Electron-phonon interaction and phonon dynamics in one-dimensional conductors

Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding

The charge density wave (CDW) instability, usually occurring in low-dimensional metals, has been a topic of interest for longtime. However, some very fundamental aspects of the mechanism remain unclear. Recently, a plethora of new CDW materials, a substantial fraction of which is two-dimensional or even three-dimensional, has been prepared and characterised as bulk and/or single-layers. As a result, the need for revisiting the primary mechanism of the instability, based on the electron-hole instability established more than 50 years ago for quasi-one-dimensional (quasi-1D) conductors, has clearly emerged. In this work, we consider a large number of CDW materials to revisit the main concepts used in understanding the CDW instability, and emphasise the key role of the momentum dependent electron-phonon coupling in linking electronic and structural degrees of freedom. We argue that for quasi-1D systems, earlier weak coupling theories work appropriately and the energy gain due to the CDW and the concomitant periodic lattice distortion (PLD) remains primarily due to a Fermi surface nesting mechanism. However, for materials with higher dimensionality, intermediate and strong coupling regimes are generally at work and the modification of the chemical bonding network by the PLD is at the heart of the instability. We emphasise the need for a microscopic approach blending condensed matter physics concepts and state-of-the-art first-principles calculations with quite fundamental chemical bonding ideas in understanding the CDW phenomenon in these materials.

Long-range order in quasi-one-dimensional conductors

We study the formation of the charge-density wave long-range order in a system of repulsive 1D electrons coupled to 3D phonons. We show that the charge-density wave can be stabilized by interaction with phonons in quasi-1D crystals and semiconducting nanowires. In the case of metallic atomic chains, interaction with phonons of a 3D substrate is not enough, and violation of the translational invariance by commensurable perturbation or disorder is needed. The possibility of stabilization of superconductivity in 1D electrons with attraction by means of tunnel coupling to a 3D metal is considered.

Electron-phonon interactions in the monocations of polyacetylenes

Electron-phonon interactions in the monocations of trans-polyacetylenes such as C2H4 (2tpa), C4H6 (2tpa), C6H8 (6tpa), and C8H10 (8tpa) are studied. The C-C stretching Ag modes around 1700 cm(-1) afford the largest electron-phonon coupling constants in the monocations of polyacetylenes. However, the C-C bending Ag modes around 1200 cm(-1) afford much smaller electron-phonon coupling constants than the C-C stretching Ag modes around 1700 cm(-1) in the monocations of polyacetylenes. The total electron-phonon coupling constants for the monocations (l HOMO) are estimated to be 0.357, 0.285, 0.281, and 0.279 eV for 2tpa, 4tpa, 6tpa, and 8tpa, respectively. The l HOMO values for polyacetylenes with C 2h geometry hardly change with an increase in molecular size while those for polyacenes with D 2h geometry significantly decrease with an increase in molecular size. The l HOMO values for polyacetylenes are larger than those for polyacenes. The calculated results are rationalized in terms of the phase patterns of the molecular orbitals in detail. The electron transfer in the positively charged polyacetylenes is also discussed. Intramolecular electron mobility (sigma(intra,monocation)) in the positively charged polyacetylenes is estimated to be smaller than those for the positively charged polyacenes. The reorganization energies for the positively charged polyacetylenes are estimated to be larger than those for the positively charged polyacenes. Thus, the larger overlap integrals between two neighboring molecules are needed for the positively charged polyacetylenes to become good conductor than those for positively charged polyacenes. On the other hand, the conditions under which the electron-electron interactions are attractive are more easily realized in the monocations of polyacetylenes than in the monocations of polyacenes. The quality as conducting materials would not significantly depend on the molecular size in the positively charged polyacetylenes, compared with that in the positively charged polyacenes. Multimode problem is also treated in order to investigate how consideration of multimode problem is closely related to the characteristics of the electron-phonon interactions.

