Electronic properties of carbon nanotubes

In this thesis we study the interplay between electronic correlations and geometry in single-walled carbon nanotubes by microscopic model calculations. Electronic correlations are expected to be strong because of the low dimensionality of carbon nanotubes. Moreover the possibility of existing in different chiralities make them an ideal model system to investigate this interplay. After reviewing the band theory we discuss the magnitude and the scaling of the single particle charge gap when electronic correlations are included. This is done within a Hartree-Fock mean field calculation and with the help of a renormalization group argument. We predict that there is a correlation induced charge gap of several meV. This result is especially important for carbon nanotubes of armchair chirality where the band gap is always zero. We also observe that this correlation gap is tunable with uniaxial strain. In another chapter we study the electronic properties when a magnetic field parallel to the tube axis is applied. The persistent currents show a strong dependence on chirality. When we look at the diffusive limit by adding disorder (impurities) we can exhibit the Altshuler-Aronov-Spivak effect. The last two chapters are concerned with the question of superconductivity in carbon nanotubes. We calculate the spingap in the Heisenberg model for the smallest tubes by an exact quantum Monte Carlo method. We relate these results to the RVB theory of superconductivity (mean-field and variational Monte Carlo) which describes the system upon hole doping. We obtain chirality dependent RVB superconducting order parameters. Compared to the two dimensional limit we observe that superconductivity is enhanced and antiferromagnetism is reduced. Wherever possible we try to put our results into relation with experimental findings.

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible representations labelled by a Young tableau with

m

boxes on each site of various lattices. Thanks to an intensive use of variational Monte Carlo method based on Gutzwiller projected fermionic wave functions, we aim to determine the ground state and its related properties of systems which are beyond the capabilities of other numerical methods. This typically means that we will study large lattices with many particles per site for

N>2

. The first part of this thesis will introduce the basic theoretical tools connected to the SU(N) Heisenberg model. A very short review of group theory introducing Young tableaux, will clarify the concept of fully antisymmetric irreducible representation of the SU(N) Lie algebra. Some properties of the Heisenberg model will be discussed and a mean-field solution will be given. The numerical methods used during this thesis and their limitations wil also be introduced. We will investigate the properties of 1-dimensional systems in the second part of this work. In particular, the chains have been studied for arbitrary

N

and

m

with non-abelian bosonisation leading to predictions about the nature of the ground state (gapped or critical) in most but not all cases. We have been able to verify these predictions for a representative number of cases with

N\leq10

and

m\leq N/2

, and we have shown that the opening of a gap is associated with a spontaneous dimerisation or trimerisation depending on the value of

m

and

N

. We have also investigated the marginal cases, where non-abelian bosonisation did not lead to any prediction. In these cases, variational Monte Carlo predicts that the ground state is critical with exponents that are consistent with conformal field theory. The other 1-dimensional system that has been studied is the ladder for which field-theory gives some predictions. For instance, the ground state of the SU(4) case in the fundamental irreducible representation is believed to consist of a 4-site plaquette state for any non-zero inter-leg coupling. We have confirmed the presence of this state, even if in the weak coupling regime, the optimal variational state is gapless. The study has been extended to various

N

and

m

values providing interesting results. The last part will present the results for 2-dimensional lattices. The square lattice will first be investigated. A mean-field analysis predicts a plaquette ground state for

3\leq N/m < 5

and of a chiral ground state for

N/m\geq 5

. By systematically studying the SU(3m) and SU(6m) Heisenberg model, we determined that the mean-field solution is valid even at small

m

(

m>1

for SU(3m) and

m>2

for SU(6m)). Then, for the SU(6m) Heisenberg model with

m

particles per site on a honeycomb lattice, we make the connection between the

m=1

case, for which the ground state has recently been shown to be in a plaquette singlet state, and the

m\rightarrow \infty

limit, where a mean-field approach has established that the ground state has chiral order. We were able to show that this system has a clear tendency toward the chiral order as soon as

m\geq 2

. This demonstrates that the chiral phase can be stabilised for not too large values of

m

, opening the way to its experimental realisations in other lattices. We will finally present results for the SU(3m) on the triangular lattice for which we find a plaquette state, when

m>1

EPFL2016

Thermal destruction of chiral order in a two-dimensional model of coupled trihedra

Pascal Viot

We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a nonplanar way at T=0. This model, consisting of coupled trihedra (or Ising-RP3 model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations, and Z2 vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and Z2 vortices proliferate near the chiral domain walls, explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized Z2 topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size effects suggest the proximity of the present model to a tricritical point. A body of results is presented, which all support this claim: (i) first-order transitions obtained by Monte Carlo simulations on several related models, (ii) approximate mapping between the Ising-RP3 model and a dilute Ising model (exhibiting a tricritical point), and, finally, (iii) mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-RP3 model.

2008

A Guide to the Design of Electronic Properties of Graphene Nanoribbons

Oleg Yazyev

Graphene nanoribbons (GNRs) are one-dimensional nanostructures predicted to display a rich variety of electronic behaviors. Depending on their structure, GNRs realize metallic and semiconducting electronic structures with band gaps that can be tuned across broad ranges. Certain GNRs also exhibit a peculiar gapped magnetic phase for which the half-metallic state can be induced as well as the topologically nontrivial quantum spin Hall electronic phase. Because their electronic properties are highly tunable, GNRs have quickly become a popular subject of research toward the design of graphene-based nanostructures for technological applications. This Account presents a pedagogical overview of the various degrees of freedom in the atomic structure and interactions that researchers can use to tailor the electronic structure of these materials. The Account provides a broad picture of relevant physical concepts that would facilitate the rational design of GNRs with desired electronic properties through synthetic techniques. We start by discussing a generic model of zigzag GNR within the tight-binding model framework. We then explain how different modifications and extensions of the basic model affect the electronic band structures of GNRs. We classify the modifications based on the following categories: (1) electronelectron and spinorbit interactions, (2) GNR configuration, which includes width and the crystallographic orientation of the nanoribbon (chirality), and (3) the local structure of the edge. We subdivide this last category into two groups: the effects of the termination of the pi-electron system and the variations of electrostatic potential at the edge. This overview of the structureproperty relationships provides a view of the many different electronic properties that GNRs can realize. The second part of this Account reviews three recent experimental methods for the synthesis of structurally well-defined GNRs. We describe a family of techniques that use patterning and etching of graphene and graphite to produce GNRs. Chemical unzipping of carbon nanotubes also provides a route toward producing chiral GNRs with atomically smooth edges. Scanning tunneling microscopy/spectroscopy investigations of these unzipped GNRs have revealed edge states and strongly suggest that these GNRs are magnetic. The third approach exploits the surface-assisted self-assembly of GNRs from molecular precursors. This powerful method can provide full control over the atomic structure of narrow nanoribbons and could eventually produce more complex graphene nanostructures.

Amer Chemical Soc2013