Session S3: 1D Electrons Outside the Luttinger Liquid Paradigm

Dynamic Response of One-Dimensional Interacting Fermions

Evaluation of the dynamic structure factor $S(q,\omega)$ of interacting one-dimensional fermions with a nonlinear dispersion relation was posing an interesting problem, which could not be addressed within the Luttinger liquid theory. The recent solution~[1] of the problem for spinless fermions uncovered new universal features of the structure factor, originating from the combined effects of the nonlinear dispersion and interactions. The sharp peak, characteristic for the Tomonaga-Luttinger model, broadens up; for a fixed wave vector $q$, the structure factor becomes finite at arbitrarily large frequency. The main spectral weight, however, is confined to a narrow frequency interval with the width of order $q^2/2m$; here mass $m$ is determined by the curvature of the dispersion relation. At the lower boundary of this interval the structure factor exhibits power-law singularity with exponent depending on the interaction strength and on the wave vector. The origin of the newly found non-analytical behavior of the structure factor is related to the physics of the Fermi-edge singularity. The constructed theory provides a link between this phenomenon, well-known in the context of electron systems, and the anomalies in the response functions of other one-dimensional systems, as there are close similarities between the dynamic responses of fermions, quantum magnets, and interacting bosons. \newline [1] M. Pustilnik, M. Khodas, A. Kamenev, and L.I. Glazman, Phys. Rev. Lett. {\bf 96}, 196405 (2006)   

Direction Controlled Coulomb Drag in Coupled One-Dimensional Quantum Wires

In a one-dimensional electron gas (1DEG) with sufficiently low density at low temperature, Coulomb interaction becomes so dominant that Wigner crystallization can occur. Wigner crystal (WC) is generally characterized by collective motion of electrons and strong incompressibility. Therefore, in the presence of an external electrostatic potential, electrons forming a WC do not contribute to microscopic screening and only respond rigidly, whereas those of a Fermi liquid (FL) freely move to screen the external potential and produce a correlation hole. In this work we show that the difference between WC and FL allows us to control the direction of Coulomb drag in coupled pairs of 1DEG wires, each having two 2DEG leads. We prepare parallel coupled pairs of quantum wires in a 2DEG defined by Schottky gates to study the current drag between the two wires. The distance between the two wires and the electron density in each wire are all tunable with gate voltages. We inject a constant current into one of the wires (drive wire) and measure the induced drag current (or voltage drop for $I_{drag}$ = 0) in the other wire (drag wire). Electrons in the drive wire usually drag electrons in the drag wire in the same direction because momentum is conserved in Coulombic scattering between the wires. However, when the electron density in the drive wire is sufficiently low that the drive wire has charge inhomogeneity and the electrons in the drag wire are strongly correlated, i.e. at low density, high perpendicular magnetic field and low temperature, the direction of the drag current can be reversed. The sign reversal occurs only when the drive wire is adjacent to the boundary between the drag wire and its lead, and can be controlled by changing the geometry of the coupled wires. These behaviors can be modeled by electron pump from WC in the drag wire to its 2DEG lead, driven by particle-like electrons in the drive wire. The drive wire electrons induce a positive screening charge only in the FL lead, which attracts WC in the drag wire.   

Aharonov-Bohm effect in the spin-incoherent regime of strongly correlated 1D electrons

Recently the spin-incoherent regime of the interacting one-dimensional electron gas has received much attention. In this regime the exchange coupling of nearest neighbor spins is so small that it is completely disrupted by the thermal motion. This regime is generic to low density 1D systems. It is not captured by the standard Luttinger liquid theory and it is expected to exhibit a number of anomalous properties. One of its unusual features is an anomalous conductance suppression reminiscent of conductance reductions observed in quantum wires and point contacts. Despite its great theoretical interest spin incoherence has not yet been demonstrated conclusively in experiments and specific probes of the regime are needed. In this talk I will discuss various tunneling and Aharonov-Bohm interference geometries [1] that can serve this purpose. Spin incoherence will be shown to have a number of distinctive signatures in such experiments such as magnetic field dependent tunneling exponents [2], a strong magnetic field dependence of the interference contrast, and an anomalous scaling of this contrast with the applied voltage [1]. In collaboration with P.W. Brouwer and A.J. Millis. [1] M. Kindermann, P. W. Brouwer, and A. J. Millis, Phys. Rev. Lett. \textbf{97}, 036809 (2006). [2] M. Kindermann and P. W. Brouwer, Phys. Rev. B \textbf{74}, 115121 (2006).