Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal ${\mathrm{Ta}}_{2}{\mathrm{Pd}}_{3}{\mathrm{Te}}_{5}$

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Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal ${Ta}_{2} {Pd}_{3} {Te}_{5}$

Peng Zhang, Yuyang Dong, Dayu Yan, Bei Jiang, Tao Yang, Jun Li, Zhaopeng Guo, Yong Huang, Haobo, Qing Li, Yupeng Li, Kifu Kurokawa, Rui Wang, Yuefeng Nie, Makoto Hashimoto, Donghui Lu, Wen-He Jiao, Jie Shen, Tian Qian, Zhijun Wang, Youguo Shi, and Takeshi Kondo

Phys. Rev. X 14, 011047 – Published 13 March 2024

Abstract

The opening of an energy gap in the electronic structure generally indicates the presence of interactions. In materials with low carrier density and short screening length, long-range Coulomb interaction favors the spontaneous formation of electron-hole pairs, so called excitons, opening an excitonic gap at the Fermi level. Excitonic materials host unique phenomena associated with pair excitations. However, there is still no generally recognized single-crystal material with excitonic order, which is, therefore, awaited in condensed matter physics. Here, we show that excitonic states may exist in the quasi-one-dimensional material ${Ta}_{2} {Pd}_{3} {Te}_{5}$ , which has an almost ideal Dirac-like band structure, with the Dirac point located exactly at the Fermi level. We find that an energy gap appears at 350 K, and it grows with decreasing temperature. The spontaneous gap opening is absent in a similar material ${Ta}_{2} {Ni}_{3} {Te}_{5}$ . Intriguingly, the gap is destroyed by the potassium deposition on the crystal, likely due to extra-doped carriers. Furthermore, we observe a pair of in-gap flat bands, which is an analog of the impurity states in a superconducting gap. All these observations can be properly explained by an excitonic order, providing ${Ta}_{2} {Pd}_{3} {Te}_{5}$ as a new and promising candidate realizing excitonic states.

Received 6 December 2022
Revised 21 December 2023
Accepted 1 February 2024

DOI:https://doi.org/10.1103/PhysRevX.14.011047

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Band gap Electronic structure Excitons

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Peng Zhang ^1,2,*,†, Yuyang Dong^3,*, Dayu Yan^4,5,*, Bei Jiang^4,5,*, Tao Yang¹, Jun Li⁴, Zhaopeng Guo^4,5, Yong Huang¹, Haobo ⁶, Qing Li¹, Yupeng Li⁴, Kifu Kurokawa³, Rui Wang^1,2, Yuefeng Nie⁶, Makoto Hashimoto⁷, Donghui Lu⁷, Wen-He Jiao⁸, Jie Shen⁴, Tian Qian^4,5, Zhijun Wang ^4,5, Youguo Shi^4,5, and Takeshi Kondo^3,9,‡

¹School of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, China
²Collaborative Innovation Center for Advanced Microstructures, Nanjing, China
³Institute for Solid State Physics, the University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁴Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
⁵University of Chinese Academy of Sciences, Beijing, China
⁶National Laboratory of Solid State Microstructures, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing, China
⁷Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California, USA
⁸Key Laboratory of Quantum Precision Measurement of Zhejiang Province, Department of Applied Physics, Zhejiang University of Technology, Hangzhou, China
⁹Trans-scale Quantum Science Institute, The University of Tokyo, Tokyo 113-0033, Japan

^*These authors contributed equally to this work.
^†zhangpeng@nju.edu.cn
^‡kondo1215@issp.u-tokyo.ac.jp

Popular Summary

In most materials, the electrical properties are determined by excitations of single particles. In some rare cases, electron-electron or electron-hole pairs could exist, and they will show very distinct properties from general single-particle excitations. Here, we present evidence of electron-hole pairs (called excitons) in a new material that hosts only excitonic states and is an ideal platform to study the novel physics of pair excitations.

Previously, only two kinds of single-crystal materials have been proposed to host excitonic states. However, in both materials there are either charge-density-wave order or structure transitions associated with the possible excitonic order, which makes it difficult to verify the excitonic order and to work on the related phenomenon. The new material we report here shows only excitonic states and basically no other transition entangling with the excitonic states. We observe that an energy gap opens with decreased temperature, the energy gap is fragile to carrier doping, and a pair of flat bands exists in the energy gap. All these observations are consistent with an excitonic order.

