Internal strain tunes electronic correlations on the nanoscale

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Science Advances  14 Dec 2018:
Vol. 4, no. 12, eaau9123
DOI: 10.1126/sciadv.aau9123
  • Fig. 1 Electronic properties of α-(BEDT-TTF)2I3 with a metal-insulator transition at TCO = 136 K.

    (A) The crystal structure contains layers of BEDT-TTF molecules slightly tilted along the ab plane, which are separated by sheets of IEmbedded Image anions. (B) A significant charge disproportionation develops below the CO transition (T < TCO), with charge-rich (A and B) and charge-poor (A′ and C) molecules alternating along the a direction, forming a stripe-like pattern oriented parallel to b (28). (C) In the normal state (TCO < T), the charges of the four inequivalent lattice sites are close to the average value 0.5 e. (D) The far-field reflectivity R exhibits pronounced changes upon crossing the CO transition (17). Integrating R in the shaded region (700 to 1000 cm−1) yields distinct values above (T = 150 K, red) and below (T = 120 K, blue) TCO. (E) The drop in the optical conductivity below 1000 cm−1 indicates the opening of a gap in the density of states when CO sets in. (F) The near-field amplitude β and (G) the corresponding phase change ϕ are calculated according to Eq. 1. Both quantities exhibit distinct variations at the CO2 laser frequency of 910 cm−1. The illustration in (F) sketches the electromagnetic near-field (red) arising from interaction of the crystal with the AFM tip upon illumination with the laser radiation (black arrow), reaching well below the sample surface. β corresponds to the scattered light detected in the experiment (red arrows). Figure reproduced from (55).

  • Fig. 2 Near-field image at the boundary between the metallic and charge-ordered regions in α-(BEDT-TTF)2I3.

    (A) The near-field amplitude β measured with a CO2 laser at T = 132.6 K slightly below TCO. The metallic regions give a larger amplitude than the CO phase. The bright area in the top left corner stems from the evaporated gold (thickness, 30 nm) used as reference. (B) In addition, the phase ϕ shows considerable contrast between the metallic and insulating regions. The position of the phase boundaries in (A) and (B) match perfectly. (C) An intensity histogram of the metallic (red) and charge-ordered (blue) regions normalized to the signal of the gold (Au) layer. (D) The respective maxima of the phase histogram are separated by an angle of ≈10°. Figure reproduced from (55).

  • Fig. 3 Near-field maps of a multiply cracked α-(BEDT-TTF)2I3 crystal.

    (A) Near-field nanoimages taken at different temperatures close to TCO = 136 K. A phase separation occurs between metallic (yellow) and insulating (red) regions, with a phase coexistence over a temperature range ΔT ≤ 6 K. The near-field amplitude β was normalized to the signal taken off a 30-nm gold layer (bright region on the right) evaporated beforehand. (B) To quantitatively analyze the temperature evolution of the two phases, we determined the pixel distribution ρ(β) of a well-defined region, which is indicated in the 132.15 K frame by masking (blue) the gold pad or separated flakes. The contour plot and black lines correspond to the amplitude distribution at the measured temperatures. In the temperature range with the largest changes (between 133.5 and 135 K), a bimodal distribution is observed, indicating the coexistence of metallic and charge-ordered regions. The trend follows the result of our subsequent far-field experiments (red line) on the same area. (C) The far-infrared reflectivity was integrated, as indicated in Fig. 1D, and the resulting temperature-dependent spectral weight (SW) was normalized to the high- and low-temperature (T2 and T1, respectively) plateau values. The temperature dependence of the average near-field intensity from (B) shows perfect correspondence to the far-field data. (D) The derivative of the SW with respect to temperature was calculated to highlight the largest rate of change. Figure reproduced from (55).

  • Fig. 4 Spatial variation of CO.

