Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session L1: Novel Probes of Electron Interactions in One-Dimensional Systems |
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Sponsoring Units: DCMP Chair: Karyn Le Hur, Yale University Room: Oregon Ballroom 201 |
Tuesday, March 16, 2010 2:30PM - 3:06PM |
L1.00001: Direct observation of spin-charge separation and interaction effects in GaAs quantum wires by momentum-conserved tunneling Invited Speaker: Christopher Ford Coulomb interactions have been predicted to have a profound effect on the behaviour of electrons in one dimension. We have fabricated a 1D system in which we observe spin-charge separation in momentum-conserved tunneling from an array of 1D wires into a 2D electron gas, and also a power-law suppression of tunneling into the wires. These are as predicted for a Tomonaga-Luttinger Liquid (TLL), the simplest analytic model of an interacting 1D system. The use of an array of wires averages out impurity effects and allows the lowest 1D subband to be probed with precise control of electron density. We observe spin-charge separation in the dispersion relation of the 1D wires, mapped by varying the in-plane magnetic field and the dc-bias [1]. We find that the separation persists beyond the regime of the TLL approximation. Furthermore, the measured 1D-2D tunneling current is suppressed at zero dc bias in the presence of a magnetic field, confirming that interactions are important in the 1D wires. This suppression has been measured as a function of temperature and source-drain voltage. These both have similar power-law dependences, as predicted by the TLL model. [1]. Y. Jompol et al., Science 325, 597 (2009). [Preview Abstract] |
Tuesday, March 16, 2010 3:06PM - 3:42PM |
L1.00002: Theory of Nonlinear Luttinger Liquids Invited Speaker: Leonid Glazman We developed a generalization of the Luttinger liquid theory which allowed us to consider threshold singularities in the momentum-resolved dynamic response functions at arbitrary momenta ({\it i.e.}, far away from the Fermi points). The main difficulty the new theory overcomes is the accounting for a generic non-linear dispersion relation of quantum particles which form the liquid. We derive an effective ``quantum impurity'' Hamiltonian which adequately describes the dynamics of the system at the near-threshold energies. The phenomenological theory for the constants of such Hamiltonian is built; it expresses the constants in terms of other measurable properties (energy spectra of the excitations) of the liquid. One of the most important dynamic correlation functions we consider is the momentum-resolved electron spectral function at arbitrary momenta. The spectral function is directly measurable in tunneling experiments. It is singular at the spectrum of the lowest-energy excitation branch. In the absence of spin polarization, this is the branch of spinon excitations. The derivation of the phenomenological relations for the threshold exponent uses the $SU(2)$ and Galilean invariance of the electron liquid. We also consider in detail the case of single-species fermions, which adequately describes the fully spin-polarized electron gas [1]. The theory of threshold exponents is valid at arbitrary wave vectors $k$, including the vicinities of Fermi points $\pm k_F$. There, the exponents approach universal values [2] which depend only on the Luttinger liquid parameter $K$. Remarkably, the found exponents differ from the predictions of the conventional linear Luttinger liquid theory. The deviations from that theory though are confined to the region close to the threshold; while being wide away from the Fermi points, the width of that region scales as $|k\pm k_F|^3$ at $k\to\pm k_F$ in the absence of spin polarization, and as $(k\pm k_F)^2$ for polarized electrons. \\[4pt] [1] A. Imambekov, L.I. Glazman, Phys. Rev. Lett., {\bf 102}, 126405 (2009)\\[0pt] [2] A. Imambekov, L.I. Glazman, Science, {\bf 323}, 228 (2009) [Preview Abstract] |
Tuesday, March 16, 2010 3:42PM - 4:18PM |
