Tuning the charge density wave quantum critical point and the appearance of superconductivity in $\mathrm{Ti}{\mathrm{Se}}_{2}$

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Tuning the charge density wave quantum critical point and the appearance of superconductivity in $Ti {Se}_{2}$

Sangyun Lee, Tae Beom Park, Jihyun Kim, Soon-Gil Jung, Won Kyung Seong, Namjung Hur, Yongkang Luo, Duk Y. Kim, and Tuson Park

Phys. Rev. Research 3, 033097 – Published 28 July 2021

Abstract

The transition metal dichalcogenide $Ti {Se}_{2}$ is an ideal correlated system for studying the interplay between superconductivity (SC) and a charge density wave (CDW) because both symmetry-breaking phases can be easily controlled by either Cu intercalation or physical pressure. SC appears in proximity to a CDW quantum critical point (QCP) induced by both Cu intercalation and applied pressure, raising the possibility of CDW-driven SC. Here, we report tuning the CDW QCP by simultaneously controlling Cu intercalation and external pressure and the appearance of a SC dome centered on the tunable QCP. When subjected to pressure, CDW ordering of Cu-intercalated ${Cu}_{0.025} Ti {Se}_{2}$ is completely suppressed at 2.3 GPa, where the residual resistivity and the resistivity-temperature exponent decrease sharply, indicating the presence of the CDW QCP. The upper critical field of ${Cu}_{0.025} Ti {Se}_{2}$ is 3.51 kOe, 16 times larger than that of pristine $Ti {Se}_{2}$ , and its temperature dependence is linear, indicating that SC of $Ti {Se}_{2}$ is switched from the two-dimensional- to anisotropic three-dimensional-like by Cu intercalation. These discoveries show that the simultaneous application of Cu intercalation and pressure move the CDW QCP and that the highest SC transition temperature is pinned to the QCP, suggesting that the SC in $Ti {Se}_{2}$ is strongly correlated with CDW quantum criticality.

Received 23 January 2021
Revised 22 June 2021
Accepted 24 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033097

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)

Charge order Phase diagrams Pressure effects Quantum criticality Quantum phase transitions Superconductivity

2-dimensional systems Low-temperature superconductors Transition metal dichalcogenides Unconventional superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sangyun Lee ^1,2,3,*, Tae Beom Park¹, Jihyun Kim¹, Soon-Gil Jung¹, Won Kyung Seong^1,†, Namjung Hur⁴, Yongkang Luo^3,‡, Duk Y. Kim², and Tuson Park^1,§

¹Center for Quantum Materials and Superconductivity (CQMS) and Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea
²Center for Integrated Nanostructure Physics (CINAP), Institute for Basic Science (IBS), Suwon 16419, Republic of Korea
³Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁴Department of Physics, Inha University, Incheon 22212, Republic of Korea

^*hansan29@skku.edu
^†Present address: Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.
^‡Present address: Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.
^§Corresponding author: tp8701@skku.edu

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Vol. 3, Iss. 3 — July - September 2021

