Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0507040

Patterning of sodium ions and the control of electrons in sodium cobaltate

M. Roger·D. J. P. Morris·D. A. Tennant·M. J. Gutmann·J. P. Goff·J. U. Hoffmann·R. Feyerherm·E. Dudzik·D. Prabhakaran·A. T. Boothroyd·N. Shannon·B. Lake·P. P. Deen
View original source ↗Read source document ↗Export metadata ↓

Abstract

NaxCoO2 has emerged as a material of exceptional scientific interest due to the potential for thermoelectric applications, and because the strong interplay between the magnetic and superconducting properties has led to close comparisons with the physics of the high-Tc cuprates. The density, x, of the sodium in the intercalation layers can be altered electrochemically, directly changing the number of conduction electrons on triangular Co layers. Recent electron diffraction measurements reveal a kaleidoscope of Na+ ion patterns as a function of concentration. Here we use single-crystal neutron diffraction supported by numerical simulations to determine the long-range three-dimensional superstructures of these ions. We show that the sodium ordering and its associated distortion field are governed by pure electrostatics, and the organizational principle is the stabilization of charge droplets that order long range at some simple fractional fillings. Our results provide a good starting point to understand the electronic properties in terms of a Hubbard Hamiltonian taking into account the electrostatic potential from the Na superstructures. The resulting depth of potential wells in the Co layer is greater than the single-particle hopping kinetic energy. As a consequence, holes occupy preferentially the lowest potential regions and, therefore, the Na+ ion patterning plays a decisive role in the transport and magnetic properties.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. Roger, D. J. P. Morris, D. A. Tennant, M. J. Gutmann, J. P. Goff, J. U. Hoffmann, R. Feyerherm, E. Dudzik, D. Prabhakaran, A. T. Boothroyd, N. Shannon, B. Lake, P. P. Deen. 2007-04-13. Patterning of sodium ions and the control of electrons in sodium cobaltate. https://doi.org/10.1038/nature05531

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Point-Group Equivariant Neural Networks for Local Dynamics in Lattice Systems

We develop point-group equivariant neural networks for learning local mappings used in dynamical simulations of lattice systems. The same network acts on a finite neighborhood around each site, respecting lattice translations through shared parameters. The local configuration is decomposed into features that transform according to irreducible representations of the point group, and hidden features retain this organization throughout the network. Equivariant linear maps and symmetry-allowed tensor products then learn nonlinear spatial correlations while preserving the required transformation laws. This approach avoids constructing a fixed set of hand-crafted invariant descriptors, whose selection requires choices about which local correlations to retain. It also allows the complexity of the learned mapping to grow without enlarging its spatial cutoff. We demonstrate the construction by learning the forces governing adiabatic dynamics in the square-lattice Holstein model. Comparisons with exact diagonalization test the accuracy of the predicted forces and the evolution of spatial correlations. Force evaluation scales linearly with system size, allowing the trained model to simulate charge-density-wave ordering on large lattices. These simulations reproduce anomalously slow coarsening of the charge-density-wave domains, illustrating the use of the learned local mapping for collective dynamics.

cond-mat.str-el↗
arXiv2026

Topological Chiral Superconductivity from Doping Correlated Charge Transfer Insulator with Orbital Magnetism

Topological chiral superconductivity has been extensively studied from the perspective of electronic structures in momentum space, while its emergence from real-space processes in strongly interacting systems remains largely unexplored. Here, we study a doped charge-transfer insulator in a strongly repulsive spinless-fermion model with three sublattices and $2π$ flux per unit cell. Combining perturbative analysis, exact diagonalization, and density matrix renormalization group simulations, we establish a topological superconducting ground state with $p+ip$ symmetry. In the large charge-transfer gap limit, chiral charge-transfer excitations generate a correlated-hopping process that provides a microscopic mechanism for electron pairing and its chiral structure. The chiral superconductivity persists into the smaller-gap regime, where chiral excitonic two-particle bound state can emerge. Our results establish a concrete real-space route to topological chiral superconductivity upon doping strongly interacting charge-transfer insulators with orbital magnetism.

cond-mat.str-el↗
arXiv2026

Solving fractional quantum Hall problems with thermodynamic-limit bootstrap

Determining correlated ground states directly in the thermodynamic limit remains a central challenge in quantum many-body physics. Here we develop a quantum many-body bootstrap that yields a rigorous and tight lower bound on the thermodynamic ground-state energy of a fractional quantum Hall system together with an optimized reduced density matrix $ρ_W^\star$ on a spatial window. For sufficiently tight bounds, we find that $ρ_W^\star$ accurately reproduces the ground-state reduced density matrix, as directly tested by its fidelity with known model states. For exactly solvable Laughlin and Moore--Read parent Hamiltonians, the bootstrap also reproduces pair correlations and orbital entanglement spectra (OES). For Landau-level-projected Coulomb interactions across multiple fillings, the energy bounds closely track established thermodynamic estimates, while the window density matrix recovers the familiar $ν=1/3$ Laughlin and $ν=5/2$ Moore--Read states and the composite Fermi liquid at $ν=1/2$. More importantly, the same framework also resolves unsettled regimes. At $ν=1/4$, the OES and real-space correlations identify a composite Fermi liquid, while at $ν=12/5$ the combined diagnostics suggest $\overline{\mathrm{RR}}_3$ as the ground-state order. Our bootstrap therefore provides direct access to both ground-state energies and many-body structure in the thermodynamic limit.

cond-mat.str-el↗