Failed excitonic quantum phase transition in ${\mathrm{Ta}}_{2}\mathrm{Ni}({\mathrm{Se}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}{)}_{5}$

Letter

Failed excitonic quantum phase transition in ${Ta}_{2} Ni ({Se}_{1 - x} S_{x})_{5}$

Pavel A. Volkov, Mai Ye, Himanshu Lohani, Irena Feldman, Amit Kanigel, and Girsh Blumberg

Phys. Rev. B 104, L241103 – Published 10 December 2021

Abstract

We study the electronic phase diagram of the excitonic insulator candidates ${Ta}_{2} Ni {({Se}_{1 - x} S_{x})}_{5}$ $(x = 0, \dots, 1)$ using polarization resolved Raman spectroscopy. Critical excitonic fluctuations are observed that diminish with $x$ and ultimately shift to high energies, characteristic of a quantum phase transition. Nonetheless, a symmetry-breaking transition at finite temperatures is detected for all $x$ , exposing a cooperating lattice instability that takes over for large $x$ . Our study reveals a failed excitonic quantum phase transition, masked by a preemptive structural order.

Received 22 April 2021
Revised 28 November 2021
Accepted 1 December 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L241103

Physics Subject Headings (PhySH)

Excitons Phase diagrams Quantum phase transitions

Bose-Einstein condensates

Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Pavel A. Volkov ^1,*, Mai Ye ^1,†, Himanshu Lohani², Irena Feldman², Amit Kanigel², and Girsh Blumberg ^1,3,‡

¹Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
²Department of Physics, Technion - Israel Institute of Technology, Haifa 32000, Israel
³National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia

^*pv184@physics.rutgers.edu
^†mye@physics.rutgers.edu
^‡girsh@physics.rutgers.edu

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Vol. 104, Iss. 24 — 15 December 2021

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Figure 1
Overview of the polarization-resolved Raman response $χ^{″} (ω, T)$ in ${Ta}_{2} Ni {({Se}_{1 - x} S_{x})}_{5}$ . (a)–(d) Response in $a a$ polarization geometry corresponding to fully symmetric ( $A_{g}$ ) excitations above (red) and below (blue) $T_{c}$ for $x = 0 - 1$ . Shading highlights the bare electronic contribution to the response. (e) and (f) Same for $a c$ geometry, probing the excitations with the symmetry of the order parameter ( $B_{2 g}$ ) for $T > T_{c}$ (red). Unlike $a a$ geometry, phonons show an extremely anisotropic Fano line shape (hatching), indicating their strong interaction with the electronic continuum (red shading). For $T < T_{c}$ (blue) excitations observed in $a a$ geometry above $T_{c}$ appear (arrow) due to symmetry breaking. (i)–(l) Temperature dependence of $χ_{a c}^{″} (ω, T)$ ; an enhancement at low energies near $T_{c}$ (arrow) is observed for $x = 0, 0.25, 0.67$ . For $x = 1$ no low-energy response is present. (m)–(p) Details of $χ_{a c}^{″} (ω, T)$ for regions marked by dashed lines in (i)–(k). (m)–(o) Fano line shape of low-energy phonons due to interaction with electronic continuum. (p) High-energy peak due to an uncondensed exciton in ${Ta}_{2} {NiS}_{5}$ .
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Figure 2
The parameters deduced from the Raman response data, Fig. 1. (a) Integrated “leakage” intensity into $a c$ scattering geometries of the lowest-energy $A_{g}$ phonon mode labeled in Figs. 1–1, normalized by the intensity in the dominant $a a$ geometry. The mode's appearance in the $a c$ scattering geometry below $T_{c}$ implies the onset of symmetry breaking. (b) Excitonic energy $Ω_{e} (T)$ , Eq. (1), obtained from the Fano fits to the line shapes in Fig. 1. Lines represent linear fits to the points.
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Figure 3
Phase diagram of ${Ta}_{2} Ni {({Se}_{1 - x} S_{x})}_{5}$ . Orange points: The symmetry-breaking transition temperature $T_{c} (x)$ obtained from the onset of phonon intensity leakage, Fig. 2. Red points and crosses: $T_{c}^{ρ} (x)$ adapted from transport studies [19, 38]. For low sulfur concentration $x$ , the soft excitonic mode [Fig. 2] would drive the transition at temperature $T_{ex} (x)$ (blue points) that is enhanced to $T_{comb} (x)$ by coupling to inert optical phonons (green points), and is further enhanced to $T_{comb}^{str} (x)$ by coupling to the $B_{2 g}$ strain (purple triangles). For large $x$ , the excitonic softening is suppressed, while a ferroelastic instability leads to a finite $T_{comb}^{FE} (x)$ (black squares). In the absence of the lattice instability, a lattice-shifted electronic QPT would have occurred at $x_{c}$ (dashed purple line). Additionally, in the same proximity, the band structure undergoes semimetal-to-semiconductor Lifschitz transition (see text).
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Physical Review B

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Failed excitonic quantum phase transition in ${Ta}_{2} Ni ({Se}_{1 - x} S_{x})_{5}$

Pavel A. Volkov, Mai Ye, Himanshu Lohani, Irena Feldman, Amit Kanigel, and Girsh Blumberg

Phys. Rev. B 104, L241103 – Published 10 December 2021

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Physical Review B

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Failed excitonic quantum phase transition in Ta2Ni(Se1−xSx)5

Pavel A. Volkov, Mai Ye, Himanshu Lohani, Irena Feldman, Amit Kanigel, and Girsh Blumberg

Phys. Rev. B 104, L241103 – Published 10 December 2021

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Failed excitonic quantum phase transition in ${Ta}_{2} Ni ({Se}_{1 - x} S_{x})_{5}$