Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that the energy states of the electrons near the Fermi level EF are not qualitatively altered by Coulomb interactions. In one-dimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system, known as a Luttinger liquid, is predicted to be distinctly different from its two- and three-dimensional counterparts1. For example, tunnelling into a Luttinger liquid at energies near the Fermi level is predicted to be strongly suppressed, unlike in two- and three-dimensional metals. Experiments on one-dimensional semiconductor wires2, 2,3 have been interpreted by using Luttinger-liquid theory, but an unequivocal verification of the theoretical predictions has not yet been obtained. Similarly, the edge excitations seen in fractional quantum Hall conductors are consistent with Luttinger-liquid behaviour4, 5, but recent experiments failed to confirm the predicted relationship between the electrical properties of the bulk state and those of the edge states6. Electrically conducting single-walled carbon nanotubes (SWNTs) represent quantum wires7,8,9,10 that may exhibit Luttinger-liquid behaviour11, 12. Here we present measurements of the conductance of bundles (‘ropes’) of SWNTs as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid. In particular, we find that the conductance and differential conductance scale as power laws with respect to temperature and bias voltage, respectively, and that the functional forms and the exponents are in good agreement with theoretical predictions.

Luttinger-liquid behaviour in carbon nanotubes

An interacting one-dimensional (1D) electron system is predicted to behave very differently than its higher-dimensional counterparts. Coulomb interactions strongly modify the properties away from those of a Fermi liquid, resulting in a Luttinger liquid (LL) characterized by a power-law vanishing of the density of states at the Fermi level. Experiments on one-dimensional semiconductor wires and fractional quantum Hall conductors have been interpreted using this picture, but questions remain about the connection between theory and experiment. Recently, single-walled carbon nanotubes (SWNTs) have emerged as a new type of 1D conductor that may exhibit LL behavior. Here we present measurements of the conductance of individual ropes of such SWNTs as a function of temperature and voltage. Power law behavior as a function of temperature or bias voltage is observed: G~ T^a and dI/dV ~ V^a. Both the power-law functional forms and the inferred exponents are in good agreement with theoretical predictions for tunneling into a LL.

Luttinger Liquid Behavior in Carbon Nanotubes

Publisher Summary A refractive index can be increased by ion implantation by changes in density and structure, by the addition of high-polarizability impurity ions, by a reduction of the plasma effect that increases the index and that is most important in the wavelength region far from the energy gap, and by absorption changing in the index in the region of the gap, that is, via the Kramers–Kronig relation. This chapter discusses the optical properties of implanted semiconductors, electrooptic components formed by ion implantation, general principles that determine most luminescent systems, effects of implantation temperature, luminescence centers in LiF-Mg-Ti radiation dosimeters, and use of line spectra in defect studies. In the LiF system, the luminescence bands are broad, and if alternative versions of the same complex exist, they cannot be resolved from the spectra. The addition, by implantation, of ions with incomplete inner electron shells opens up new possibilities as the lattice distortions of the free-ion energy levels are strongly perturbed by the defects in the neighborhood of the ion.

Optical Effects of Ion Implantation

I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

/pdf/quantum-transport-in-semiconductor-nanostructures-1n3dkljf6x.pdf

Quantum Transport in Semiconductor Nanostructures

Publisher Summary Quantum transport is conveniently studied in a two-dimensional electron gas (2DEG) because of the combination of a large Fermi wavelength and large mean free path. Semiconductor nanostructures are unique in offering the possibility of studying quantum transport in an artificial potential landscape. This is the regime of ballistic transport in which scattering with impurities are neglected. The chapter presents a self-contained account of these three novel transport regimes in semiconductor nanostructures. The study of quantum transport in semiconductor nanostructures is motivated by more than scientific interest. The fabrication of nanostructures relies on sophisticated crystal growth and lithographic techniques that exist because of the industrial effort toward the miniaturization of transistors. Conventional transistors operate in the regime of classical diffusive transport, which breaks down on short length scales. The discovery of novel transport regimes in semiconductor nanostructures provides options for the development of innovative future devices.

/pdf/quantum-transport-in-semiconductor-nanostructures-3vpunw3uta.pdf

Reduction of quantized conductance at low temperatures observed in 2 to 10 μm-long quantum wires

We study interactions between electrons and nuclear spins by using the resistance ( Rxx) peak which develops near the Landau-level filling factor nu = 2/3 as a probe. Temporarily tuning nu to a different value, nu(temp), with a gate demonstrates that the Rxx peak regenerates even after complete depletion ( nu(temp) = 0), while it rapidly relaxes on either side of nu(temp) = 1. This indicates that the nu = 2/3 domain morphology is memorized by the nuclear spins which can be rapidly depolarized by Skyrmions. An additional enhancement in the nuclear spin relaxation around nu = 1/2 and 3/2 suggests a Fermi sea of partially polarized composite fermions.

/pdf/electrically-controlled-nuclear-spin-polarization-and-4afg9nek4v.pdf

Electrically controlled nuclear spin polarization and relaxation by quantum-Hall states.

Lateral dimensions of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs double-barrier diodes were restricted by use of focused Ga ion-beam implantation. The diode with a restricted lateral dimension exhibited a series of resonant-tunneling current peaks corresponding to the laterally confined one-dimensional levels superimposed on to the ground state confined by the heterojunctions. The resonant peaks were more pronounced in the diode with the smaller lateral dimension and consequently stronger lateral confinement. The spectral feature of the resonant peaks suggests mixing of even- (odd-) parity one-dimensional subbands in the double-barrier structure with two-dimensional subbands of the same parity in the contact. The diode with two restricted lateral dimensions also exhibited a series of resonant peaks corresponding to the laterally confined zero-dimensional levels.

Resonant tunneling through one- and zero-dimensional states constricted by Al x Ga 1-x As/GaAs/Al x Ga 1-x As heterojunctions and high-resistance regions induced by focused Ga ion-beam implanation

An almost single‐mode waveguiding layer has been fabricated by thermal diffusion of TiO2 into LiNbO3. The refractive‐index change in the layer is 2–3×10−3 for both ne and no, and the propagation loss is 0.7–0.8 dB/cm. The electro‐optic coefficients are found to be nearly equal to those of the bulk crystal. An amplitude modulation has been made with a stripe waveguide 10 μm wide and planar electrodes. The half‐wave voltage is 17 V and the maximum extinction ratio is 12 dB.

Electro‐optic amplitude modulation using three‐dimensional LiNbO3 waveguide fabricated by TiO2 diffusion

Thermal diffusion and electrodiffusion of Cu into LiTaO3 have been investigated. By an appropriate choice of diffusion conditions, a single‐mode waveguiding layer has been fabricated using the electrodiffusion method. The refractive‐index change at the surface is 5×10−3 for both ne and no and the diffusion depth is about 4 μm. The layer supports only the fundamental modes TE0 and TM0, and exhibits good waveguiding properties.

Tadashi Saku

Papers

Reduction of quantized conductance at low temperatures observed in 2 to 10 μm-long quantum wires

Electrically controlled nuclear spin polarization and relaxation by quantum-Hall states.

Resonant tunneling through one- and zero-dimensional states constricted by Al x Ga 1-x As/GaAs/Al x Ga 1-x As heterojunctions and high-resistance regions induced by focused Ga ion-beam implanation

Electro‐optic amplitude modulation using three‐dimensional LiNbO3 waveguide fabricated by TiO2 diffusion

Fabrication of optical waveguiding layer in LiTaO3 by Cu diffusion