistant professor in the Department of Physics, University of Connecticut.

Speaking about his motivation behind conducting this research, Han said, “One of my dreams has been to identify and propose new mechanisms that can help achieve high-temperature superconductivity.”

Dr Volkov said: “The superconductivity of doped strontium titanate was discovered more than 50 years ago, but its mechanism remains an open question, with conventional mechanisms unlikely. That’s why I started looking for alternative mechanisms for coupling electrons and phonons.”

Linear coupling and its challenges for superconductivity

As mentioned earlier, coupling can be categorized as linear or quadratic coupling.

Linear coupling refers to the scenario where the coupling is proportional to the phonon displacement. On the other hand, quadratic coupling depends on the square of the phonon displacement.

They can be identified by studying the symmetry of the material, experimental observations and theoretical frameworks. However, their implications for superconductivity appear to be quite different.

The linear coupling observed in most superconducting materials has been extensively studied due to its prevalence in many materials and has a theoretical framework.

However, conventional superconductors with linear electron-phonon coupling face limitations. These materials have a low critical temperature, which is the temperature below which the material can exhibit superconductivity.

Hahn explained, “The critical temperatures for these superconductors are typically below 30 Kelvin, or -243.15 degrees Celsius. This is in part because the Cooper pair binding energy and kinetic energy are exponentially suppressed in the weak and strong binding modes, respectively.”

In weak coupling, the electron-phonon interactions are weak due to the low binding energy. In strong coupling, the interactions are stronger, leading to a higher effective mass of Cooper pairs, suppressing superconductivity.

However, the suppression hinders any efforts to improve the critical temperatures in such materials by simply increasing the coupling strength, encouraging researchers to explore materials with quadratic electron-phonon coupling, which are not as well understood.

Holstein model and quantum bipolarons

The Holstein model is a theoretical framework used to describe the interaction between electrons and phonons. It has previously been used to study the general physics of linear electron-phonon coupling.

The researchers extended Holstein’s model to include quadratic electron-phonon coupling in their study.

Holstein’s model helps calculate quantities such as the binding energy of Cooper pairs and the critical temperature of superconductors.

In conventional materials, phonon-mediated electron coupling leads to the formation of Cooper pairs.

The interaction is linear, meaning that the strength of the bond increases with the amplitude of the lattice vibrations. This interaction can be understood using the principles of classical physics and is well supported by experimental observations such as isotope effects.

In the case of quadratic coupling it is completely different. By extending Holstein’s model to include the second-order dependence of the coupling on the phonon displacement, the researchers accounted for the quantum fluctuations (random motion) of the phonons and the zero-point energy (the phonon energy at 0 Kelvin).

The electrons interact with the quantum fluctuations of the phonons, forming “quantum bipolarons”. Unlike linear coupling, the origin of attractive interactions is purely quantum mechanical.

Superconductivity in the limit of weak and strong coupling

The researchers found that when the electron-phonon interaction is weak, the mechanism by which electrons pair up to form Cooper pairs is not efficient, similar to the linear case. This leads to a low critical temperature that can be affected by the mass of the ions (isotope effect), but in a different way than in the linear case.

In other words, the (low) critical temperature of a material can change significantly with different atomic masses.

Conversely, when the electron-phonon interactions are strong, we get the formation of quantum bipolarons, which can become superconducting at a temperature set by their effective mass and density.

Below the critical temperature, the condensate of quantum bipolarons can move freely without disturbing the crystal. Greater mobility leads to a superconducting state that is more stable and has a higher critical temperature. In contrast to the linear mechanism, the mass of the quantum bipolaron is only slightly enhanced with coupling, allowing for higher critical temperatures.

“Our work shows that this mechanism allows for higher transition temperatures, at least for strong coupling. What is also good is that this mechanism does not require any special preconditions to work, and there are quite realistic conditions under which it will be dominant,” explained Dr. Volkov.

Hahn predicted, “Based on fundamental physical constants applicable to solid materials, an optimistic estimate of the critical temperature achievable by this mechanism could be on the order of 100 Kelvin.”

Future job

“The potential significance, first of all, would be to raise the temperature of the superconducting transition. Superconductivity also depends sensitively on the properties of the electrons; so to achieve strong coupling we propose to use specially designed superlattices for electrons,” explained Dr. Volkov.

The researchers mention that theoretically the next step would be to find the optimal binding force regime for superconductivity. The researchers also hope that experimenters will probe superlattice materials with large squared electron-phonon couplings.

“Experimentally, creating superlattices by patterning or using interfaces between twisted materials could be a promising route to realizing the type of superconductivity we predicted,” said Dr. Volkov.

Hahn also pointed out, “It is crucial to identify materials with large quadratic electron-phonon couplings from ab initio calculations, as this has not been systematically investigated.”

© 2024 Science X Network