Vibronic interactions and possible electron pairing in positively charged cyanodienes

The conditions under which the attractive electron-electron interactions are realized in the monocations of sigma-conjugated cyanodienes such as C(6)N(4)H(4), C(8)N(6)H(4), and C(10)N(8)H(4) and of pi-conjugated acenes are discussed. The total electron-phonon coupling constants for the monocations l(HOMO) of cyanodienes are much larger than those for the monocations of acenes. The strong sigma orbital interactions between two neighboring atoms in the highest occupied molecular orbitals (HOMO) of sigma-conjugated cyanodienes are the main reason for the calculated results. Furthermore, we discuss how the conditions under which the monocation crystals become good conductor are related to the molecular size. Both the l(HOMO) values and the reorganization energies between the neutral molecules and the monocations decrease with an increase in molecular size in cyanodienes. The calculated results for the sigma-conjugated cyanodienes are compared with those for the pi-conjugated acenes in order to investigate how the CH-N substitutions in cyanodienes are closely related to the l(HOMO) values and the reorganization energies. Both the l(HOMO) and the reorganization energies in the positively charged sigma-conjugated cyanodienes are much larger than those in the positively charged pi-conjugated acenes. This means that in order to become good conductors, the positively charged sigma-conjugated cyanodienes need larger overlap integral between two adjacent molecules than the positively charged pi-conjugated acenes. On the other hand, since the l(HOMO) values for cyanodienes are much larger than those for acenes, the condition of attractive electron-electron interactions is more easily to be realized in the monocations of cyanodienes than in the monocations of acenes. It is suggested that the positively charged sigma-conjugated cyanodienes cannot easily become good conductors, but the conditions under which the electron-electron interactions become attractive are realized more easily in the positively charged sigma-conjugated cyanodienes than in the positively charged pi-conjugated acenes.

Vibronic Interactions in Negatively Charged Polyacetylene

Electron-phonon interactions in the monoanions of polyacetylenes such as C2H4 (2tpa), C4H6 (4tpa), C6H8 (6tpa), and C8H10 (8tpa) are studied and compared with those in the monoanions of polyacenes. The C-C stretching A(g) modes around 1500 cm(-1) the most strongly couple to the lowest unoccupied molecular orbitals (LUMO) in polyacetylenes. The estimated total electron-phonon coupling constants for the monoanions (l(LUMO)) are 0.579, 0.555, 0.463, and 0.401 eV for 2tpa, 4tpa, 6tpa, and 8tpa, respectively. The l(LUMO) values for polyacetylenes are much larger than those for polyacenes. Furthermore, the l(LUMO) value for polyacetylene with C(2h) geometry is estimated to be 0.254 eV, and is larger than that (0.024 eV) for polyacene with D(2h) geometry. The phase patterns difference between the LUMO of polyacenes localized on the edge part of carbon atoms, and the delocalized LUMO of polyacetylenes is the main reason for the calculated results. The single charge transfer through the molecule in polyacetylenes are also discussed. The reorganization energies between the neutral molecule and the corresponding monoanion are estimated to be 0.164, 0.144, 0.125, and 0.113 eV for 2tpa, 4tpa, 6tpa, and 8tpa, respectively. Such reorganization energy decreases with an increase in molecular size. The conditions under which the attractive electron-electron interactions are realized in the monoanions of polyacetylenes and polyacenes are discussed. In terms of the electron-phonon interactions and the reorganization energies, the relationships between the normal and possible superconducting states are briefly discussed. We find that the monoanions with smaller molecular size cannot easily become good conductors, however, the conditions under which the interactions between two electrons are attractive are more easily realized in the monoanions with smaller molecular size than in the monoanions with larger molecular size.

Luttinger liquid of polarons in one-dimensional boson-fermion mixtures

We use the bosonization approach to investigate quantum phases of boson-fermion mixtures (BFM) of atoms confined to one dimension by an anisotropic optical lattice. For a BFM with a single species of fermions we find a charge-density wave phase, a fermion pairing phase, and a phase separation regime. We also obtain the rich phase diagram of a BFM with two species of fermions. We demonstrate that these phase diagrams can be understood in terms of polarons, i.e., atoms "dressed" by screening clouds of the other atom species. Techniques to detect the resulting quantum phases are discussed.

Finite temperature spectral function of Mott insulators and charge density wave states

We calculate the low-temperature spectral function of one-dimensional incommensurate charge density wave states and half filled Mott insulators. At T=0 there are two dispersing features associated with the spin and charge degrees of freedom, respectively. We show that already at very low temperatures (compared to the gap) one of these features gets severely damped. We comment on implications of this result for photoemission experiments.

Phase diagram of an asymmetric spin ladder

We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.