It was recently pointed out that Fermi surfaces can remain even in superconductors under symmetric spin-orbit interaction and broken time-reversal symmetry. Using the linear response theory, we study the instability of such systems toward ordering, which is an intrinsic property of Fermi surfaces. The ordered states are classified into diagonal and off-diagonal ones, which respectively indicate the Pomeranchuk instability and Cooper pairing not of original electron but of Bogoliubov particles (bogolons). The corresponding order parameters are expanded by multipole moments (diagonal order parameter) and multiplet pair amplitudes (off-diagonal order parameter) of original electrons, which are induced by the internal fields arising from bogolon ordering. While the bogolons' order parameters partially inherit the characters of the original electrons, many order parameter components mix with similar magnitude. Hence, there is no clear-cut distinction for whether the phase transition is diagonal or off-diagonal ordering in terms of the original electrons. These ordering instabilities inside the superconducting states provide insights into superconductors which have the second phase transition below the first transition temperature.

• Received 15 April 2020
• Revised 31 May 2020
• Accepted 2 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.024505