arXiv subjects

J. Gonzalez

Publications and source records attributed to J. Gonzalez.

At least 91 records · Page 5Linked to original sources

arXiv2005

Modulation of Luttinger liquid exponents in multi-walled carbon nanotubes

We develop in this paper a theoretical framework that applies to the intermediate regime between the Coulomb blockade and the Luttinger liquid behavior in multi-walled carbon nanotubes. Our main goal is to confront the experimental observations of transport properties, under conditions in which the thermal energy is comparable to the spacing between the single-particle levels. For this purpose we have devised a many-body approach to the one-dimensional electron system, incorporating the effects of a discrete spectrum. We show that, in the crossover regime, the tunneling conductance follows a power-law behavior as a function of the temperature, with an exponent that oscillates with the gate voltage as observed in the experiments. Also in agreement with the experimental observations, a distinctive feature of our approach is the existence of an inflection point in the log-log plots of the conductance vs temperature, at gate voltages corresponding to peaks in the oscillation of the exponent. Moreover, we evaluate the effects of a transverse magnetic field on the transport properties of the multi-walled nanotubes. For fields of the order of 4 T, we find changes in the band structure that may be already significant for the outer shells, leading to an appreciable variation in the power-law behavior of the conductance. We then foresee the appearance of sensible modulations in the exponent of the conductance for higher magnetic fields, as the different subbands are shifted towards the development of flat Landau levels.

cond-mat.str-el↗

arXiv2005

Electronic instabilities in 3D arrays of small-diameter (3,3) carbon nanotubes

We investigate the electronic instabilities of the small-diameter (3,3) carbon nanotubes by studying the low-energy perturbations of the normal Luttinger liquid regime. The bosonization approach is adopted to deal exactly with the interactions in the forward-scattering channels, while renormalization group methods are used to analyze the low-energy instabilities. In this respect, we take into account the competition between the effective e-e interaction mediated by phonons and the Coulomb interaction in backscattering and Umklapp channels. Moreover, we apply our analysis to relevant experimental conditions where the nanotubes are assembled into large three-dimensional arrays, which leads to an efficient screening of the Coulomb potential at small momentum-transfer. We find that the destabilization of the normal metallic behavior takes place through the onset of critical behavior in some of the two charge stiffnesses that characterize the Luttinger liquid state. From a physical point of view, this results in either a divergent compressibility or a vanishing renormalized velocity for current excitations at the point of the transition. We observe anyhow that this kind of critical behavior occurs without the development of any appreciable sign of superconducting correlations.

cond-mat.str-el↗

arXiv2005

Coulomb screening and electronic instabilities of small-diameter (5,0) nanotubes

We investigate the instabilities that may lead to the breakdown of the Luttinger liquid in the small-diameter (5,0) nanotubes, paying attention to the competition between the effective interaction mediated by phonon-exchange and the Coulomb interaction. We use bosonization methods to achieve an exact treatment of the Coulomb interaction at small momentum-transfer, and apply next renormalization group methods to analyze the low-energy behavior of the electron system. This allows us to discern the growth of several response functions for charge-density-wave modulations and for superconducting instabilities with different order parameters. We show that, in the case of single nanotubes exposed to screening by external gates, the Luttinger liquid is unstable against the onset of a strong-coupling phase with very large charge-density-wave correlations. The temperature of crossover to the new phase depends crucially on the dielectric constant $κ$ of the environment, ranging from $T_{C}\sim 10^{-4} {\rm K}$ (at $κ\approx 1$) up to a value $T_{C} \sim 10^{2} {\rm K}$ (reached from $κ\approx 10$). The physical picture is however different when we consider the case of a large array of nanotubes, in which there is a 3D screening of the Coulomb interaction over distances much larger than the intertube separation. The electronic instability is then triggered by the divergence of one of the charge stiffnesses in the Luttinger liquid, implying a divergent compressibility and the appearance of a regime of phase separation into spatial regions with excess and defect of electron density.

cond-mat.str-el↗

arXiv2005

Crossover from Luttinger liquid to Coulomb blockade regime in carbon nanotubes

We develop a theoretical approach to the low-energy properties of 1D electron systems aimed to encompass the mixed features of Luttinger liquid and Coulomb blockade behavior observed in the crossover between the two regimes. For this aim we extend the Luttinger liquid description by incorporating the effects of a discrete single-particle spectrum. The intermediate regime is characterized by a power-law behavior of the conductance, but with an exponent oscillating with the gate voltage, in agreement with recent experimental observations. Our construction also accounts naturally for the existence of a crossover in the zero-bias conductance, mediating between two temperature ranges where the power-law behavior is preserved but with different exponent.

