The method called density functional theory or DFT. It is used in physics, chemistry, and materials science to study the electronic structure of many-body systems like atoms and molecules. DFT is a powerful tool for performing ab-initio calculations of materials by simplified treatment of the electron interactions. However, DFT is susceptible to spurious interactions of the electron with its self â€“ what physicists refer to as the “self-interaction problem,” leading to the incorrect description of polarons, which are often destabilized.

Physicists at EPFL have developed a new approach for solving a major shortcoming of a well-established theory that physicists use to study the interactions of electrons in materials. They have introduced a theoretical formulation for electron self-interaction that solves the problem of polaron localization in density functional theory.

In simple words, the formulation could solve the longstanding problem of electron self-interaction when studying polarons â€“ quasiparticles produced by electron-phonon interactions in materials.

The fact that quantum mechanics can represent particles and waves is one of its many peculiarities. The photon, a light-related particle, is a typical example.

Electrons can be perceived as waves that spread across the entire system in orderly structures known as crystals, which paints a very harmonious picture. Ions are periodically organized in space as electrons pass through the crystal. If adding an electron to the crystal, its negative charge could make the ions around it move away from their equilibrium positions. A new particle called a polaron would be created due to the electron charge localizing in space and coupling to the crystal’s surrounding structural distortions, or “lattices.”

Stefano Falletta at EPFL’s School of Basic Sciences said, “*Technically, a polaron is a quasiparticle, made up of an electron “dressed” by its self-induced phonons, representing the quantized vibrations of the crystal. The stability of polarons arises from a competition between two energy contributions: the gain due to charge localization and the cost due to lattice distortions. When the polaron destabilizes, the extra electron delocalizes over the entire system, while the ions restore their equilibrium positions.”*

*“Our new method gives access to accurate polaron stabilities within a computationally-efficient scheme. Our study paves the way to unprecedented calculations of polarons in large systems, in systematic studies involving large sets of materials, or in molecular dynamics evolving over long periods.”*

**Journal Reference:**

- Stefano Falletta, Alfredo Pasquarello. Many-Body Self-Interaction and Polarons. Phys. Rev. Lett. 129, 126401, 14 September 2022. DOI: 10.1103/PhysRevLett.129.126401
- Stefano Falletta, Alfredo Pasquarello. Polarons free from many-body self-interaction in density functional theory. Phys. Rev. B 106, 125119, 14 September 2022. DOI: 10.1103/PhysRevB.106.125119