On the density fluctuations of the superconducting state

Tetsuro Saso, Yoshikazu Suzumura

Effects of random impurities on one-dimensional interacting electron systems are studied by use of the quantum Monte Carlo method and the phase variable representation of charge density and superconducting fluctuations. The impurities pin the phase variable of charge density fluctuation, whereas the quantum fluctuation around the pinned state reduces the pinning effect yielding increase of the superconducting fluctuation since the charge density and the superconducting fluctuations are complementary to each other. Such interplay between randomness and interactions is shown explicitly by calculating spatial dependence of quantum fluctuations, metastable states and correlation functions for superconductivity. Quantum character of metastable states is discussed. It is found that superconducting state is more sensitive to impurities than charge density wave state when the interaction between electrons is weak.

Katsuhiko Higuchi, Eina Miki, Masahiko Higuchi

We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as basic variables in the density functional scheme. The diagonal elements of the RDM2 are called pair-density (PD), which is explicitly related to the fluctuation of the particle number of the system. In this paper, we argue that the fluctuation of the particle number can become an indication of the superconducting state, and that the density functional scheme in which the PD is chosen as a basic variable would be a promising first-principles theory for superconductors.

김범준

Qiaoyi Li, Yang Qi, Wei Li

The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-$T_c$ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the $t$-$t^\prime$ Hubbard model. On the electron-doped side, we find a $d$-wave superconducting (dSC) regime, supporting the scenario of high-$T_c$ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near $(0, π)$, distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-$T_c$ superconductors.

Jonathan Ruhman, Patrick A. Lee