Electronic multipoles and multiplet pairs induced from Pomeranchuk and Cooper instabilities of Bogoliubov Fermi surfaces

It has recently been pointed out that Fermi surfaces can remain even in the superconductors under the 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 the Fermi surfaces. The ordered states are classified into diagonal and offdiagonal ones, each of which respectively indicates 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 (offdiagonal order parameter) of original electrons, which are induced by the internal fields arising from bogolons 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 whether the phase transition is diagonal or offdiagonal ordering in terms of the original electrons. These ordering instabilities inside the superconducting states provide insights into the superconductors which have the second phase transition below the first transition temperature.