ABSTRACT
We review the recent theoretical progress in understanding the superconductivity observed in ultrathin 4-Angstrom carbon nanotubes (CNTs) embedded in the linear channels of the aluminophosphate-five (AlPO4−5, AFI) zeolite crystals. To identify the ground state of the (5,0) CNT@AFI system, we have carried out second-order renormalization group (RG) analysis to show that if arranged in an array structure in the channels of an AFI crystal, superconductivity can dominate over the Peierls distortion mechanism to be the favored state. However, if the array is very thin, then the manifestation would be that of one-dimensional (1D) superconductivity, displaying finite resistance at finite temperatures. We give a brief description of the phase slip mechanism underlying this behavior. With transverse Josephson coupling between the (5,0) CNT arrays, a 1D to three-dimensional (3D) crossover transition
can occur at a temperature below which 3D superconducting behaviors appear. By carrying out Monte Carlo (MC) simulations on a transversely discretized Ginzburg-Landau (GL) model, we show that both the thermal specific heat and electrical data can be well explained. In particular, just above the dimensional crossover transition, the phase correlation function exhibits the signature of a Berezinskii-Kosterlitz-Thouless transition in good agreement with the measured temperature dependence of resistance. 1.1 Introduction
Since the first observation of superconductivity in ultrathin carbon nanotubes (CNTs) embedded in AFI zeolite crystals [1], there has been much experimental and theoretical works devoted to this subject. In this chapter, we summarize the recent progress in the theoretical analysis of superconductivity in 4-Angstrom CNT arrays. The paper is organized as follows. Section 1.2 gives a brief introductory description of the relevant material system. Section 1.3 is devoted to the RG analysis of such CNT@AFI system, aimed at identifying the zero temperature ground state between two competing mechanisms-superconductivity and the Peierls distortion (the charge density wave, or CDW) state. In Section 1.4, we give a short review on the origin of electrical resistance in 1D superconductors, based on the physical picture of phase slips as mathematically formulated by the Langer-Ambegaokar-McCumber-Halperin theory. In Section 1.5, we use Monte Carlo simulation of the Ginzburg-Landau model to explain the specific heat and electronic transport characteristics in the (1D to 3D) dimensional crossover transition, leading to the observed 3D superconductivity. We conclude in Section 1.6 with an overview summary of the salient points. 1.2 The CNT@AFI System
CNTs were first grown inside the channels of porous AFI zeolite with pyrolysis of the precursor molecules-tripropylamine [2]. AFI is a micro-porous zeolite crystal with aligned linear channels. The channels are hexagonally close packed in the transverse a-b plane, each with an inner diameter of 7.3 Å and separated by a
center to center distance of 13.7 Å. Inside the channels, a fraction of the carbon atoms, from the pyrolysis of tripropylamine precursor, formed single-wall carbon nanotubes that are ∼4 Å in diameter. This is confirmed by high-resolution transmission electron microscopy observation [2], adsorption spectra [3], and Raman spectra [4-6], in which the characteristic radial breathing mode, particular to the tube structure, was observed. A sketch of the AFI zeolite with embedded CNTs is shown in Fig. 1.1.
