Research ArticleCONDENSED MATTER PHYSICS

Topological charge transport by mobile dielectric-ferroelectric domain walls

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Science Advances  15 Nov 2019:
Vol. 5, no. 11, eaax8720
DOI: 10.1126/sciadv.aax8720
  • Fig. 1 Pressure-temperature phase diagram of TTF-CA and resistivity profiles.

    (A) Pressure-temperature (P-T) phase diagram consisting of three phases in TTF-CA. 1D alternating stacks of TTF and CA molecules show the N phase (left), Ipara phase (top right), and Iferro phase (bottom right). The colored clouds schematically drawn on the molecules show the hole density in the HOMO of the TTF molecule and the electron density in the LUMO of the CA molecule. In the P-T phase diagram (center), the orange circles indicate the positions of the kinks in the resistivity in (B), which correspond well to the dimerization transition points determined by previous nuclear quadrupole resonance (NQR) measurements (open squares) (12). The range of colors in the phase diagram indicates the magnitude of the conductivity. (B) Temperature dependence of the resistivity of TTF-CA along the a axis at pressures below (left) and above (right) 9 kbar.

  • Fig. 2 Pressure dependence of the conductivity and its anisotropy in TTF-CA at room temperature.

    (A) Pressure dependence of the conductivity along the a axis. (B) Pressure dependence of the anisotropies of the conductivities defined as the ratio of conductivities along the a and b axes, σab, and the ratio of conductivities along the a and c axes, σac. (C) Schematics of electrical terminal configurations with respect to the molecular stacks in the resistivity measurements. Gold wires were attached on the side and top surfaces, using carbon paste, as current leads and voltage terminals, respectively. (D) Molecular arrangement of TTF and CA in the b-c plane perpendicular to the a axis (13).

  • Fig. 3 Conductivity profile in the NI crossover region in TTF-CA.

    (A) Conductivity profile in the P-T plane. The black curves represent the temperature dependence of the conductivity for fixed pressures, which are set at approximately 0.1-kbar intervals in the range of 5.5 to 11.5 kbar. In the bottom panel, the range of colors indicates the magnitude of the conductivity; the gray line is the Widom line, Pc(T), on which the conductivity is maximum with respect to pressure [also shown in (B)], and the orange circles indicate the dimerization transition points. (B) Traces of the conductivity as a function of pressure, P, at fixed temperatures. (C) Plot of the data in (B) as a function of ΔP = PPc. Both in (B) and (C), the vertical axes are in arbitrary units, and the data plots for different temperatures are shifted vertically for clarity. (D) Arrhenius plot of the resistivity on the Pc line. The black line is a fit to the data, giving an estimate of the activation energy of 0.055 eV. (E) Activation energy as a function of ΔP.

  • Fig. 4 Topological excitations carrying electrical currents and the pressure profile of the electrical conductivity and spin excitations.

    (A) Three types of topological excitations in the NI transition systems: NIDWs (I), spin solitons (II), and charge solitons (III). Donor and acceptor molecules are represented as D and A, respectively. The NIDW has an effective charge of ±eI − ρN)/2, where ρI and ρN are the degrees of charge transfer in the ionic and neutral states, respectively, and are 0.7 to 0.8 and 0.3 to 0.4 around the NI crossover (8, 9). The spin and charge solitons have effective charges of ±e(1 − ρI) and ±eρI, respectively, corresponding to excessive and deficient charges from the dimerized-ionic background, as depicted. These charges are called topological charges, as their fractional nature has the topological origin in the charge degrees of freedom; however, they take noninvariant values and thus are distinguished from the topological charge characterized by quantum numbers. (B) Pressure dependence of the conductivity (black circles) and 13C-NMR T1−1 (open squares) at room temperature. The mechanism of electrical conduction is divided into three regimes: In the N phase at low pressures (blue-colored region), spin solitons sandwiched by NIDWs (called polarons), which carry both charges and spins, are sparsely excited in the neutral background and lead to electrical conduction. In the NI crossover region at middle pressures (red-colored region), the NIDWs and spin solitons are excited with comparable densities and carry electrical currents (section S3). In the I phase at high pressures (orange-colored region), the charge solitons are sparsely excited in the ionic background and, in conjunction with more densely excited spin solitons, carry electrical currents.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaax8720/DC1

    Section S1. Temperature dependence of the resistivity

    Section S2. Analysis of the conductivity in the NI transition region in terms of the Ising model

    Section S3. Electrical current by the NIDW and spin soliton excitations

    Section S4. 13C-NMR spectra and relaxation curves of nuclear magnetization

    Fig. S1. Temperature dependence of the resistivity in the NI crossover region.

    Fig. S2. Correspondence between molecular states and virtual spins.

    Fig. S3. Fitting of the temperature dependence of the conductivity by the 1D ferromagnetic spin model.

    Fig. S4. Schematic of the transport of NIDWs and spin solitons that contribute to the electrical conductivity.

    Fig. S5. Schematic of the transport of NIDWs that do not contribute to the electrical conductivity.

    Fig. S6. 13C-enriched TTF molecule, 13C-NMR spectrum, and relaxation curve.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Temperature dependence of the resistivity
    • Section S2. Analysis of the conductivity in the NI transition region in terms of the Ising model
    • Section S3. Electrical current by the NIDW and spin soliton excitations
    • Section S4. 13C-NMR spectra and relaxation curves of nuclear magnetization
    • Fig. S1. Temperature dependence of the resistivity in the NI crossover region.
    • Fig. S2. Correspondence between molecular states and virtual spins.
    • Fig. S3. Fitting of the temperature dependence of the conductivity by the 1D ferromagnetic spin model.
    • Fig. S4. Schematic of the transport of NIDWs and spin solitons that contribute to the electrical conductivity.
    • Fig. S5. Schematic of the transport of NIDWs that do not contribute to the electrical conductivity.
    • Fig. S6. 13C-enriched TTF molecule, 13C-NMR spectrum, and relaxation curve.

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