cond-mat.str-el↗

arXiv2004

Localization of electronic states by fullerene charges in carbon nanotubes

We study the effects of the electrostatic interaction produced by charged fullerenes encapsulated in carbon nanotubes, showing that they are able to modify locally the electronic density of states in the hybrid system. In the cases where the interaction is felt as an attractive potential by the electrons in the nanotube, localized electronic states are formed in the nanotubes around the position of the fullerenes. This produces an effective narrowing of the gap in semiconducting nanotubes over a distance of a few nanometers, in agreement with the spatial modulation of the gap observed in the experiments.

cond-mat.mes-hall↗

arXiv2004

Current instability and diamagnetism in small-diameter carbon nanotubes

We investigate the electronic instabilities in carbon nanotubes of short radius, looking for the breakdown of the Luttinger liquid regime from the singular behavior of the charge stiffnesses at low energies. We show that such a breakdown is realized in the undoped (3,3) nanotubes through the onset of phase separation into regions with opposite electronic current. The phenomenology derived from this regime is consistent with the formation of a pseudogap in the single-particle spectrum as well as with a divergent diamagnetic susceptibility, as observed in the experiments carried out in carbon nanotubes of small diameter.

cond-mat.str-el↗

arXiv2003

Insulating, superconducting and large-compressibility phases in nanotube ropes

The superconducting properties of carbon nanotube ropes are studied using a new computational framework that incorporates the renormalization of intratube interactions and the effect of intertube Coulomb screening. This method allows to study both the limits of thin and thick ropes ranging from purely one-dimensional physics to the setting of three-dimensional Cooper-pair coherence, providing good estimates of the critical temperature as a function of the rope physical parameters. We discuss the connection of our results with recent experiments.

cond-mat.str-el↗

arXiv2003

Transport approach to the superconducting proximity effect in carbon nanotubes

A microscopic approach is developed to account for the magnitudes of the supercurrents observed experimentally in carbon nanotubes placed between superconducting contacts. We build up a model for the nanotube ropes encompassing the electron repulsion from the Coulomb interaction and the effective attraction given by phonon exchange. We show that the available experimental data are consistent with the expected decay of the supercurrents along the length of the nanotube samples. Our results stress that the propagation of the Cooper pairs is favored in the thick ropes, as a consequence of the reduction in the strength of the Coulomb interaction from the electrostatic coupling between the metallic nanotubes. We also provide an explanation for the temperature dependence of the supercurrents observed in the experiments, remarking the existence of a crossover from a very flat behavior at low temperatures to a pronounced decay in the long nanotubes.

cond-mat.str-el↗

arXiv2003

Doping- and size-dependent suppression of tunneling in carbon nanotubes

We study the effect of doping in the suppression of tunneling observed in multi-walled nanotubes, incorporating as well the influence of the finite dimensions of the system. A scaling approach allows us to encompass the different values of the critical exponent $α$ measured for the tunneling density of states in carbon nanotubes. We predict that further reduction of $α$ should be observed in multi-walled nanotubes with a sizeable amount of doping. In the case of nanotubes with a very large radius, we find a pronounced crossover between a high-energy regime with persistent quasiparticles and a low-energy regime with the properties of a one-dimensional conductor.

cond-mat.str-el↗

arXiv2003

Spin and superconducting instabilities near a Van Hove singularity

We apply a wilsonian renormalization group approach to the system of electrons in a two-dimensional square lattice interacting near the saddle-points of the band, when the correlations at momentum ${\bf Q} = (π, π)$ prevail in the system. The detailed consideration of the spin degrees of freedom allows to discern the way in which the SU(2) spin invariance is preserved in the renormalization process. Regarding the spin correlations, we find two different universality classes which correspond, in the context of the extended Hubbard model, to having the bare on-site interaction $U$ repulsive or attractive. The first class is characterized by a spin instability which develops through the condensation of particle-hole pairs with momentum ${\bf Q}$, with the disappearance of the Fermi line in the neighborhood of the saddle-points. Within that class, the attractive or repulsive character of the nearest-neighbor interaction $V$ dictates whether there is or not a d-wave superconducting instability in the system. For the Hubbard model with just on-site interaction, we show that some of the irrelevant operators are able to trigger the superconducting instability. The naturalness of the competing instabilities is guaranteed by the existence of a range of doping levels in which the chemical potential of the open system is renormalized to the level of the saddle-points. We incorporate this effect to obtain the phase diagram as a function of the bare chemical potential, which displays a point of optimal doping separating the regions of superconductivity and spin instability.

cond-mat.str-el↗

arXiv2003

Large N Effects and Renormalization of the Long-Range Coulomb Interaction in Carbon Nanotubes

