Abstract
Pair density waves, identified by Cooper pairs with finite center-of-mass momentum, have recently been observed in copper oxide based high T c superconductors (cuprates). A charge density modulation or wave is also ubiquitously found in underdoped cuprates. Within a general mean-field one-band model we show that the coexistence of charge density waves (CDWs) and uniform superconductivity in d-wave superconductors like cuprates, generates an odd-frequency spin-singlet pair density wave, in addition to the even-frequency counterparts. The strength of the induced odd-frequency pair density wave depends on the modulation wave vector of the CDW, with the odd-frequency pair density waves even becoming comparable to the even-frequency ones in parts of the Brillouin zone. We show that a change in the modulation wave vector of the CDW from bi-axial to uni-axial, can enhance the odd-frequency component of the pair density waves. Such a coexistence of superconductivity and uni-axial CDW has already been experimentally verified at high magnetic fields in underdoped cuprates. We further discuss the possibility of an odd-frequency spin-triplet pair density wave generated in the coexistence regime of superconductivity and spin density waves, applicable to the iron-based superconductors. Our work thus presents a route to bulk odd-frequency superconductivity in high T c superconductors.
Highlights
Broken symmetry phases characterize different condensed matter systems and define their phase diagrams
We showed that the d-wave nature of the superconducting state in the cuprate high-temperature superconductors leads to induced odd-frequency pair density wave (OPDW) correlations in the region of the phase diagram where the SC coexists with a charge density waves (CDW)
We considered several different CDW wave vectors relevant to the cuprates and showed that the existence of the OPDW is extremely robust to the choice of the wave vector and to the variations in the band structure found between different families of cuprates
Summary
Broken symmetry phases characterize different condensed matter systems and define their phase diagrams. We investigate a time-independent Hamiltonian of coexisting CDW and uniform SC, described by equal time BCSlike Cooper pairs with zero center-of-mass momentum, as commonly assumed present in cuprates We find that this conventional time-independent Hamiltonian induces PDW correlations consisting of unequal time and finite-momentum Cooper pairs, and among those an OPDW. The OPDW does not alter the ground state of the Hamiltonian This makes our work much more general in comparison to the earlier works finding modulated odd-frequency superconductivity in quasi-one-dimensional models.[97,98,99] We find that the OPDW is accompanied with an even-frequency pair density wave (EPDW). By exploring various possible CDW modulation wave vectors and different band structures, we show that the OPDW is a generic feature of all cuprates, whereas the relative strength of OPDW and EPDW depends on the specific material. V, we summarize our results and discuss various experimental consequences in cuprates and the relevance of our findings in the context of other materials showing coexistence phases
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