Our results provide evidence of the first clean candidate of an excitonic insulator, although further experimental work is needed to reach a definitive conclusion. This new material will be highly advantageous for developing the condensed matter physics on excitonic states.

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Evidence for an Excitonic Insulator State in ${Ta}_{2} {Pd}_{3} {Te}_{5}$

Jierui Huang et al.

Phys. Rev. X 14, 011046 (2024)

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Figure 1
The crystal structure and electronic properties of ${Ta}_{2} {Pd}_{3} {Te}_{5}$ . (a) Crystal structure of ${Ta}_{2} {Pd}_{3} {Te}_{5}$ . The Ta-Te chains are along the $b$ axis. (b) Resistivity curve from 250 to 400 K. The inset shows the overall behavior from 2 to 400 K. (c) Electron-diffraction measurement of the [100] zone axis. The data are taken at 94 and 370 K, respectively. (d) Temperature evolution of the (00l) peaks. The vertical intensity axis is in a log scale. See Supplemental Material [32] Fig. 1 for the same plot in a linear scale. (e) Intensity mapping in $k$ space around the $Γ − Z$ line measured by a 7-eV laser ARPES. The data are taken at $- 30 meV$ [dashed blue line in (f)] and integrated over an energy window of $\pm 5 meV$ . The left and right insets show the bulk Brillouin zone and the curvature plot of the data in gray scale, respectively. (f),(g) Band structures measured at 10 K by ARPES, perpendicular to the chain [cut 1 in (e)] with $s$ -polarized light and along the chain [cut 2 in (e)] with $p$ -polarized light, respectively.
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Figure 2
Temperature evolution of the band structure and energy gap in ${Ta}_{2} {Pd}_{3} {Te}_{5}$ . (a1) The curvature plot of (a2). (a2)–(a6) The electronic structure along the chain direction at $k_{c} = 0$ measured by ARPES from 350 to 20 K with 30-eV photons. (b1) The curvature plot of (b2). (b2)–(b6) The same data as (a2)–(a6) but measured with 67-eV photons. The black dashed lines in (a5) and (a6) and (b5) and (b6) sketch the conduction band above $E_{F}$ . The black arrows in (a6) and (b6) mark the in-gap impurity states (ISs), which do not cross the Fermi level [see their high-resolution EDCs in Fig. 5]. The details of impurity states are discussed in Fig. 5. All data are divided by the Fermi function at measured temperatures to remove the cutoff effect above $E_{F}$ . (c) Sketch of band dispersions extracted from 30- and 67-eV data. The cone-shaped bands crossing $E_{F}$ and the $m$ -shaped band not crossing $E_{F}$ are represented by solid and dashed lines, respectively. The conduction bands from 30- and 67-eV data have slightly different dispersions. (d) Intensity difference between 250 and 350 K data measured with 30-eV photons. The blue area around $E_{F}$ indicates the opening of the energy gap $Δ$ . (e) EDC curvature plot for the 30-eV data enlarging the valence-band top [dashed box in (a5)] for three different temperatures (200, 100, and 20 K). The valence-band top [red arrow in (a5)] is extracted from the curvature-enhanced dispersion. (f) EDCs of the conduction band at $k_{b} = k_{c} = 0$ extracted from 67-eV data for different temperatures. The blue dots indicate the conduction-band bottom [blue arrow in (b3)]. (g) Temperature dependence of the valence-band top ( $E_{v}$ ) and conduction-band bottom ( $E_{c}$ ) demonstrating the gap evolution. The $E_{v}$ (solid red line) is extracted from (e), and $E_{c}$ (solid blue line) is extracted from (f). The $E_{c}$ curve in cyan color is extracted from EDCs in 30-eV data in (a). As both $E_{c}$ and $E_{v}$ values are acquired at 150 and 200 K and they are roughly equal, it is reasonable to assume that the band gap opens symmetrically to $E_{F}$ . Then we get the full temperature evolution of the conduction and valence bands by mirroring the blue, cyan, and red lines. The entire evolution of the gap with the temperature is illustrated by the dashed black lines.
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Figure 3
Temperature evolution of the band structure in ${Ta}_{2} {Ni}_{3} {Te}_{5}$ . (a)–(d) The electronic structure along the chain direction at $k_{c} = 0$ measured from 300 to 10 K with 7-eV photons. (e)–(h) The curvature plot of (a)–(d). The red lines in (e) and (h) are the same curve, which is extracted from EDC peaks in (h). (i) Evolution of EDCs with temperature at $k_{b} = 0$ . (j) Shift of valence-band top with temperature. Blue dots are extracted from EDC peaks in (e)–(h).
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Figure 4
Effect of potassium deposition on the band structure of ${Ta}_{2} {Pd}_{3} {Te}_{5}$ . (a) Evolution of the band structure along the chain direction at $k_{c} = 0$ with potassium deposition taken at 10 K. (b) Curvature intensity plot of (a). The energy states (small red dots) near $E_{F}$ in one-, two- and four-minute data are extracted from the peak positions of MDCs. The red lines are parabolic fits to the red dots. (c) Variations of MDCs at $E_{F}$ with the time of potassium deposition. Dashed lines illustrate the change of the Fermi vector $k_{F}$ of the conduction bands. (d) Evolution of the conduction band (CB) with potassium deposition. The red dots represent the band bottom of the fitted bands in (b). The solid red line is a linear fit to the red dots, and the dashed red line is the extrapolation of it to zero minutes.
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Figure 5
Observation of double flat bands inside the energy gap in ${Ta}_{2} {Pd}_{3} {Te}_{5}$ . (a) Band structure observed perpendicular to the chain direction at $k_{b} = 0$ measured at 10 K with $s$ -polarized light. To enhance the visibility of in-gap states, the color scale is adjusted to saturate the intensities of valence bands. (b) The same data as (a) but normalized to the intensities of the valence band to remove the matrix element effect. (c) Band structure observed along the chain direction at $k_{c} = 0$ measured at 10 K with $p$ -polarized light. (d) EDCs focusing on the in-gap flat bands. EDC 1 and EDC 2 are integrated over momentum regions indicated by the arrows in (a) and (c), respectively. These EDCs are measured with both $s$ - and $p$ -polarized light. The dashed lines mark peak energies of about $- 8$ and $- 18 meV$ .
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Physical Review X

Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal ${Ta}_{2} {Pd}_{3} {Te}_{5}$

Peng Zhang, Yuyang Dong, Dayu Yan, Bei Jiang, Tao Yang, Jun Li, Zhaopeng Guo, Yong Huang, Haobo, Qing Li, Yupeng Li, Kifu Kurokawa, Rui Wang, Yuefeng Nie, Makoto Hashimoto, Donghui Lu, Wen-He Jiao, Jie Shen, Tian Qian, Zhijun Wang, Youguo Shi, and Takeshi Kondo

Phys. Rev. X 14, 011047 – Published 13 March 2024

Abstract

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Evidence for an Excitonic Insulator State in ${Ta}_{2} {Pd}_{3} {Te}_{5}$

Jierui Huang et al.

Phys. Rev. X 14, 011046 (2024)

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Physical Review X

Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal Ta2Pd3Te5

Peng Zhang, Yuyang Dong, Dayu Yan, Bei Jiang, Tao Yang, Jun Li, Zhaopeng Guo, Yong Huang, Haobo, Qing Li, Yupeng Li, Kifu Kurokawa, Rui Wang, Yuefeng Nie, Makoto Hashimoto, Donghui Lu, Wen-He Jiao, Jie Shen, Tian Qian, Zhijun Wang, Youguo Shi, and Takeshi Kondo

Phys. Rev. X 14, 011047 – Published 13 March 2024

Abstract

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Evidence for an Excitonic Insulator State in Ta2Pd3Te5

Jierui Huang et al.

Phys. Rev. X 14, 011046 (2024)

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Spontaneous Gap Opening and Potential Excitonic States in an Ideal Dirac Semimetal ${Ta}_{2} {Pd}_{3} {Te}_{5}$

Evidence for an Excitonic Insulator State in ${Ta}_{2} {Pd}_{3} {Te}_{5}$