Spectroscopic fingerprints of many-body renormalization in $1T\text{\ensuremath{-}}{\mathrm{TiSe}}_{2}$

Spectroscopic fingerprints of many-body renormalization in $1 T − {TiSe}_{2}$

J. Zhao, Kyungmin Lee, J. Li, D. B. Lioi, G. Karapetrov, Nandini Trivedi, and U. Chatterjee

Phys. Rev. B 100, 045106 – Published 8 July 2019

Abstract

We have investigated many-body renormalizations of the single-particle excitations in $1 T − {TiSe}_{2}$ by employing high resolution angle-resolved photoemission spectroscopy (ARPES) measurements. The energy distribution curves (EDCs) of the ARPES data reveal an intrinsic single band peak-dip-hump (PDH) feature. Furthermore, the renormalized electronic dispersion extracted from the momentum distribution curves (MDCs) highlights a well-defined kink structure. These are canonical signatures of many-body correlations in the system. Theoretical modeling of the electrons coupled to an Einstein mode illustrates that a study of the renormalized dispersion from the MDCs enable direct access to the characteristic features of these many-body correlations, such as the energy scale of the relevant collective mode and the strength of its coupling with the electrons in the system. This model also demonstrates the difficulty to determine these features in a straightforward way from the PDH structure of the EDCs. The self-energy analysis of our ARPES data suggest compelling evidence for a bosonic mode having energy $\sim 26 meV$ , with which the electrons in $1 T − {TiSe}_{2}$ couple to. This correlates with the ab initio phonon-dispersion calculations and the observation of breathing ( $A_{1 g}$ ) phonon mode in Raman scattering experiments.

Received 20 December 2018

DOI:https://doi.org/10.1103/PhysRevB.100.045106

Physics Subject Headings (PhySH)

Charge density waves Electron-phonon coupling

Transition metal dichalcogenides

Angle-resolved photoemission spectroscopy Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Zhao¹, Kyungmin Lee², J. Li¹, D. B. Lioi³, G. Karapetrov³, Nandini Trivedi², and U. Chatterjee ^1,*

¹Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
²Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
³Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA

^*uc5j@virginia.edu

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Vol. 100, Iss. 4 — 15 July 2019