    (A) Optical near-field map of the α-(BEDT-TTF)2I3 crystal at T = 133.95 K. The green double-headed arrow indicates the distance d of the metal-insulator boundary (dashed green line) with respect to the top right crack. The blue frame corresponds to the 10 μm by 10 μm area magnified in (B) with a high spatial resolution of 20 nm. A pronounced pattern is seen with basically parallel lines of alternating metallic and insulating regions of approximately equal width. The blue double-headed arrows illustrate the periodicity. (C) The intensity profile recorded along the white line in (B) reveals a stripe periodicity of 2 μm and a phase boundary width of few hundred nanometers (gray). (D) The distance d between the crack and the metal-insulator phase boundary, illustrated in (A), was determined at several temperatures. When T falls below TCO, a large area parallel to the crack becomes charge ordered within a fraction of a kelvin (≤0.35 K). This quick propagation of the phase boundary is attributed to a temperature gradient smaller than 6 K/mm. Below 134.5 K, the metallic phase retreats at a much slower rate, implying that the effect is not caused by a temperature gradient. (E) Pressure-dependent studies reveal that uniaxial strain along the b axis more efficiently suppresses CO than hydrostatic compression [TCO data taken from (28, 29)]. Comparison with near-field data from our experiments estimates an effective uniaxial pressure pb ≈ 0.5 to 1 kbar on the α-(BEDT-TTF)2I3 sample under investigation. (F) Attaching the sample at both ends and cooling on a sapphire substrate imposes tensile strain along the a axis and compression along b due to differential thermal contraction. The calculated strain profile upon tensile stress reveals large strain at the center of the segment and small values close to the edges. Figure reproduced from (55).

  • Fig. 5 Strain dependence of the charge gap.

    (A) The interplay of metallic and charge-ordered phases is simulated at different temperatures throughout the phase transition. Very similar to the experimental data from Figs. 3A and 4 (A to C), CO successively grows from the edges of the segment, while the metallic phase is repressed toward the center, forming a characteristic stripe pattern. (B) A line cut of the near-field amplitude (along the white line in the inset) reveals reduced signal at the edges of the segment compared to its center. (C) The Arrhenius plot of the temperature-dependent resistance allows extracting the energy gap ΔCO at different uniaxial pressures applied along the b axis [data taken from (29)]. (D) In addition, the hydrostatic pressure shifts the metal-insulator transition, weakens CO, and thus suppresses the spectral gap [data taken from (30)]. (E) Consistently, the transport gap ΔCO determined from (C) is reduced with pressure as well. At the CO2 laser frequency of 910 cm−1, the optical conductivity is gradually enhanced with pressure. Therefore, the drop of near-field intensity in (B) indicates a larger optical gap due to smaller strain close to the edges, imposing a local modulation of the correlation strength.

  • Fig. 6 Possible scenarios of metal-insulator transitions in solids.

    A general distinction can be made between (A) abrupt first-order phase transitions and (B) gradual mean-field–like second-order transitions. (C) In the case of a bimodal phase coexistence of an originally first-order transition, the macroscopic order parameter looks very similar to the second-order scenario. Such a spatial phase separation may be the result of a nonuniform field caused by internal strain or defects that couple energetically to the relevant order parameter. At TCO, we observe differences in the optical near-field maps of samples with distinct characteristics. (D) Homogeneous α-(BEDT-TTF)2I3 single crystals exhibit a well-defined phase boundary that follows the temperature gradient on the sample. Upon proper thermalization, the macroscopic transition happens instantaneously (within a few hundred millikelvins) on the whole crystal, similar to that in Fig. 2. (E) In geometrically nonuniform samples, the internal strain spatially modulates electronic correlations, resulting in a complex phase coexistence that extends over several kelvins (compare Fig. 3). Figure reproduced from (55).

Supplementary Materials

  • Supplementary material for this article is available at

    Section S1. Sample preparation

    Section S2. Optical far-field experiments

    Section S3. Landau free energy calculations

    Fig. S1. AFM profile of the sample surface.

    Fig. S2. Far-field reflectivity on different spots of the cracked sample.

    Fig. S3. Temperature-dependent far-field experiments.

    Fig. S4. Schematics of the geometry used to treat the elasticity problem.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Sample preparation
    • Section S2. Optical far-field experiments
    • Section S3. Landau free energy calculations
    • Fig. S1. AFM profile of the sample surface.
    • Fig. S2. Far-field reflectivity on different spots of the cracked sample.
    • Fig. S3. Temperature-dependent far-field experiments.
    • Fig. S4. Schematics of the geometry used to treat the elasticity problem.

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