Junctions of spin-incoherent Luttinger liquids with ferromagnets and superconductors

Abstract

We discuss the properties of a strongly interacting spin-charge separated one dimensional system coupled to ferromagnets and/or superconductors. Our results are valid for arbitrary temperatures with respect to the spin energy, but require temperature be small compared to the charge energy. We focus mainly on the spin-incoherent regime where temperature is large compared to the spin energy, but small compared to the charge energy. In the case of a ferromagnet we study spin pumping and the renormalized dynamics of a precessing magnetic order parameter. We find the interaction-dependent temperature dependence of the spin pumping can be qualitatively different in the spin-incoherent regime from the Luttinger liquid regime, allowing an identification of the former. Likewise, the temperature dependence of the renormlized magnetization dynamics can be used to identify spin-incoherent physics. For the case of a spin-incoherent Luttinger liquid coupled to two superconductors, we compute the ac and dc Josephson current for a wire geometry in the limit of tunnel coupled superconductors. Both the ac and dc response contain "smoking gun" signatures that can be used to identify spin-incoherent behavior. Experimental requirements for the observation of these effects are laid out.

Singular responses of spin-incoherent Luttinger liquids

“…To date, our best experimental evidence comes from momentum-resolved tunneling on cleaved-edge overgrowth quantum wires (Steinberg et al 2006), transport in split-gate devices (Hew et al 2008), and somewhat more speculatively in transport measurements on gated single-wall carbon nanotubes with low electron density (Deshpande and Bockrath 2008). Given that the existing theory now encompasses hybrid structures of SILLs with ferromagnets and superconductors as well (Tilahun andFiete 2008, 2009)), the number of experimental groups poised to make contributions to this exciting field is greatly enlarged. For a recent discussion of numerous possible experiments that would provide strong evidence for spin-incoherent Luttinger liquid behavior see (Fiete 2007).…”

“…For a general discussion of the SILL see (Fiete 2007). For SILL physics in ferromagnetic and superconducting hybrid structures see (Tilahun andFiete 2008, 2009), and in cold atomic gases see (Kakashvili et al 2008).…”

Hall effect between parallel quantum wires

“…This regime is a generic property of interacting electrons at low densities, when a Wigner crystal with large inter-electron spacing is formed. As one of the few known regimes of one-dimensional conductors that displays physics qualitatively different from the conventional Luttinger liquid, this limit has drawn much recent theoretical attention [5][6][7]. Experimentally, however, it has not been identified conclusively, yet.…”

“…edge singularity [19,20] has a magnetic-field-dependent tunneling exponent, as predicted in eq. (7).…”