Imaginary time instantons and pseudogap state in superconducting cuprates.

• Applicant: Professor Dr. Ilya Eremin, since 9/2021
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 408024965

We propose and investigate properties of a new state with an unusual order parameter. It is characterized by a periodic chain of instantons in the imaginary time with the total length 1/T, where T is temperature. We have introduced a model of interacting fermions and bosonic modes having this new state. Then, we demonstrated both analytically and numerically that the new state can correspond to the minimum of the free energy in a broad region of parameters of the model. This state is unique and contrasts conventional phases in Landau-type theories with static long-range orders. We have called this state "instanton crystal". The model we suggested might originate from an effective "spin-fermion model with overlapping hot spots" developed in our earlier publications for description of low temperature properties of superconducting cuprates.Now we continue our study of the instanton crystal by calculating real-time-dependent correlation functions. The main question concerns investigating a possibility of non-decaying real-time oscillations of correlation functions of physical quantities. In conventional thermodynamically stable systems, they decay and it is believed that the non-decaying oscillations are impossible in macroscopic models in the limit of theinfinite volume. Nevertheless, the situation in the instanton crystal can, in principle, be different and we investigate this question both analytically and numerically. The thermodynamic correlation function of the loop currents in the model considered, provided it shows oscillation in real time, can give peaks at finite frequencies in neutron scattering. Further, we plan to study kinetic physical quantities like, e.g., conductivity and investigate effects of fluctuations.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr. Konstantin Efetov, until 10/2021 (†)