Magnetic field–induced pair density wave state in the cuprate vortex halo

High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N(r) within the halo surrounding Bi2Sr2CaCu2O8 vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N(r) modulations with wave vectors QP and 2QP, with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO2 unit-cell periodicity and coexisting with its secondary CDWs.

The electron-pair density distribution of the 1,3Πu excited states of H2

The non-monotonic behavior of the electron repulsion energy and the inter-electronic distance, as a function of the internuclear separation, in the 3Πu excited state of the hydrogen molecule has been assessed by explicit calculation and analysis of the electron-pair density distribution functions from high level ab initio full configuration interaction wave functions, for both the 3Πu and the 1Πu states. Additionally, Hund’s rule as applied to these two states has been accounted for in terms of simple electronic shielding effects induced by wave function antisymmetrization.