The history of luttinger liquid theory actually goes back to the work of. Finally, chapter 8 will discuss measurements on metallic samples with extremely long mean free paths. These experiments show evidence of this luttinger liquid behavior, in which the electronelectron interactions lead to a qualitatively different ground state. Electronelectron interactions in such systems are predicted to give rise to nonfermi luttinger liquid behavior at low temperature. Pdf crossover from marginal fermi liquid to luttinger. Sensing kondo correlations in a suspended carbon nanotube. Strong electronelectron interactions have been demonstrated with the charge transport in swnts, leading to many phenomena such as coulomb blockade 49, 50, kondo effects 51, 52, and luttinger liquid behavior 53, 54.
Tomonaga luttingerliquid behavior in singlewalled carbon. Toshiyuki ohashi, liming dai, in carbon nanotechnology, 2006. With minor modifications, the same conclusions apply to transport in ropes of singlewall nanotubes. Walled carbon nanotubes prober lab yale university.
Luttinger liquid behavior in carbon nanotubes springerlink. Mceuen department of physics, university of california and materials sciences division, lawrence berkeley national. Transition from a tomonagaluttinger liquid to a fermi. Supercurrents through singlewalled carbon nanotubes science. Using scatteringtype scanning nearfield optical microscopy s. Electric resistivity of multiwalled carbon nanotubes at. Quantum confined tomonagaluttinger liquid in mo6se6.
Observation of a luttingerliquid plasmon in metallic singlewalled carbon nanotubes zhiwen shi1, xiaoping hong1,hansa. Crossover from marginal fermi liquid to luttinger liquid behavior in carbon nanotubes. Spin gap and luttinger liquid description of the nmr relaxation in carbon nanotubes. Singlewall carbon nanotubes cornell laboratory of atomic and. Carbon nanotubes cnts have been considered as an ideal platform for. We realized the realspace imaging of luttinger liquid plasmons in semiconducting singlewalled carbon nanotubes sswcnts and studied the effects of chemicaldopinginduced charge carrier density modulation on plasmons. Citeseerx luttinger liquid behavior in singlewall nanotubes. Pdf direct observation of tomonagaluttingerliquid state in. Luttinger liquids university of illinois at urbana. Spin gap and luttinger liquid description of the nmr. New devices and geometries while the above experiments demonstrate that many of the basic properties of singlewall carbon nanotubes are now.
Luttinger liquid behavior in carbon nanotubes arxiv. A comprehensive theory for the magnetic field and temperature dependent nmr c spin. Transport properties of metallic singlewall nanotubes are examined based on the luttinger liquid theory. Tian x 1, gu q, duan j, chen r, liu h, hou y, chen j. We study the effect of doping in the suppression of tunneling observed in multiwalled nanotubes, incorporating as well the influence of the finite dimensions of the system. Luttinger liquid behavior in carbon nanotubes article pdf available.
Luttingerliquid behaviour in carbon nanotubes nature. Depending on diameter and helicity, singlewalled carbon nanotubes swnts have, at most, two conducting channels with minimum resistance in the absence of disorder predicted to be h4e 2 6. To unambiguously demonstrate the luttinger liquid behavior, one can combine the study of nanotube plasmon which can determine the luttinger liquid parameter g with electrical. Luttingerliquid behavior of heliumthree in nanotubes j.
Luttinger liquid behavior in carbon nanotubes nasaads. Consequently, the luttinger liquid behavior is rigorous in metallic nanotubes with a temperature up to thousands of kevin. Carbon nanotubes are exceptionally interesting from a fundamental research point of view. Mceuen laboratory of atomic andsolidstate physics, department of physics, cornell university, ithaca, newyork 14853, usa. Characteristic luttinger liquid power laws are found for the tunneling density of states, with exponents approaching their fermi liquid value only very slowly as the. Recently, singlewalled carbon nanotubes swnts have emerged as a new type of 1d conductor that may exhibit ll behavior. Singlewall carbon nanotubes are truly onedimensional conductors and are thus expected to behave as lls. For singlewall nanotubes, the electronelectron interaction destroys the fermi liquid state and leads to luttinger liquid behavior. Letters measurement of the quantum capacitance of interacting electrons in carbon nanotubes s. A luttinger liquid, or tomonaga luttinger liquid, is a theoretical model describing interacting electrons or other fermions in a onedimensional conductor e. Electrically conducting singlewalled carbon nanotubes swnts represent quantum wires 7,8,9,10 that may exhibit luttingerliquid behaviour 11, 12. We analyze a recent nmr experiments by singer et al.
