# Multistage Electronic Nematic Transitions in Cuprate Superconductors: Functional-Renormalization-Group Analysis

## TL;DR

This paper uses a functional-renormalization-group approach to analyze complex multistage nematic phase transitions in cuprate superconductors, revealing uniform and density-wave nematic orders driven by spin fluctuations.

## Contribution

It uncovers the dominant uniform nematic instability and subsequent density-wave order in cuprates without assuming specific wavevectors, highlighting multistage transitions driven by fluctuation processes.

## Key findings

- Uniform ($q=0$) d-symmetry charge modulation is dominant.
- A nematic p-orbital density wave appears at $Q_a = (rac{ ext{pi}}{2}, 0)$.
- Multistage nematic transitions are driven by fluctuation-exchange processes.

## Abstract

Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic $d$-$p$ Hubbard model. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform ($q = 0$) charge modulation on the $p_x$ and $p_y$ orbitals, which possesses the d-symmetry. This uniform nematic order triggers another nematic p-orbital density wave along the axial (Cu-Cu) direction at $Q_a = (\pi/2,0)$. It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at $q = Q_a$ is triggered by the uniform order. The predicted multistage nematic transitions are caused by the Aslamazov-Larkin-type fluctuation-exchange processes.