The collective excitation spectrum of interacting electrons in one dimension has been measured by controlling the energy and momentum of electrons tunneling between two closely spaced, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. The excitation spectrum deviates from the noninteracting spectrum, attesting to the importance of Coulomb interactions. An observed 30% enhancement of the excitation velocity relative to noninteracting electrons with the same density, a parameter determined experimentally, is consistent with theories on interacting electrons in one dimension. In short wires, 6 and 2 micrometers long, finite size effects, resulting from the breaking of translational invariance, are observed.
We have measured the low temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island. Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic line width decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusaki's model for resonant tunneling in a Luttinger-liquid.PACS numbers: 73.20. Dx, 73.23.Ad, 73.23.Ps, 73.50.Jt One-dimensional (1D) electronic systems are expected to show unique transport behavior as a consequence of the Coulomb interaction between carriers [1]. Unlike in two and three dimensions [2], where the Coulomb interaction affects the transport properties only perturbatively, in 1D it completely modifies the ground state from its well-known Fermi-liquid form and the Fermi surface is qualitatively altered even for weak interactions. Today, it is well established theoretically that the low temperature transport properties of interacting 1D-electron systems are described in terms of a Luttinger-liquid rather than a Fermi-liquid [3,4]. The difference between a Luttingerliquid and Fermi-liquid becomes dramatic already in the presence of a single impurity. According to Landauer's theory the conductance of a single channel wire with a barrier is given by G = |t| 2 · e 2 /h, where |t| 2 is the transmission probability through the barrier. This result holds even at finite temperatures, assuming the transmission probability is independent of energy, as is often the case for barriers that are sufficiently above or below the Fermi energy. In 1D, interactions play a crucial role in that they form charge density correlations. These correlations, similar in nature to charge density waves [5], are easily pinned by even the smallest barrier, resulting in zero transmission and, hence, a vanishing conductance at zero temperature. At finite temperatures the correlation length is finite and the conductance decreases as a power-law of temperature,Herewhere U is the Coulomb energy between particles and E F is the Fermi energy in the wire. Despite the vast theoretical understanding of Luttingerliquids only a handful of experiments have been interpreted using such models. For example, in clean semiconductor wires prepared by the cleaved edge overgrowth (CEO) method [6], contrary to theory, the conductance is suppressed from its universal value [7]. Although not fully understood this suppression is believed to be a result of Coulomb interactions that suppress the coupling between the reservoirs and the wire region. Other measurements done on weakly disordered wires [8] show a weak temperature dependence of the conductance that is attributed to the Coulomb forces between electrons in the wire. Finally, The strongest manifestation of interaction in the clean limit comes from tunneling experiments such as the one recently reported on single walled carbon na...
Understanding the flow of spins in magnetic layered structures has enabled an increase in data storage density in hard drives over the past decade of more than two orders of magnitude [1]. Following this remarkable success, the field of 'spintronics' or spin-based electronics [1,2,3] is moving beyond effects based on local spin polarisation and is turning its attention to spin-orbit interaction (SOI) effects, which hold promise for the production, detection and manipulation of spin currents, allowing coherent transmission of information within a device [1,2]. While SOIinduced spin transport effects have been observed in two-and three-dimensional samples, these have been subtle and elusive, often detected only indirectly in electrical transport or else with more sophisticated techniques [4,5,6,7,8,9]. Here we present the first observation of a predicted 'spinorbit gap' in a one-dimensional sample, where counter-propagating spins, constituting a spin current, are accompanied by a clear signal in the easily-measured linear conductance of the system [10,11].We first introduce the class of phenomena we dub 'the one-dimensional spin-orbit gap' using a simple example adapted from Ref. [10], then describe our experiment in detail, and finally present a more elaborate model which captures most of the features seen in our data.The spin-orbit interaction is a relativistic effect where a charged particle moving in an electric field experiences an effective magnetic field which couples to its spin [12]. In semiconductor heterostructures, the electric field can arise as a result of either the lack of an inversion centre in the crystal (bulk inversion asymmetry, BIA) or a lack of symmetry in an external confining potential (structural inversion asymmetry, SIA) due to crystal interfaces or additional structures such as metallic gates [13]. The strength of the resulting effective magnetic field is proportional to both the particle's momentum and the original electric field.Consider a spin-degenerate one-dimensional subband with a Hamiltonian H 0 = 2 k 2 2m , where is Planck's constant, k the particle's momentum and m its mass ( Figure 1a). The leading order SO contribution to the Hamiltonian iswhere − → σ is the particle's spin, V the electrostatic potential and β a material-dependent parameter [14]. This term breaks the spin-degeneracy of the system and results in two spinful subbands separated by a lateral (wave vector) shift as shown in Figure 1b.Despite this rather striking change in the band structure, measurements of conductance through the system cannot distinguish the situation shown in Figure 1b from the case where the spins are degenerate. In both cases the edges of the two spin subbands occur at the same energy, so in both cases the conductance rises by G 0 = 2e 2 /h when the Fermi level of the system is tuned through this energy (e.g. by applying a voltage to a nearby gate) [15,16,17]. (Figure 1d.) To detect the SO shift in a transport measurement, a different approach is needed.Note that the spins as shown in Figure ...
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