As opposed to fermi liquid model where the interaction between electrons is turned on adiabatically from corresponding fermi gas model. Transition from a tomonaga luttinger liquid to a fermi liquid in potassiumintercalated bundles of singlewall carbon nanotubes h. Carbon nanotubes by stephanie reich overdrive rakuten. It is characterized by collective behavior of electrons in contrast to quasiparticle description of fermi liquid. Carbon nanotubes cnts provide an ideal medium for testing the behavior of onedimensional electron systems and are promising candidates for electronic applications such as sensors or fieldeffect transistors. Martin2, kenji watanabe3, takashi taniguchi3, yuenron shen1,4 and feng wang1,4,5 surface plasmons1, collective oscillations of conduction elec trons, hold great promise for the nanoscale integration of. Many concepts of onedimensional physics have been verified experimentally such as electron and phonon confinement or the onedimensional singularities in the density of states. Such a model is necessary as the commonly used fermi liquid model breaks down for one dimension. Electrically conducting singlewalled carbon nanotubes swnts represent quantum wires that may exhibit luttinger liquid behaviour.
A scaling approach allows us to encompass the different values of the critical exponent. Luttinger liquid model describes the behavior of id interacting electron gases. By modeling the nanotube as a nano transmission line with. Electrically conducting single walled carbon nanotubes swnts represent quantum wires710 that may exhibit luttingerliquid behaviour11,12.
Metallic singlewalled carbon nanotubes swnts are considered to be ideal. Improving luttingerliquid plasmons in carbon nanotubes by. Improving luttinger liquid plasmons in carbon nanotubes by chemical doping. Pdf luttinger liquid behavior in carbon nanotubes paul. The predictions of correlated electron behavior in carbon nanotubes treated as a 1d. Luttinger liquid behavior of heliumthree in nanotubes subject. Focusing on a nanotube transistor setup, the linear conductance is computed from the kubo formula using perturbation theory in the leadtube tunnel conductances. Confining interacting particles in onedimension 1d changes the electronic behavior of the system fundamentally, which has been studied extensively in the past. Here we present measurements of the conductance of individual ropes of such swnts as a function of temperature and voltage. Characteristic luttinger liquid power laws are found for the tunneling density of states, with exponents approaching their fermi liquid value only very slowly as the number of conducting shells increases. The functional form is consistent with the powerlaw behaviour predicted for tunnelling into a. Our results can be well fitted with a power law of t within the framework of one dimensional luttinger liquid theory with. Coulomb interaction effects have pronounced consequences in carbon nanotubes due to their 1d nature. Lobb, department of physics carbon nanotubes cnts provide an ideal medium for testing the behavior of.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Fermi level both exhibit powerlaw behaviour with almost identical exponents in good. Electrically conducting singlewalled carbon nanotubes swnts represent quantum wires 7,8,9,10 that may exhibit luttinger liquid behaviour 11, 12. Mcm41 nanotubes at temperatures near the fermi degeneracytemperature,t. Observation of a luttingerliquid plasmon in metallic. In particular, correlations imply the breakdown of fermi liquid theory and typically lead to luttinger liquid behavior characterized by pronounced powerlaw suppression of the transport current and the density of states, and spincharge separation. Luttinger liquid theory of nanotubes predicts 1,2 that, since tube diameter is larger than carbon separation, the 1d electron coupling is mainly accounted for by the longrange electron. Power law behavior as a function of temperature or bias voltage is observed.
Abstract the electrical conduction behavior of singlewalled carbon nanotube networks was investigated. The electric resistivity of a clean multiwalled carbon nanotube mwnt mat sample was studied at temperatures t between 300 and 1900 k. In particular, correlations imply the breakdown of fermi. For sufficiently long nanotubes and high temperature, phonon backscattering should lead to an anomalous temperature dependence. Coulomb blockade oscillations, luttinger liquid behavior,3 kondo. Luttinger liquid theory as a model of the gigahertz. Luttinger liquid behavior in multiwall carbon nanotubes. Luttinger liquid behavior in metallic carbon nanotubes core. The lowenergy theory for multiwall carbon nanotubes including the longranged coulomb interactions, internal screening effects, and singleelectron hopping between graphite shells is derived and analyzed by bosonization methods. Luttinger liquid behavior in carbon nanotubes core. Thermal emission spectra from individual suspended carbon. Luttinger liquid behavior of heliumthree in nanotubes.
In semiconducting nanotubes, the electron dispersion is hyperbolic and the fermi energy can be tuned across a large range with electrostatic gating. Examples of 1d metallic systems include carbon nanotubes, quasi1d organic conductors, metal chains, and domain boundary defects in monolayer thick transitionmetal dichalcogenides such as mose2. How we measure reads a read is counted each time someone. Luttinger liquid behavior in metallic carbon nanotubes. Our observed quantum plasmon behaviour agrees quantitatively with the. Luttinger liquid in carbon nanotubes capri spring school. Terahertz spectroscopy of individual singlewalled carbon.
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