Modulated Superconductivity

Vesna Mitrovic
Dept Physics, Brown University

Superconductivity is a quantum phenomenon arising, in its simplest form, from the pairing of fermions with opposite      spin into a state with zero net momentum. Whether superconductivity can occur in fermionic systems with an unequal       number of two species distinguished by spin is an important open question.  The imbalance between spin-up and            spin-down electrons that form the Cooper pairs can  be induced by a magnetic field and/or proximity to a                 ferromagnet.  Both the  applied magnetic field and quantum mechanical exchange interaction between spins in a            ferromagnet  tend to align the spins, whereas the spins in a Cooper pair are antiparallel. Those antagonistic            
tendencies lead to pair breaking. When the pair breaking effect is sufficiently large, a Cooper pair has two options    
for survival.  It can become a triplet pair, in which the two spins point in the same direction with the magnetic       
field; and/or, it remains in the singlet state with the spins pointing in opposite directions and acquire instead a     
finite center-of-mass momentum. This momentum leads to a spatially inhomogeneous state consisting of periodically       
alternating ‘normal/ferromagnetic’ and ‘superconducting’ regions. In this seminar, I will describe our recent nuclear
magnetic resonance (NMR) measurements that establish that the hallmark of this spatially modulated state is the         
appearance of spatially localized and spin-polarized quasiparticles forming the so-called Andreev bound states (ABS).