We develop a dimensional regularization approach to deal with the low-energy effects of the long-range Coulomb interaction in 1D electron systems. The method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D = 1, providing at the same time insight about the fixed-points of the theory. We show that the effect of increasing the number N of subbands at the Fermi level is opposite to that of approaching the bare Coulomb interaction in the limit D --> 1. Then, we devise a double scaling limit, in which the large N effects are able to tame the singularities due to the long-range interaction. Thus, regular expressions can be obtained for all observables right at D = 1, bearing also a dependence o the doping level of the system. Our results imply a variation with N in the value of the exponent for the tunneling density of states, which is in fair agreement with that observed in different transport experiments involving carbon nanotubes. As the doping level is increased in nanotubes of large radius and multi-walled nanotubes, we predict a significant reduction of order N^{-1/2} in the critical exponent of the tunneling density of states.

cond-mat.str-el↗

arXiv2002

Properties of electrons near a Van Hove singularity

The Fermi surface of most hole-doped cuprates is close to a Van Hove singularity at the M point. A two-dimensional electronic system, whose Fermi surface is close to a Van Hove singularity shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. The renormalization group approach is reviewed with emphasis on the underlying physical processes. General properties of the phase diagram and possible deformations of the Fermi surface due to the Van Hove proximity are described.

cond-mat.str-el↗

arXiv2002

Superconductivity in carbon nanotube ropes

We investigate the conditions in which superconductivity may develop in ropes of carbon nanotubes. It is shown that the interaction among a large number of metallic nanotubes favors the appearance of a metallic phase in the ropes, intermediate between respective phases with spin-density-wave and superconducting correlations. These arise in samples with about 100 metallic nanotubes or more, where the long-range Coulomb interaction is very effectively reduced and it may be overcome by the attractive interaction from the exchange of optical phonons within each nanotube. We estimate that the probability for the tunneling of Cooper pairs between neighboring nanotubes is much higher than that for single electrons in a disordered rope. The effect of pair hopping is therefore what establishes the intertube coherence, and the tunneling amplitude of the Cooper pairs dictates the scale of the transition to the superconducting state.

cond-mat.str-el↗

arXiv2002

Microscopic model of superconductivity in carbon nanotubes

We propose the model of a manifold of one-dimensional interacting electron systems to account for the superconductivity observed in ropes of nanotubes. We rely on the strong suppression of single-particle hopping between neighboring nanotubes in a disordered rope and conclude that the tunnelling takes place in pairs of electrons, which are formed within each nanotube due to the existence of large superconducting correlations. Our estimate of the transition temperature is consistent with the values that have been measured experimentally in ropes with about 100 metallic nanotubes.

cond-mat.str-el↗

arXiv2001

Superconducting and pseudogap phases from scaling near a Van Hove singularity

We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.

cond-mat.str-el↗

arXiv2001

Consistency of superconducting correlations with one-dimensional electron interactions in carbon nanotubes

We show that a model of interacting electrons in one dimension is able to explain the order of magnitude as well as the temperature dependence of the critical supercurrents recently measured in nanotube samples placed between superconducting contacts. We use bosonization methods to compute superconducting correlations in the presence of the long-range Coulomb interaction, ending up with a picture in which the critical current does not follow the temperature dependence of the gap in the contacts, in contrast to the prediction of the conventional proximity effect. Our results also reveal the presence of a short-range attractive interaction in the nanotubes, which accounts for a significant enhancement of the critical supercurrents.

cond-mat.str-el↗

arXiv2001

Crossover from marginal Fermi liquid to Luttinger liquid behavior in carbon nanotubes

We study graphene-based electron systems with long-range Coulomb interaction by performing an analytic continuation in the number of dimensions. We characterize in this way the crossover between the marginal Fermi liquid behavior of a graphite layer and the Luttinger liquid behavior at $D = 1$. The former persists for any dimension above $D = 1$. However, the proximity to the $D = 1$ fixed-point strongly influences the phenomenology of quasi-onedimensional systems, giving rise to an effective power-law behavior of observables like the density of states. This applies to nanotubes of large radius, for which we predict a lower bound of the corresponding exponent that turns out to be very close to the value measured in multi-walled nanotubes.

cond-mat.str-el↗

arXiv2000

Charge instabilities near a Van Hove singularity

The charge instabilities of electron systems in the square lattice are analyzed near the Van Hove singularity by means of a wilsonian renormalization group approach. We show that the method preserves the spin rotational invariance at all scales, allowing a rigorous determination of spin and charge instabilities of the $t-t'$ Hubbard model. For $t'$ above $\approx 0.276 t$, repulsive interactions fall into two different universality classes. One of them has nonsingular response functions in the charge sector, while the other is characterized by the splitting of the Van Hove singularity. At the level of marginal perturbations, the Hubbard model turns out to be at the boundary between the two universality classes, while extended models with nearest-neighbor repulsive interactions belong to the latter class. In the case of open systems allowed to exchange particles with a reservoir, we show the existence of a range of fillings forbidden above and below the Van Hove singularity. This has the property of attracting the Fermi level in the mentioned range, as the system reaches its lowest energy when the Fermi energy is at the singularity.

cond-mat.str-el↗