Research ArticleCONDENSED MATTER PHYSICS

Doublon-holon pairing mechanism via exchange interaction in two-dimensional cuprate Mott insulators

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Science Advances  07 Jun 2019:
Vol. 5, no. 6, eaav2187
DOI: 10.1126/sciadv.aav2187
  • Fig. 1 Attractive interaction between a doublon and a holon due to antiferromagnetic exchange interactions in half-filled 2D Mott insulators.

    (A) Ground state. (B) A pair of a doublon (D) and a holon (H) apart from each other. The energy increase of the spin sector is +8J. (C) A pair of a doublon and a holon located at two neighboring sites. The energy increase of the spin sector is +7J, which is smaller than that in (B).

  • Fig. 2 Crystal and electronic structures in undoped cuprates of Nd2CuO4, La2CuO4, and Sr2CuO2Cl2.

    (A) Crystal structures. (B) Schematic electronic structure in CuO2 planes. U is the on-site Coulomb repulsion, and ECT is the energy of the CT transition (see main text). (C) Spectra of the imaginary part of the dielectric constant ε2 obtained from the polarized reflectivity spectra along the a axis.

  • Fig. 3 THz pulse-pump optical reflectivity probe spectroscopy on Nd2CuO4.

    (A) A schematic of the experimental setup. The probe pulse is changed from visible (Vis) to infrared (IR) region. (B) A typical electric field waveform ETHz(td) of a THz pulse used as an excitation. (C) Fourier power spectrum of the THz pulse shown in (B) and the polarized absorption spectrum of Nd2CuO4 along the a axis. (D) Time evolutions of reflectivity changes ΔR(td)/R by the THz electric field shown in (B) at 0.95, 1.55, and 1.70 eV. Blue solid lines represent normalized waveforms of [ETHz(td)]2. (E) Polarized reflectivity (R) spectrum along the a axis and the spectrum of the reflectivity change at the time origin, ΔR(0)/R. The inset shows the structure of CuO unit forming the 2D CuO plane.

  • Fig. 4 Imχ(3)(−ω; 0, 0, ω) spectra and their analyses in undoped cuprates.

    (A) Nd2CuO4, (B) Sr2CuO2Cl2, (C) La2CuO4. ε2, and Imχ(3)(−ω; 0, 0, ω) spectra are shown by the thick solid lines at the top and bottom of each figure, respectively. The red dashed line at the top of each figure shows the fitting curve of the Lorentzian function. The red-colored and green-colored areas correspond to the optical transition to the odd-parity exciton and that to the doublon-holon continuum, respectively. The red dashed line at the bottom of each figure shows the fitting curve based on the three-level model (see main text). The vertical dotted lines show the energy positions of the odd-parity exciton (ℏω1) and the even-parity exciton (ℏω2). The insets show the structures of CuO units forming the 2D CuO planes.

  • Fig. 5 Physical parameters associated with odd-parity and even-parity excitons dominating nonlinear optical responses in undoped cuprates.

    (A) Energy-level structures and schematic wave functions of excitons. (B to D) Physical parameters as a function of the odd-parity exciton energy ℏω1; (B) exchange interaction J, (C) splitting between the odd-parity and even-parity excitons Es(= ℏω1 − ℏω2), (D) max∣Imχ(3)(−ω; 0, 0, ω)∣, and the squares of the transition dipole moments 〈0∣x∣1〉2 and 〈1∣x∣2〉2. (E and F) Physical parameters as a function of J; (E) Es, (F) max∣Imχ(3)(−ω; 0, 0, ω)∣, 〈0∣x∣1〉2, and 〈1∣x∣2〉2. (G) Calculated values of Es as a function of J with J/t = 0.4 for three cases: V = 0, V = 1.5t, and V = 3t.

  • Table 1 Parameter values evaluated from the analyses of ε2 and Imχ(3)(−ω; 0, 0, ω) spectra and other important parameters in Nd2CuO4, Sr2CuO2Cl2, and La2CuO4.

    ℏω1 (eV)ℏω2 (eV)ℏγ1 (eV)ℏγ2 (eV)0x1 (Å)1x2 (Å)max|Imχ(3)| (esu)Es (eV)J (meV)dCu─O (Å)
    Nd2CuO41.571.340.1820.1960.4653.032.0 × 10−100.23155141.97317
    Sr2CuO2Cl21.951.870.1860.1620.3905.806.5 × 10−100.08125151.98618
    La2CuO42.162.010.2920.1130.4013.221.5 × 10−100.15133141.90516

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/6/eaav2187/DC1

    Section S1. KK analyses of reflectivity spectra

    Section S2. Electric field dependence of electric field–induced reflectivity changes

    Section S3. Analyses of electric field–induced reflectivity changes

    Section S4. Transient reflectivity changes by the THz pulse and their analyses in La2CuO4 and Sr2CuO2Cl2

    Section S5. Contributions of continuum states on Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra in Sr2CuO2Cl2

    Fig. S1. Comparison of polarized absorption (α) spectra with the electric fields of lights parallel to the a axis.

    Fig. S2. Electric field dependence of reflectivity changes ΔR(0)/R at the time origin in Sr2CuO2Cl2.

    Fig. S3. Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra and their analyses in Nd2CuO4.

    Fig. S4. Transient reflectivity changes in La2CuO4 and Sr2CuO2Cl2.

    Fig. S5. Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra and their analyses in La2CuO4 and Sr2CuO2Cl2.

    Fig. S6. Comparison of the fitting analyses of Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra with three-, four-, and five-level models in Sr2CuO2Cl2.

    Table S1. Parameter values with errors obtained from the fitting analyses on the ε2 spectra.

    Table S2. Parameter values with errors obtained from the fitting analyses on the Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra.

    Table S3. Parameter values obtained from the fitting analyses with three-, four-, and five-level models in Sr2CuO2Cl2.

    Table S4. Products of dipole moments associated with nonlinear optical spectra in Sr2CuO2Cl2.

    References (47, 48)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. KK analyses of reflectivity spectra
    • Section S2. Electric field dependence of electric field–induced reflectivity changes
    • Section S3. Analyses of electric field–induced reflectivity changes
    • Section S4. Transient reflectivity changes by the THz pulse and their analyses in La2CuO4 and Sr2CuO2Cl2
    • Section S5. Contributions of continuum states on Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra in Sr2CuO2Cl2
    • Fig. S1. Comparison of polarized absorption (α) spectra with the electric fields of lights parallel to the a axis.
    • Fig. S2. Electric field dependence of reflectivity changes ΔR(0)/R at the time origin in Sr2CuO2Cl2.
    • Fig. S3. Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra and their analyses in Nd2CuO4.
    • Fig. S4. Transient reflectivity changes in La2CuO4 and Sr2CuO2Cl2.
    • Fig. S5. Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra and their analyses in La2CuO4 and Sr2CuO2Cl2.
    • Fig. S6. Comparison of the fitting analyses of Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra with three-, four-, and five-level models in Sr2CuO2Cl2.
    • Table S1. Parameter values with errors obtained from the fitting analyses on the ε2 spectra.
    • Table S2. Parameter values with errors obtained from the fitting analyses on the Reχ(3)(−ω; 0, 0, ω) and Imχ(3)(−ω; 0, 0, ω) spectra.
    • Table S3. Parameter values obtained from the fitting analyses with three-, four-, and five-level models in Sr2CuO2Cl2.
    • Table S4. Products of dipole moments associated with nonlinear optical spectra in Sr2CuO2Cl2.
    • References (47, 48)

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