Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

José M. P. Carmelo, Tilen Čadež, David K. Campbell, Michael Sing, and Ralph Claessen

Phys. Rev. B 100, 245202 – Published 5 December 2019

Abstract

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k, ω)$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

Received 28 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.245202

Physics Subject Headings (PhySH)

Electronic structure

Organic compounds

Angle-resolved photoemission spectroscopy Hubbard model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

José M. P. Carmelo^1,2,3,4, Tilen Čadež^3,5,6, David K. Campbell ¹, Michael Sing⁷, and Ralph Claessen⁷

¹Boston University, Department of Physics, 590 Commonwealth Ave, Boston, Massachusetts 02215, USA
²Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA
³Center of Physics of University of Minho and University of Porto, P-4169-007 Oporto, Portugal
⁴Department of Physics, University of Minho, Campus Gualtar, P-4710-057 Braga, Portugal
⁵CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁶Beijing Computational Science Research Center, Beijing 100193, China
⁷Physikalisches Institut and Würzburg-Dresden Cluster of Excellence Complexity and Topology in Quantum Matter, Universität Würzburg, D-97074 Würzburg, Germany

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Issue

Vol. 100, Iss. 24 — 15 December 2019

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Images

Figure 1
Sketch of the (i) $ω < 0 s$ (spin) and $c$ and $c^{'}$ (charge) branch lines, (ii) $ω > 0 s^{'}$ (spin), $c^{″}$ and $c^{‴}$ (charge) branch lines, and (iii) $ω < 0$ and $ω > 0 c - s$ boundary lines in the one-electron removal and addition spectral functions for momentum values $k > 0$ of the models discussed in this paper. Their spectra are defined below in Eqs. (i) (17), (ii) (18), and (iii) (20), respectively. (The branch and boundary lines correspond to the solid and dotted lines, respectively.) The soft gray region refers to the small spectral-weight distribution continuum. The darker gray regions below the one-electron removal branch lines, above the one-electron addition branch lines, and both below and above the boundary lines typically display more weight. In the actual spectral function this applies in the case of the branch lines to $k$ intervals for which the exponents that control the line shape near them are negative.
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Figure 2
Raw TTF-TCNQ ARPES data and second-derivative ARPES map showing the experimental dispersions obtained along the easy-transport axis and matching theoretical boundary lines and branch lines for the $k > 0$ intervals for which the exponents of the latter are negative. Their choice is justified in Sec. 6b. The theoretical lines refer to (i) $u = U / 4 t = 0.800$ and $t = 0.29$ eV and (ii) $u = 1.225$ and $t = 0.24$ eV for the (i) TTF (orange) and (ii) TCNQ (green) stacks of molecules, respectively. The branch and boundary lines are represented by solid and dotted lines, respectively. The spectral function line shape near and below the branch lines has the singular form given in Eq. (16) for the $k$ intervals for which the corresponding exponents are negative. Its line shape near both sides of the boundary lines is provided in Eq. (21). (The TTF related $s^{'}$ and $c^{‴}$ branch lines do not appear in the figure because their exponents are positive.) The TCNQ and TTF stacks of molecules related boundary lines emerge from the $c^{'}$ and $c^{″}$ branch lines at $k = k_{c s}^{Q} = 0.115 Å^{- 1}$ and $k = k_{c s}^{F} = 0.520 Å^{- 1}$ , respectively, and run up to $k = π / a_{0} \approx 0.823 Å^{- 1}$ .
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Figure 3
The exponents, Eq. (19), in the spectral function, Eq. (16), that control the line shape near the theoretical $c^{″}$ branch line, two branches of the $c^{‴}$ branch line, and $s^{'}$ branch line in Fig. 1 for $n_{e}^{F} = 2 - n_{e} = 1.41, u = U / 4 t = 0.80$ , and $l = 12$ . The $k$ intervals for which these exponents are negative describe the $(k, ω)$ -plane location of the corresponding experimental high-energy structures in the ARPES maps of Fig. 2 related to the TTF stacks of molecules. This holds for the specific exponent lines corresponding to the parameter values ${\tilde{ξ}}_{c} = {\tilde{ξ}}_{c}^{F} = 0.649$ and $α = α^{F} = 0.739$ for which $ζ_{c^{″}} (k)$ crosses zero at $k = k_{c s}^{F} = 0.520 Å^{- 1}$ and all exponents meet the agreement criteria. The $- 1 / 2$ exponent dashed-dotted line refers to the $c − s$ boundary line.
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Figure 4
The exponents, Eq. (19), in the spectral function, Eq. (16), that control the line shape near the theoretical $c, c^{'}$ , and $s$ branch lines in Fig. 1 for $n_{e}^{Q} = n_{e} = 0.59, u = U / 4 t = 1.225$ , and $l = 6$ . The $k$ intervals for which these exponents are negative describe the $(k, ω)$ -plane location of the corresponding experimental high-energy structures in the ARPES maps of Fig. 2 related to the TCNQ stacks of molecules. This applies to the specific exponent lines corresponding to the parameter values ${\tilde{ξ}}_{c}^{C} = 0.734$ and $α_{C} = 0.495$ for which $ζ_{c^{'}} (k)$ crosses zero at $k = k_{c s}^{Q} = 0.115 Å^{- 1}$ and all exponents meet the agreement criteria. The $- 1 / 2$ exponent dashed-dotted line refers to the $c − s$ boundary line.
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