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Condensed Matter Physics

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Figure 1
(a) Schematic phase diagram of ${Cu}_{x} Ti {Se}_{2}$ as a function of the degree of Cu intercalation [12]. The concentration $x = 0.025$ is marked with an arrow, and open symbols represent current experiments. (b) Crystal structure of ${Cu}_{x} Ti {Se}_{2}$ . The Ti atom is located at the center of an octahedral structure formed by six Se atoms. These structures form Se-Ti-Se layers (the Ti and Se atoms are blue and green, respectively). The Cu atoms (orange) are intercalated in the van der Waals gap between the Se-Ti-Se layers. (c) Powder x-ray diffraction pattern (PXRD) of the $x = 0.025$ sample is plotted as a function of the angle and compared with the calculated pattern obtained via Rietveld refinement.
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Figure 2
Electrical resistivity of ${Cu}_{0.025} Ti {Se}_{2}$ . The electrical resistivity (ρ) and its first derivative (dρ/ $dT$ ) are plotted for pressures of 0.3, 0.9, 1.7, 2.5, and 3.1 GPa in (a) and (b), respectively. The arrows in (b) mark the minimum dρ/ $dT$ , which are assigned as $T_{CDW}$ . (c) Magnified view of ρ near $T_{c}$ plotted for 1.7, 2.5, and 3.1 GPa, where the down arrows mark the onset of the superconducting phase transition. (d) Analysis of the low-temperature resistivity by using the power-law form of $ρ (T) = ρ_{0} + A T^{n}$ , where the best result of the least squares fitting is plotted as a black curve. ρ( $T$ ) is rigidly shifted for clarity with an offset offset ( $ρ_{offset}$ ) against values at ambient pressure (1 bar), where it is 48, 230, 245, and 250 for 0.9, 1.7, 2.5, and 3.1 GPa, respectively. (e) Overlay of the residual resistivity ( $ρ_{0}$ ) and the temperature exponent $n$ in the $T$ vs $P$ phase diagram. A sharp reduction of $ρ_{0}$ and $n$ is observed in the vicinity of $P_{c}$ , where $T_{c}$ is maximum.
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Figure 3
Temperature-dependent upper critical field ( $H_{c 2}$ ) of ${Cu}_{0.025} Ti {Se}_{2}$ . Electrical resistivity for the magnetic field applied within ( $H ∥ a b$ ) and perpendicular to the plane ( $H ∥ c$ ) plotted as a function of temperature in (a) and (b), respectively. (c) Temperature dependences of the upper critical field plotted for $H ∥ a b$ (circles) and $H ∥ c$ (squares), obtained from the onset of the superconductivity (SC) transition temperature $T_{c, onset}$ . (d) The anisotropy ratio of the upper critical field ( $Γ = H_{c 2}^{a b} / H_{c 2}^{c}$ ). Notice that Γ is almost independent of temperature. (e) Upper critical field divided by $T_{c}$ . The data for $x = 0$ and 0.07 are from Refs. [17, 18], respectively. (f) Reduced upper critical field ( $h$ ) plotted as a function of the reduced temperature ( $t$ ) and fitted with the linear and square root forms of $h = α_{i} (1 - t)$ and $h = {(1 - t)}^{1 / 2}$ , respectively, where the best results are sequentially plotted using solid and dotted lines.
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Figure 4
(a) Temperature vs pressure phase diagram of ${Cu}_{x} Ti {Se}_{2}$ . The solid and open symbols represent $T_{CDW}$ (squares) and $T_{c}$ (circles) for the $x = 0.025$ and 0 compounds [18, 19], respectively. The dotted line for $x = 0.025$ is an extrapolated phase boundary that ends at 2.3 GPa, the projected charge density wave (CDW) quantum critical point (QCP). (b) Cu intercalation–pressure–temperature ( $x - P - T$ ) phase diagram representing three datasets: (i) at ambient pressure, $T_{CDW}$ and $T_{c}$ in the $x - T$ plane, (ii) at $x = 0, T_{CDW}$ and $T_{c}$ in the $P - T$ plane, and (iii) at $x = 0.025, T_{CDW}$ and $T_{c}$ in the $P - T$ plane. The results from previous studies [12, 14, 17, 18, 19] are plotted together with those from this paper. The superconductivity (SC) transition temperature ( $T_{c}$ ) is multiplied by 20 for visibility.
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Physical Review Research

Tuning the charge density wave quantum critical point and the appearance of superconductivity in TiSe2

Sangyun Lee, Tae Beom Park, Jihyun Kim, Soon-Gil Jung, Won Kyung Seong, Namjung Hur, Yongkang Luo, Duk Y. Kim, and Tuson Park

Phys. Rev. Research 3, 033097 – Published 28 July 2021

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Tuning the charge density wave quantum critical point and the appearance of superconductivity in $Ti {Se}_{2}$