Machine learning on the electron-phonon spectral function and the superconductor gap function

Ming-Chien Hsu^1*, Wan-Ju Li^1,2, Ting-Kuo Lee¹, Shin-Ming Huang¹

¹Physics, National Sun Yat-sen University, Kaohsiung, Taiwan
²Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Ming-Chien Hsu, email:mingchienh@gmail.com

The phonon mediated superconductor can be described well by the Eliashberg equation. Once the electron-phonon spectral function is known either ab initially or estimated from experiments, the superconductor properties such as the gap function and the wave function renormalization can be solved self-consistently from the Eliashberg equation. However, it is important to investigate in a reverse way by inferring the possible original spectral function from known superconductor properties. The mapping can be learned by using the machine learning technique. We generate various spectral functions with numerous peaks and different shapes and solve their gap functions self consistently. With these data, the relation between each pair of the gap function and the corresponding spectral function can be learned by the machine. The functions are learned and recognized in terms of the basis function found by the neural network. The loss function will be hugely reduced each time when the neuron successfully learns a basis function. We find that in general, the neural network is very efficient to learn the correspondence between the electron-phonon spectral function with the superconductor functions mentioned.

Keywords: gap function, electron-phonon spectral function, machine learning