Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session B1: Strongly Correlated Electrons in One Dimension |
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Sponsoring Units: DCMP Chair: Gil Refael, California Institute of Technology Room: Morial Convention Center LaLouisiane AB |
Monday, March 10, 2008 11:15AM - 11:51AM |
B1.00001: Narrow-gap Luttinger liquid in carbon nanotubes Invited Speaker: Single-walled carbon nanotubes are the thinnest and the cleanest among the currently available nanoscale quantum wires. Transport properties of nanotubes depend on the presence of a gap in electron spectrum, defining two main nanotube types, metallic and semiconducting. Semiconducting tubes attract interest in particular because of the sensitivity of their properties to external fields and doping. Among semiconducting tubes there is an interesting class of narrow-gap tubes, or so-called chiral metallic tubes, which exhibit a narrow semiconducting gap arising due to curvature [1]. The Luttinger liquid effects, which are strong in all nanotubes, are particularly interesting in the narrow-gap tubes. Interaction strongly affects the energy gap, reinforcing it and making it sensitive to the long-wavelength charge mode dynamics [2]. We discuss new types of charge carriers possible in the gapped states and their relation to recent experimental work [3]. \newline [1] C.L. Kane and E.J. Mele, Phys. Rev. Lett. 78, 1932 (1997) \newline [2] L. S. Levitov, A. M. Tsvelik, Phys. Rev. Lett. 90, 016401 (2003) \newline [3] V. V. Deshpande, M. Bockrath, arXiv:0710.0683 [Preview Abstract] |
Monday, March 10, 2008 11:51AM - 12:27PM |
B1.00002: Observation of spin-charge separation and localization in one-dimensional quantum wires Invited Speaker: We have been able to measure hallmark properties of electrons confined to one-dimensional (1D) wires. Profoundly affected by interactions, the 1D electron liquid is a Luttinger-liquid. Single particle elementary excitations, which survive in spite of interactions in higher dimensions, completely lose their integrity in a Luttinger-liquid. Instead, the elementary excitations of the 1D electron liquid are all collective, with long range correlations and are spin-charge separated. In spite of the drastic influence of electron-electron interactions on the many-body states, the observation of these effects in experiment has been elusive. Our wires were fabricated from a GaAs/AlGaAs heterostructure using cleaved edge overgrowth. The sample I shall discuss contained two parallel wires, 20nm and 30nm thick, which were separated by a 6nm insulating AlGaAs barrier. A series of top gates allowed us to contact each wire separately, and thus allowed us to control both the energy and the momentum of the electrons tunneling between the wires. The resulting tunneling conductance was a direct measure of the spectral function in each of the wires, and thus enabled us to map the dispersions of the 1D many-body elementary excitations. Pushing the wires to low density allowed us to probe the regime where interactions dominate over kinetic energy. In this regime we clearly observed two spin modes and one charge mode of the coupled wires. Mapping the dispersion velocities as a function of decreasing density, we found good agreement between the data and theoretical calculations of the velocity of the antisymmetric charge mode of the coupled wires. The theory also predicted an additional symmetric charge mode, that was not observed. The spin velocities were found, within experimental precision, to be smaller than theoretically predicted. Reducing the density of electrons even further, we found an abrupt transition in the extent of the 1D states along the wires: At high densities they were extended and had well defined momenta, while at low densities they localized as a result of interactions and exhibited Coulomb blockade physics. A simultaneous measurement of the two-terminal conductance, which displayed the typical stepwise drop with decreasing density, showed that a localization transition was concurrent with each conductance drop. [Preview Abstract] |
Monday, March 10, 2008 12:27PM - 1:03PM |