L1.00003: Superconducting tunneling spectroscopy in carbon nanotubes Invited Speaker: Nadya Mason In this talk I will discuss measurements of electron energies and interactions in carbon nanotubes using superconducting tunneling probes. Carbon nanotubes (CNTs) can act as model one-dimensional or zero-dimensional (quantum dot) systems, and are often considered leading candidates for nanoscale electronics applications. We developed techniques to perform tunneling spectroscopy on nanotubes using non-invasive superconducting probes placed over the bulk of the tubes. The superconducting probe enhances weak spectroscopic features: measurements of a CNT quantum dot shows clear signals of co-tunneling and weak inelastic scattering. We are also able to measure the shape of the electron energy distribution functions in CNTs that have bias voltages applied between their ends (non-equilibrium tunneling spectroscopy). The distribution functions are related to energy relaxation rates, and we find that at low temperatures electrons interact weakly in nanotubes of a few microns channel length, independent of end-to-end conductance values. In general, tunneling spectroscopy with a superconducting probe may be a powerful new tool for characterizing electron behavior in molecular systems. [Preview Abstract] |
Tuesday, March 16, 2010 4:18PM - 4:54PM |
L1.00004: Non-equilibrium Luttinger liquids: bosonization and tunneling spectroscopy Invited Speaker: Alexander Mirlin We develop the bosonization technique for Luttinger liquids out of equilibrium. The formalism is employed to study an interacting quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green functions, which can be measured via tunneling spectroscopy technique and carry the information about energy distribution, zero-bias anomaly, and dephasing, are expressed in terms of functional determinants of single-particle ``counting'' operators. The corresponding time-dependent scattering phase is found to be intrinsically related to ``fractionalization'' of electron-hole excitations in the tunneling process and at boundaries with leads. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution function of electrons over energies. The energy relaxation is controlled by the plasmon scattering on the boundary between regions with different interaction strength and affects the distribution function of electrons in the wire as well as of those emitted from the interacting regions into electrodes. We further calculate the dephasing which governs the smearing of zero-bias anomalies in the tunneling density of states. For double-step distributions, the dephasing rates are oscillatory functions of the interaction strength. Results are generalized to the case of spinful particles as well to Green functions at different spatial points (relevant to the problem of dephasing in Luttinger liquid interferometers). \\[0.2cm] The work has been done in collaboration with D. Gutman (Bar Ilan University) and Y. Gefen (Weizmann Institute) [Preview Abstract] |
Tuesday, March 16, 2010 4:54PM - 5:30PM |
L1.00005: Electron-Phonon and Electron-Electron Interactions in Individual Suspended Carbon Nanotubes Invited Speaker: Stephen Cronin The fabrication of pristine, nearly defect-free, suspended carbon nanotubes (CNTs) enables the observation of several phenomena not seen before in carbon nanotubes, including breakdown of the Born-Oppenheimer approximation$^{1}$, mode selective electron-phonon coupling$^{2}$, and a Mott insulator transition$^{3}$. Raman spectroscopy of these nanotubes under applied gate and bias potentials reveals exceptionally strong electron-phonon coupling, arising from Kohn anomalies, which result in mode selective electron-phonon coupling, negative differential conductance (NDC), and non-equilibrium phonon populations$^{2,4}$. Due to the extremely long electron lifetimes, we observe a breakdown of the Born-Oppenheimer approximation, as deduced from the gate voltage-induced changes in the vibrational energies of suspended carbon nanotubes$^{1}$. We also report strikingly large variations in the Raman intensity of pristine metallic CNTs in response to gate voltages, which are attributed to a Mott insulating state of the strongly correlated electrons$^{3}$. As will be shown, preparing clean, defect-free devices is an essential prerequisite for studying the rich low-dimensional physics of CNTs. (1.) Bushmaker, A.W., Deshpande, V.V., Hsieh, S., Bockrath, M.W., and Cronin, S.B., ``Direct Observation of Born-Oppenheimer Approximation Breakdown in Carbon Nanotubes.'' Nano Letters, 9, 607 (2009). (2.) Bushmaker, A.W., Deshpande, V.V., Bockrath, M.W., and Cronin, S.B., ``Direct Observation of Mode Selective Electron-Phonon Coupling in Suspended Carbon Nanotubes.'' Nano Letters, 7, 3618 (2007) (3.) Bushmaker, A.W., Deshpande, V.V., Hsieh, S., Bockrath, M.W., and Cronin, S.B., ``Large Modulations in the Intensity of Raman-Scattered Light from Pristine Carbon Nanotubes.'' Physical Review Letters, 103, 067401 (2009). (4.) Bushmaker, A.W., Deshpande, V.V., Hsieh, S., Bockrath, M.W., and Cronin, S.B., ``Gate Voltage Controlled Non-Equilibrium and Non-Ohmic Behavior in Suspended Carbon Nanotubes.'' Nano Letters, 9, 2862 (2009) [Preview Abstract] |
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