Dimensionality plays a critical role in determining the properties of materials due to, for example, the different ways that electrons interact in three-dimensional, twodimensional (2D), and one-dimensional (1D) structures.1-5 The study of dimensionality has a long history in chemistry and physics, although this has been primarily with the prefix “quasi” added to the description of materials; that is, quasi-1D solids, including square-planar platinum chain and metal trichalcogenide compounds,2,6 and quasi2D layered solids, such as metal dichalcogenides and copper oxide superconductors.3-5,7,8 The anisotropy inherent in quasi-1D and -2D systems is central to the unique properties and phases that these materials exhibit, although the small but finite interactions between 1D chains or 2D layers in bulk materials have made it difficult to address the interesting properties expected for the pure low-dimensional systems. Are pure low-dimensional systems interesting and worth pursuing? We believe that the answer to this question is an unqualified yes from the standpoints of both fundamental science and technology. One needs to look no further than past studies of the 2D electron gas in semiconductor heterostructures, which have produced remarkably rich and often unexpected results,9,10 and electron tunneling through 0D quantum dots, which have led to the concepts of the artificial atom and the creation of single electron transistors.11-15 In these cases, lowdimensional systems were realized by creating discrete 2D and 0D nanostructures. 1D nanostructures, such as nanowires and nanotubes, are expected to be at least as interesting and important as 2D and 0D systems.16,17 1D systems are the smallest dimension structures that can be used for efficient transport of electrons and optical excitations, and are thus expected to be critical to the function and integration of nanoscale devices. However, little is known about the nature of, for example, localization that could preclude transport through 1D systems. In addition, 1D systems should exhibit density of states singularities, can have energetically discrete molecularlike states extending over large linear distances, and may show more exotic phenomena, such as the spin-charge separation predicted for a Luttinger liquid.1,2 There are also many applications where 1D nanostructures could be exploited, including nanoelectronics, superstrong and tough composites, functional nanostructured materials, and novel probe microscopy tips.16-29 To address these fascinating fundamental scientific issues and potential applications requires answers to two questions at the heart of condensed matter chemistry and physics research: (1) How can atoms or other building blocks be rationally assembled into structures with nanometer-sized diameters but much longer lengths? (2) What are the intrinsic properties of these quantum wires and how do these properties depend, for example, on diameter and structure? Below we describe investigations from our laboratory directed toward these two general questions. The organization of this Account is as follows. In section II, we discuss the development of a general approach to the rational synthesis of crystalline nanowires of arbitrary composition. In section III, we outline key challenges to probing the intrinsic properties of 1D systems and illustrate solutions to these challenges with measurements of the atomic structure and electronic properties of carbon nanotubes. Last, we discuss future directions and challenges in section IV.

http://cmliris.harvard.edu/assets/AccChemRes_32_435.pdf

Chemistry and Physics in One Dimension: Synthesis and Properties of Nanowires and Nanotubes

Tetrathiafulvalenes, oligoacenenes, and their buckminsterfullerene derivatives: the brick and mortar of organic electronics.

This article discusses fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies are derived for extracting information concerning such local order from experiments, with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems---an exactly solvable one-dimensional (1D) electron gas with an impurity, and a weakly interacting 2D electron gas. Experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies are extensively reviewed. The authors adduce evidence that stripe correlations are widespread in the cuprates. They compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi-liquid state, and strong coupling, in which the magnetism is associated with well-defined localized spins, and stripes are viewed as a form of micro phase separation. The authors present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

How to detect fluctuating stripes in the high-temperature superconductors

We review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particle-hole bubble, producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless 1D quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom, fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a Luttinger liquid implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t-J- or the extended Hubbard model. In addition, 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.

https://iopscience.iop.org/article/10.1088/0034-4885/58/9/002/pdf

One-dimensional Fermi liquids

The character of the ground state of an antiferromagnetic insulator is fundamentally altered following addition of even a small amount of charge1. The added charge is concentrated into domain walls across which a π phase shift in the spin correlations of the host material is induced. In two dimensions, these domain walls are ‘stripes’ which can be insulating2,3 or conducting4,5,6 — that is, metallic ‘rivers’ with their own low-energy degrees of freedom. However, in arrays of one-dimensional metals, which occur in materials such as organic conductors7, interactions between stripes typically drive a transition to an insulating ordered charge-density-wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large compared tothe CDW coupling between stripes. As a consequence, there should exist electronic quantum liquid-crystal phases, which constitute new states of matter, and which can be either high-temperature superconductors or two-dimensional anisotropic ‘metallic’ non-Fermi liquids. Neutron scattering and other experiments in the copper oxide superconductor La1.6−xNd0.4SrxCuO4 already provide evidence for the existence of these phases in at least one class of materials.

