On the origin of the anomalous peak in the resistivity of ${\mathrm{TiSe}}_{2}$

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On the origin of the anomalous peak in the resistivity of ${TiSe}_{2}$

Matthew D. Watson, Adam M. Beales, and Philip D. C. King

Phys. Rev. B 99, 195142 – Published 23 May 2019

Abstract

Resistivity measurements of ${TiSe}_{2}$ typically show only a weak change in gradient at the charge density wave transition at $T_{CDW} \approx 200 K$ , but more prominently feature a broad peak at a lower $T_{peak} \sim 165 K$ , which has remained poorly understood despite decades of research on the material. Here we present quantitative simulations of the resistivity using a simplified parametrization of the normal state band structure, based on recent photoemission data. Our simulations reproduce the overall profile of the resistivity of ${TiSe}_{2}$ , including its prominent peak, without implementing the CDW at all. We find that the peak in resistivity corresponds to a crossover between a low-temperature regime with electronlike carriers only, to a regime around room temperature where thermally activated and highly mobile holelike carriers dominate the conductivity. Even when implementing substantial modifications to model the CDW below the transition temperature, we find that these thermal population effects still dominate the transport properties of ${TiSe}_{2}$ .

Received 2 March 2019
Revised 12 April 2019

DOI:https://doi.org/10.1103/PhysRevB.99.195142

Physics Subject Headings (PhySH)

Charge density waves Electrical conductivity Electronic structure

Transition metal dichalcogenides

Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matthew D. Watson^*, Adam M. Beales, and Philip D. C. King^†

SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom

^*mdw5@st-andrews.ac.uk
^†philip.king@st-andrews.ac.uk

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Vol. 99, Iss. 19 — 15 May 2019

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Figure 1
Model band structure of ${TiSe}_{2}$ . (a) ARPES data at 300 K, adapted from [15], overlaid with parabolas corresponding to the assumed dispersions of the hole and electronlike carriers, respectively. (b) Available density of states for the 2D hole band (cyan line) and 3D electron band (orange line), also showing the thermally occupied population of each carrier type (shaded areas) at 300 K, and (c) 10 K. The dashed line indicates the location of the chemical potential. (d) Chemical potential as a function of temperature. Note that in (b)–(d), the top of the valence band is defined to be at zero energy, whereas in (a) the data are referenced to the experimental chemical potential.
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Figure 2
(a) Temperature dependence of electron- and holelike carrier densities [see Figs. 1 and 1 for visualization at two selected temperatures]. (b) The assumed scattering rates, following the Bloch-Grüneisen formula for electron-phonon scattering with an additional elastic impurity scattering term. (c) Corresponding simulation of resistivity. Dashed line is the experimental resistivity, from Ref. [1].
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Figure 3
(a) The scattering rate due to acoustic phonons according to the Bloch-Grüneisen formula, and (b) calculated resistivity (both reproduced from Fig. 2). [(c) and (d)] Equivalent plots, in which scattering from both acoustic and optical phonons is considered. [(e) and (f)] Equivalent plots in which the scattering rate is assumed to be proportional to $T^{2}$ . In all cases, a constant impurity scattering term is also included.
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Figure 4
(a) Simulated resistivity curves for various values of the extrinsic doping $N_{d}$ . All other parameters are held fixed, including the elastic impurity scattering term, which in reality would be likely to scale with $N_{d}$ . (b) Variation of the resistivity with the band gap. Note that for the case of the band overlap, the resistivity is multiplied by a factor of 10 for greater visibility. (c) Simulations with various assumed values of the electron mass.
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Figure 5
Simulation of the Hall coefficient, for two values of the electron effective mass, compared with experimental data [1] (dashed line). The saturation of $R_{H}$ below $\sim 100 K$ and a sign change of $R_{H}$ by room temperature are qualitatively reproduced.
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Figure 6
(a) Resistivity curves, in which different approaches to the CDW are implemented below $T_{CDW} = 202 K$ . [(b)–(d)] Corresponding temperature dependence of the band gap in each case; in model 1 the band gap fully opens up, while in model 2 the hole DOS is split into two components below $T_{CDW}$ , one of which does not evolve with temperature. (e) Derivative of resistivity with respect to temperature, for model 2 and without CDW. Even without any CDW, $d ρ / d T$ shows a minimum at $T_{der}$ , which in this case is meaningless. (f) A sharp peak in the second derivative is the better indicator for $T_{CDW}$ .
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Physical Review B

covering condensed matter and materials physics

On the origin of the anomalous peak in the resistivity of ${TiSe}_{2}$

Matthew D. Watson, Adam M. Beales, and Philip D. C. King

Phys. Rev. B 99, 195142 – Published 23 May 2019

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Physical Review B

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On the origin of the anomalous peak in the resistivity of TiSe2

Matthew D. Watson, Adam M. Beales, and Philip D. C. King

Phys. Rev. B 99, 195142 – Published 23 May 2019

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On the origin of the anomalous peak in the resistivity of ${TiSe}_{2}$