One-dimensional Wigner Lattices Research Articles

Magnetism of one-dimensional Wigner lattices and its impact on charge order

The magnetic phase diagram of the quarter-filled generalized Wigner lattice with nearest-neighbor and next-nearest-neighbor hoppings, ${t}_{1}$ and ${t}_{2}$, is explored. We find a region at negative ${t}_{2}$ with fully saturated ferromagnetic ground states that we attribute to kinetic exchange. Such interaction disfavors antiferromagnetism at ${t}_{2}<0$ and stems from virtual excitations across the charge gap of the Wigner lattice, which is much smaller than the Mott-Hubbard gap $\ensuremath{\propto}U$. Remarkably, we find a strong dependence of the charge structure factor on magnetism even in the limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$, in contrast to the expectation that charge ordering in the Wigner lattice regime should be well described by spinless fermions. Our results, obtained using the density-matrix renormalization group and exact diagonalization, can be transparently explained by means of an effective low-energy Hamiltonian.

Fractional charges and spin-charge separation in one-dimensional Wigner lattices

We study density response N(k,omega) and one-particle spectra A(k,omega) for a Wigner lattice model at quarter filling using exact diagonalization. We investigate these observables for models with short and long-range electron-electron interaction and show that truncation of the electron repulsion can lead to very different results. The spectra show clear signatures of charge fractionalization into pairs of domain walls, whose interaction can be attractive or repulsive and is controlled by the formal fractional charges. In striking contrast to a bound exciton in N(k,omega), we find an antibound quasi-particle in A(k,omega), which undergoes spin-charge separation. We present a case of extreme particle-hole asymmetry, where photoemission shows spin-charge separation, while inverse photoemission exhibits an uncorrelated one-particle band.

Anderson transition of the plasma oscillations of one-dimensional disordered Wigner lattices

We report the existence of a localization-delocalization transition in the classical plasma modes of a one-dimensional Wigner crystal with a white-noise potential environment at T=0. Finite-size scaling analysis reveals a divergence of the localization length at a critical eigenfrequency. Further scaling analysis indicates power law behavior of the critical frequency in terms of the relative interaction strength of the charges. A heuristic argument for this scaling behavior is consistent with the numerical results. Additionally, we explore a particular realization of random-bond disorder in a one-dimensional Wigner lattice in which all of the collective modes are observed to be localized.

High-temperature superconductivity in cuprates and a Wigner lattice of electron pairs

A model of high-temperature superconductivity in cuprates where delocalization of one-dimensional Wigner lattices of electron pairs is responsible for superconductivity is suggested. The milestones of the model are as follows: 1. Symmetric polarization of oxygen ions in the CuO 2 layer by two neighboring copper ions leading to formation of one-electron σ bonds between the ions. 2. Asymmetric polarization of oxygen ions in the electric field around a CuO 2 layer resulting in the excitation of singlet electron pairs of oxygen ions from the 2p z state into a (2p z 3s) state, the singlet nature of the pair being preserved. 3. Lowering of the CuO 2 layer symmetry under doping and formation of quasi-one-dimensional chains of copper and oxygen ions bound by one-electron σ bonds. 4. Formation of one-dimensional Wigner lattices of electron pairs due to a strong Coulomb interaction between these pairs. 5. Formation of delocalized π orbitals along ion chains and delocalization of Wigner lattices of electron pairs at the temperature regarded as the temperature of transition to superconductivity. The model allows one to explain the co-existence of superconductivity and magnetism, orbital ion ordering, the role of local lattice distortions, the stripe structure of the electron density, and a quasi-one-dimensional character of superconductivity.

Domain-wall excitations and optical conductivity in one-dimensional Wigner lattices

Motivated by the recent finding that doped edge-sharing Cu-O chain compounds like Na$_3$Cu$_2$O$_4$ and Na$_8$Cu$_5$O$_{10}$ are realizations of one-dimensional Wigner crystals, we study the optical spectra of such systems. Charge excitations in 1D Wigner crystals are described in terms of domain wall excitations with fractional charge. We investigate analytically and numerically the domain-wall excitations that dominate the optical absorption, and analyse the dispersion and the parameter range of exciton states characteristic for the long-ranged Coulomb attraction between domain walls. Here we focus on the Wigner lattice at quarter-filling relevant for Na$_3$Cu$_2$O$_4$ and analyze in particular the role of second neighbor hopping $t_2$ which is important in edge-sharing chain compounds. Large $t_2$ drives an instability of the Wigner lattice via a soft domain-wall exciton towards a charge-density wave with a modulation period distinct from that of the Wigner lattice. Furthermore we calculate the temperature dependence of the DC-conductivity and show that it can be described by activated behavior combined with a $T^{-\alpha}$ dependent mobility.

Wigner Crystallization inNa3Cu2O4andNa8Cu5O10Chain Compounds

We report the synthesis of novel edge-sharing chain systems Na(3)Cu(2)O(4) and Na(8)Cu(5)O(10), which form insulating states with commensurate charge order. We identify these systems as one-dimensional Wigner lattices, where the charge order is determined by long-range Coulomb interaction and the number of holes in the d-shell of Cu. Our interpretation is supported by X-ray structure data as well as by an analysis of magnetic susceptibility and specific heat data. Remarkably, due to large second neighbor Cu-Cu hopping, these systems allow for a distinction between the (classical) Wigner lattice and the 4k_F charge-density wave of quantum mechanical origin.

Effects of Coulomb interaction in intentionally disordered semiconductor superlattices

The interplay between disorder and electron–electron interaction is studied using measurements of the vertical dc conductivity of intentionally disordered GaAs/Al0.3Ga0.7As superlattices. At low temperatures a quasimetallic behavior is observed even for large disorder which is attributed to an inhomogeneous charge distribution reducing the disorder potential. At low doping levels and low temperatures, exchange–correlation interaction leads to an inhomogeneous charge distribution over the wells of ordered superlattices similar to a one-dimensional Wigner lattice.

Co-tunneling via the one-dimensional Wigner lattice

We have calculated the rates of the two-electron co-tunneling via Wigner lattice confined to a one-dimensional quantum dot. The co-tunneling rate is shown to be suppressed by the formation of the Wigner lattice more strongly that the rate of the single-electron tunneling.

Tunneling to and from the one-dimensional Wigner lattice.

We have calculated the rates of electron tunneling between the one-dimensional (1D) Wigner lattice and the noninteracting electron gas. The rates determine electron transport properties (I-Y characteristic and conductance) of a 1D quantum dot in the regime of low electron density

Finite-bandwidth effects in one-dimensional Wigner lattices

The Feynman path-integral formalism is used to calculate the thermodynamic properties of a one-dimensional (1D) spinless fermion model with nearest- and next-nearest-neighbor interaction. The mapping of this 1D quantum model on a two-dimensional classical model allows the use of a Monte Carlo method to calculate the properties of long chains. We present results for typical values of the interaction parameters, density, and temperature. We find that a finite bandwidth smears out the details of the classical ground-state configurations discussed by Hubbard. If the density $\ensuremath{\rho}\ensuremath{\ne}\frac{1}{2}$, we find that the static structure factor and the static susceptibility display a maximum at $2{k}_{F}$ only when the next-nearest-neighbor interaction is nonzero.