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arXiv:0706.3418 · Physical Review B

Tunneling density of states, pair correlation, and Josephson current in spin-incoherent Luttinger-liquid/superconductor hybrid systems

Dagim Tilahun, Gregory A. Fiete

Published Apr 18, 2008• 6 citations
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Abstract

We study a hybrid system consisting of a spin-incoherent Luttinger liquid adjoined at one or both ends to a superconductor. We find that the tunneling density of states diverges at low energies and exhibits a universal frequency dependence independent of the strength of the interactions in the system. We show that in spite of exponentially decaying pair correlations with distance into the spin-incoherent Luttinger liquid, the Josephson current remains robust. Compared to the zero temperature Luttinger-liquid case, there is a factor of 2 reduction in the critical current and a halving of the period in the phase difference between the superconductors. We hope these results motivate a class of experiments in the spin-incoherent regime of one-dimensional systems.

DOI
10.1103/physrevb.77.140505

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A theory describing a one-dimensional Luttinger liquid in contact with a superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wave function in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary conditions describing Andreev reflection. \textcopyright{} 1996 The American Physical Society.
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In a one-dimensional electron gas at low enough density, the magnetic (spin) exchange energy JJJ between neighboring electrons is exponentially suppressed relative to the characteristic charge energy, the Fermi energy EF{E}_{F}EF​. At nonzero temperature TTT, the energy hierarchy J⪡T⪡EFJ⪡T⪡{E}_{F}J⪡T⪡EF​ can be reached, and we refer to this as the spin-incoherent Luttinger liquid state. We discuss the Coulomb drag between two parallel quantum wires in the spin-incoherent regime, as well as the crossover to this state from the low-temperature regime by using a model of a fluctuating Wigner solid. As the temperature increases from zero to above JJJ for a fixed electron density, the 2kF2{k}_{F}2kF​ oscillations in the density-density correlations are lost. As a result, the temperature dependence of the Coulomb drag is dramatically altered and nonmonotonic dependence may result. Drag between wires of equal and unequal density are discussed, as well as the effects of weak disorder in the wires. We speculate that weak disorder may play an important role in extracting information about quantum wires in real drag experiments.
We investigate spin-incoherent Luttinger liquid of a one-dimensional spin-1 Bose gas in a harmonic trap. In this regime highly degenerate spin configurations emerge since the energy splitting between different spin states is much less than the thermal energy of the system, while the temperature is low enough that the lowest energetic orbitals are occupied. As an example we numerically study the momentum distribution of a one-dimensional spin-1 Bose gas in Tonks-Girardeau gas limit and in the sector of zero magnetization. We find that the momentum distributions broaden as the number of atoms increase due to the averaging of spin function overlaps. Large momentum (ppp) asymptotic is analytically derived, showing the universal 1/p41/{p}^{4}1/p4 dependence. We demonstrate that the spin-incoherent Luttinger liquid has a momentum distribution also distinct from spinless bosons at finite temperature.