Singular-mode functional renormalization-group approach to the electron nematic state and unconventional superconductivity in two-dimensional electron systems

The electron nematic states have been the recent main topics in the strongly-correlated electron systems [1,2]. For the theoretical description of the electron nematic states, we have to go beyond the standard theory, e.g., RPA. The functional renormalization group method is a powerful theoretical tool that can treat the correlation effects in an unbiased way [3]. In the present study, we employ the singular-mode functional renormalization group (SM-FRG) method [4] to analyze the electron nematic states. In the SM-FRG, the interaction vertex is decomposed into the spin, charge, and superconducting channels, and the physical interpretation of the mutual interactions among them becomes apparent. We found that the SM-FRG can describe the spin-fluctuation-induced nematic fluctuations and studied the interference between the superconducting and nematic fluctuations in detail. In the present study, we also focused on the staggered d-wave superconducting state in the spinless two-band model with two fermi pockets [5]. We applied the SM-FRM method to the spinful Hubbard model and found that the staggered d-wave state is also enhanced in more realistic models.

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[2] R. Tazai, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, J. Phys. Soc. Jpn. 90, 111012 (2021).

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[5] Y. He, K. Yang, J. B. Hauck, E. J. Bergholtz, and D. M. Kennes, Phys. Rev. Research 5, L012009 (2023).