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Figure 1
Peak-dip-hump structure of the ARPES data. (a) Schematic crystal structure and (b) Brillouin zone of the normal state of $1 T − {TiSe}_{2}$ ; the high-symmetry points are marked. (c) Plots of the in-plane resistivity $ρ$ vs $T$ (red curve) and $\frac{d ρ}{d T}$ vs $T$ (blue dashed curve). $T_{CDW}$ is determined from the minimum (pointed by the black arrow) of $\frac{d ρ}{d T}$ vs $T$ plot. (d) The energy-momentum intensity map (EMIM) of the conduction band around the $L$ point. (e) Energy distribution curves (EDCs) along the trajectory between two Fermi momenta marked by the black ( $k_{F}$ ) and blue ( $- k_{F}$ ) dots in (d). These EDCs are offset for visual clarity. Peak-dip-hump (PDH) structure of these EDCs are clearly visible. Peaks are shown by the open squares, while the humps are shown by the dashed lines. The ARPES data, shown in this figure, were recorded with $h ν = 21.2 eV$ at 20 K.
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Figure 2
ARPES data with different incident photon energies. EMIMs, similar to that in Fig. 1, are displayed in (a) and (b) with $h ν = 24$ and 43 eV, respectively. The sequence of EDCs corresponding to (a) and (b) are shown in (c) and (d), respectively. The PDH structure of the EDCs is visible in (c) and (d) like in Fig. 1.
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Figure 3
Results from a model calculation. (a) Intensity map of the calculated single-particle spectral function $A (k, \bar{ω})$ . (b) Dispersions extracted from the calculated $A (k, \bar{ω})$ . Blue and yellow markers represent the dispersions obtained by tracking the peaks of the EDCs and MDCs, respectively. MDC-derived dispersion clearly exhibits a kink, whose $\bar{ω}$ location coincides with the mode energy $Ω$ . EDC-derived dispersion, on the other hand, shows a two-branched behavior—the upper branch corresponds to the dispersion of the quasiparticle peak and the lower branch to that of the hump. (c) Real part $Σ^{'}$ and imaginary part $Σ^{''}$ of (dimensionless) normalized self energy as functions of $\bar{ω}$ . (d) Mass renormalization as a function of the coupling strength between the electrons and the bosonic mode. (e–g) EDCs at several momenta, which are equispaced and located between $- k_{F}$ and $k_{F}$ , for (e) $α_{f} = 0$ , (f) $α_{f} = 0.5$ , and (g) $α_{f} = 1$ . Blue and black curves in (e-f) represent the EDCs at $- k_{F}$ and $k_{F}$ , respectively. The green curves mark the EDCs located at the band bottom, i.e., at $k = 0$ . Black squares denote the locations of the “peaks” of the EDCs in the energy window: $- 2 Ω \leq \bar{ω} \leq 0$ , while the black circles point the positions of the humps as defined by the local maxima of the EDCs in the energy range $\bar{ω} \leq - Ω$ .
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Figure 4
Self-energy analysis of ARPES data. (a) MDCs for a series $\bar{ω}$ 's along the momentum line, shown by the black dashed arrow in Fig. 1. These MDCs are offset for visual clarity. Renormalized band dispersion (orange markers) from MDC analysis is superimposed on the second derivative of the energy-momentum intensity map of Fig. 1 with respect $\bar{ω}$ in (b). Approximated bare band dispersion is shown by the red line, whose slope determines $v_{F}^{0}$ . The slope of the blue line, which corresponds to the slope of the renormalized dispersion at $\bar{ω} = 0$ , determines $v_{F}^{*}$ . A Kink structure at $\bar{ω} \sim - 26 meV$ can easily be discerned from the renormalized dispersion. $Σ^{'} (\bar{ω})$ and $W (\bar{ω})$ are displayed in (c) and (d), respectively. Black arrow in (c) points the peaky structure of $Σ^{'} (\bar{ω})$ at $\bar{ω} \sim - 26 meV$ . From (b), (c), and (d), it can be seen that the $\bar{ω}$ location of the black arrows approximately matches with the $\bar{ω}$ , at which the slope of $W (\bar{ω})$ changes. Note that $Σ^{'} (\bar{ω})$ is directly proportional to $W (\bar{ω})$ . The black dotted circles mark the features in the dispersion as well as in $Σ^{'} (\bar{ω})$ for $| \bar{ω} | <$ 26 meV. These features are not clearly resolved and they can be related to the shear phonon mode and/or the CDW amplitude modes. Here, we show the data corresponding to the left branch of the intensity map. We check that the right branch also gives similar result. (e) Temperature evolution of Raman spectra of $1 T − {TiSe}_{2}$ single crystal. Raman data display energy scales of the $A_{1 g}$ CDW amplitude mode, and breathing ( $A_{1 g}$ ) and shear ( $E_{g}$ ) phonon modes.
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Physical Review B

covering condensed matter and materials physics

Spectroscopic fingerprints of many-body renormalization in $1 T − {TiSe}_{2}$

J. Zhao, Kyungmin Lee, J. Li, D. B. Lioi, G. Karapetrov, Nandini Trivedi, and U. Chatterjee

Phys. Rev. B 100, 045106 – Published 8 July 2019

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Physical Review B

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Spectroscopic fingerprints of many-body renormalization in 1T−TiSe2

J. Zhao, Kyungmin Lee, J. Li, D. B. Lioi, G. Karapetrov, Nandini Trivedi, and U. Chatterjee

Phys. Rev. B 100, 045106 – Published 8 July 2019

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Spectroscopic fingerprints of many-body renormalization in $1 T − {TiSe}_{2}$