Thermodynamic compressibility and spin-splitting in one-dimensional quantum wires

We study spin-splitting and the much-debated $0.7$ structure in GaAs quantum wires using compressibility measurements that directly probe the thermodynamic density of states. Two quantum wires are simultaneously defined in the upper and lower well of a GaAs/AlGaAs double quantum well heterostructure, using midline-gated split-gate devices [1]. The lower wire probes the ability of the upper wire to screen the electric field from a biased surface gate. The technique is sensitive enough to resolve spin splitting of the 1D subbands in the presence of an in-plane magnetic field. The compressibility response of the $0.7$ structure is measured, and its evolution with increasing temperature and magnetic field is studied [2]. Despite the sensitivity of our measurements we see no evidence of the formation of the quasibound state predicted by the Kondo model of the $0.7$ structure. Instead our data are more consistent with theories which predict that the $0.7$ structure arises as a result of spontaneous spin polarization. \\[4pt] [1] I.M. Castleton \emph{et al}, Physica B 249, 157 (1998).\\[0pt] [2] L.W. Smith \emph{et al}, Phys. Rev. Lett. 107, 126801 (2011)