Electronic liquid-crystal phases of a doped Mott insulator

1 Introduction to Highly Conducting One-Dimensional Solids.- 1. Introduction.- 2. Some Preliminary Thoughts.- 3. Excitonic Superconductivity.- 4. TCNQ Salts and KCP.- 4.1. NMP-TCNQ.- 4.2. TTF-TCNQ.- 4.3. KCP.- 5. TTF-TCNQ and TSeF-TCNQ.- 5.1. Structural Transitions in TTF-TCNQ.- 5.2. Electromagnetic Properties of TTF-TCNQ.- 5.3. ESR and Alloys of TTF-TCNQ and TSeF-TCNQ.- 6. Theory.- 7. Some Concluding Thoughts.- References.- 2 X-Ray and Neutron Scattering from One-Dimensional Conductors.- 1. Introduction.- 1.1. Lattice Instabilities and Phonon Anomalies.- 1.2. X-Ray Diffuse Scattering.- 1.3. Neutron Scattering.- 2. Structural Studies of KCP and Related Platinum Chain Complexes.- 2.1. Structure and One-Dimensional Electrical Properties of KCP.- 2.2. X-Ray Diffuse Scattering from KCP.- 2.3. Neutron Scattering Studies of KCP.- 2.4. Study of Other Platinum Complexes.- 3. Structural Studies of Organic One-Dimensional Conductors.- 3.1. Structure and TTF-TCNQ Crystals.- 3.2. High-Temperature Precursor Scattering in TTF-TCNQ.- 3.3. The Modulated Phases of TTF-TCNQ.- 3.4. Spin Waves in TTF-TCNQ?.- 3.5. The Interpretation of the Sequence of Modulated Phases in TTF-TCNQ.- 3.6. Study of Other Organic One-Dimensional Conductors.- 4. Concluding Remarks.- References and Notes.- 3 Charge-Density Wave Phenomena in One-Dimensional Metals: TTF-TCNQ and Related Organic Conductors.- 1. Introduction.- 2. Strength of Interactions Bandwidth, Electron-Electron and Electron-Phonon Interactions.- 2.1. One-Electron Energies Band Structure.- 2.2. Electron-Electron Interactions: Nuclear Magnetic Resonance and Magnetic Susceptibility.- 2.3. Electron-Phonon Interaction.- 3. The Peierls Instability in TTF-TCNQ: Structural Aspects and Phonon Softening.- 4. The Pseudogap: Optical Properties.- 5. Electrical Conductivity.- 5.1. DC Measurements.- 5.2. Microwave Measurements.- 6. The Transition Region 38 K<TTc1.- 4.1. Transport Properties.- 4.2. Magnetic Properties.- 4.3. Phonon Anomalies.- 5. Metal-Semiconductor Phase Transition.- 5.1. Variation of Transition Temperature Tc1 with Alloying.- 5.2. Thermodynamics and Critical Behavior of the Metal-Semiconductor Phase Transition.- 6. Semiconducting Phase, T< Tc1.- 6.1. Transport Properties in the Semiconducting Phase.- 6.2. Magnetic Properties.- 6.3. Superlattices and Phonon Anomalies.- 7. Summary.- References and Notes.- 5 Perturbation Approach to Lattice Instabilities in Quasi-One-Dimensional Conductors.- 1. Introduction.- 2. The One-Dimensional Electron-Phonon System.- 3. Fluctuations in the One-Dimensional System.- 4. Effects of Interchain Coupling.- 5. Effects of Impurities.- References and Notes.- 6 Theory of the One-Dimensional Electron Gas.- 1. Basic Physics.- 1.1. Introduction.- 1.2. Phase Transitions and Long-Range Order.- 1.3. Mathematical Model.- 1.4. Strong Coupling.- 2. Spinless Fermions.- 2.1. Definition of the Continuum Limit.- 2.2. Boson Representations and the Free Energy.- 2.3. Boson Representations of Fermion Fields.- 2.4. Correlation Functions of the Interacting System.- 3. Large "On-Site" Interaction.- 3.1. Attractive Interaction.- 3.2. Repulsive Interaction.- 3.3. Correlation Functions.- 4. Continuum Limit-Energy Gaps.- 4.1. Separation of Charge and Spin Degrees of Freedom.- 4.2. Reduction to Spinless Fermions.- 4.3. Solution of the Spinless Fermion Problems.- 4.4. Correlation Functions.- 4.5. Relationship to Other Problems.- 5. Renormalization Group Method.- 5.1. Scaling Equations.- 5.2. Trajectories and Energy Scales.- 5.3. Low-Temperature Properties.- 5.4. Four-Particle Functions.- Appendix A: Some Results That Are Useful for Working with Boson Representations.- Appendix B: Anticommutation of Different Fermion Fields.- Appendix C: Charge-Density Wave Gap and CDW Correlations.- References.- 7 The Prospects of Excitonic Superconductivity.- 1. Introduction.- 2. The Nature of Superconductivity.- 2.1. Background.- 2.2. Phonon Mechanism.- 2.3. Limitation on Tc.- 2.4. Isotope Effect.- 2.5. Exciton Mechanism.- 3. Problems of Superconductivity Unique to the Exciton Mechanism.- 3.1. Exchange.- 3.2. Apparent Limitation on ???*.- 3.3 Vertex Corrections.- 3.4. Equation for Tc.- 3.5. The Kernel U(p, k).- 3.6. Effects of the Phonons on the Exciton Mechanism.- 4. Effects of Limited Dimensionality.- 4.1. Effects of Fluctuations.- 4.2. Types of Order in a One-Dimensional Electron Gas.- 4.3. Relevance of g-ology.- 4.4. Interchain Coupling.- 4.5. Localization and Impurities.- 4.6. Effects of Screening.- 5. Real Models.- 5.1. Model of a Filamentary Excitonic Superconductor.- 5.2. Discussion.- 6. Summary.- References.- 8 Recent Developments and Comments.- 1. Introduction.- 2. Nature of the Phase Transitions.- 2.1. Transition in KCP.- 2.2. Transitions in TCNQ Compounds.- 2.3. Transitions in TaS3, NbSe3.- 3. Coulomb Interactions and Magnetic Susceptibility.- 3.1. Limitations of the Hubbard Model.- 3.2. Magnetic Susceptibility.- 3.3. Problem of TTF-TCNQ.- 3.4. Properties of NMP-TCNQ.- 4. Collective Transport.- 4.1. Superconductivity and One-Dimensional Fluctuations.- 4.2. Dielectric Properties.- 4.3. Transport above Tc.- 4.4. Nonlinear Field Dependence of Conductivity.- 5. Concluding Comments.- References.- Author Index.

Roger P. Evrard

Papers

Highly conducting one-dimensional solids