B1.00003: The One-Dimensional Wigner Crystal in Carbon Nanotubes Invited Speaker: Electron-electron interactions strongly affect the behavior of low-dimensional systems. In one dimension (1D), arbitrarily weak interactions qualitatively alter the ground state producing a Luttinger liquid (LL) which has now been observed in a number of experimental systems. Interactions are even more important at low carrier density, and in the limit when the long-ranged Coulomb potential is the dominant energy scale, the electron liquid is expected to become a periodically ordered solid known as the Wigner crystal. In 1D, the Wigner crystal has been predicted to exhibit novel spin and magnetic properties not present in an ordinary LL. However, despite recent progress in coupled quantum wires, unambiguous experimental demonstration of this state has not been possible due to the role of disorder. We demonstrate using low-temperature single-electron transport spectroscopy that a hole gas in low-disorder carbon nanotubes with a band gap is a realization of the 1D Wigner crystal [1]. We observe for the first time three distinct regimes as a function of carrier density and axial magnetic field: (I) a completely spin and isospin polarized state, (II) an isospin polarized, spin antiferromagnetic state, and (III) an unpolarized state with a four-fold addition energy period. The transitions among these regimes can be quantitatively and intuitively explained using a Wigner crystal picture based on a gapped LL model [2] with the carriers represented by spatially localized solitons. Our observation provides a clean platform for testing theories of interacting electrons in 1D and also indicates the possibility of using this many-body state for solid-state quantum information processing. [1] V. V. Deshpande and M. Bockrath, arXiv:0710.0683v1 [cond-mat.str-el] [2] L. S. Levitov and A. M Tsvelik, Phys. Rev. Lett. 90, 016401 (2003) [Preview Abstract] |
Monday, March 10, 2008 1:03PM - 1:39PM |
B1.00004: Fermi-Edge Singularity in a Spin-Incoherent Luttinger Liquid Invited Speaker: In recent years the spin-incoherent Luttinger liquid, obtained in the energy window $E_{\rm spin}\ll k_B T \ll E_{\rm charge}$, has attracted much attention because of its qualitatively distinct properties relative to the more familiar Luttinger liquid [1]. Some of the most remarkable effects appear in correlations in which the number of particles is abruptly changed, such as a single particle Green's function [2] or in the Fermi-edge singularity when a particle-hole pair is photo-excited [3]. In this talk, I draw on the methods developed in Ref.[2] to study the Fermi-edge singularity in the spin-incoherent Luttinger liquid [3]. Both cases of finite and infinite core hole mass are explored, as well as the effect of a static external magnetic field of arbitrary strength. For a finite mass core hole the absorption edge behaves as $(\omega-\omega_{\rm th})^\alpha/\sqrt{|\ln(\omega-\omega_{\rm th})|}$ for frequencies $\omega$ just above the threshold frequency $\omega_{\rm th}$. The exponent $\alpha$ depends on the interaction parameter $K_c$ of the interacting one dimensional system, the electron-hole coupling, and is independent of the magnetic field strength, the momentum, and the mass of the excited core hole (in contrast to the spin-coherent case). In the infinite mass limit, the spin-incoherent problem can be mapped onto an equivalent problem in a spinless Luttinger liquid for which the logarithmic factor is absent, and backscattering from the core hole leads to a universal contribution to the exponent $\alpha$.\\ \\ $[1]$ G. A. Fiete, Rev. Mod. Phys. {\bf 79}, 801 (2007).\\ $[2]$ G. A. Fiete and L. Balents, Phys. Rev. Lett. {\bf 93}, 226401 (2004).\\ $[3]$ G. A. Fiete, Phys. Rev. Lett. {\bf 97}, 256403 (2006).\\ [Preview Abstract] |
Monday, March 10, 2008 1:39PM - 2:15PM |
B1.00005: Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires Invited Speaker: At low density, all electrons in a quantum wire occupy the lowest state of transverse quantization, and it is natural to view the system as one-dimensional. As the density is increased, the electrons start to populate the second subband, resulting in a transition to a quasi-one-dimensional state. I will discuss this transition in the presence of electron-electron interactions in a model that neglects electron spins. Clearly, in the non-interacting case the transition is accompanied by the emergence of a second gapless excitation mode. On the other hand, at very strong interactions, the one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains. Unlike the non-interacting electrons, this two-row (zigzag) crystal still has only one acoustic excitation branch. This raises the question of how the nature of the transition to a quasi-one-dimensional state changes with interaction strength. We can show that in the vicinity of the transition already arbitrarily weak interactions open a gap in the second excitation mode. We then argue that only one gapless mode exists near the transition at any interaction strength. [Preview Abstract] |
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