Carrier-Density Control of the Quantum-Confined $1T\text{\ensuremath{-}}{\mathrm{TiSe}}_{2}$ Charge Density Wave

Carrier-Density Control of the Quantum-Confined $1 T − {TiSe}_{2}$ Charge Density Wave

T. Jaouen, A. Pulkkinen, M. Rumo, G. Kremer, B. Salzmann, C. W. Nicholson, M.-L. Mottas, E. Giannini, S. Tricot, P. Schieffer, B. Hildebrand, and C. Monney

Phys. Rev. Lett. 130, 226401 – Published 31 May 2023

Abstract

Using angle-resolved photoemission spectroscopy, combined with first principle and coupled self-consistent Poisson-Schrödinger calculations, we demonstrate that potassium (K) atoms adsorbed on the low-temperature phase of $1 T − {TiSe}_{2}$ induce the creation of a two-dimensional electron gas (2DEG) and quantum confinement of its charge-density wave (CDW) at the surface. By further changing the K coverage, we tune the carrier density within the 2DEG that allows us to nullify, at the surface, the electronic energy gain due to exciton condensation in the CDW phase while preserving a long-range structural order. Our Letter constitutes a prime example of a controlled exciton-related many-body quantum state in reduced dimensionality by alkali-metal dosing.

Received 6 October 2022
Accepted 10 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.226401

Physics Subject Headings (PhySH)

Adsorption Charge density waves Doping effects Electronic structure Excitons Order parameters Phase diagrams

Density functional theory Photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Jaouen ^1,*, A. Pulkkinen ^2,3, M. Rumo ^2,4, G. Kremer ^2,5, B. Salzmann ², C. W. Nicholson ^2,6, M.-L. Mottas², E. Giannini⁷, S. Tricot ¹, P. Schieffer¹, B. Hildebrand ², and C. Monney ²

¹Univ Rennes, CNRS, (IPR Institut de Physique de Rennes)—UMR 6251, F-35000 Rennes, France
²Département de Physique and Fribourg Center for Nanomaterials, Université de Fribourg, CH-1700 Fribourg, Switzerland
³New Technologies Research Centre, University of West Bohemia, CZ-30100 Pilsen, Czech Republic
⁴Haute école d’ingénierie et d’architecture de Fribourg, CH-1700 Fribourg, Switzerland
⁵Institut Jean Lamour, UMR 7198, CNRS-Université de Lorraine, Campus ARTEM, 2 allée André Guinier, BP 50840, 54011 Nancy, France
⁶Fritz-Haber-Institute der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
⁷Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland

^*Corresponding author. thomas.jaouen@univ-rennes1.fr

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Vol. 130, Iss. 22 — 2 June 2023

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Figure 1
(a) K $3 p$ core-level evolution upon sequential K depositions. $h ν = 40.8 eV$ . (b),(c) $12 \times 12 {nm}^{2}$ constant-current STM images of the pristine surface (b) and of a 0.33 ML K-covered (c) surface. $V_{bias} = - 1 V$ , $I = 0.2 nA$ , $T = 4.6 K$ . Also shown, as insets, are the corresponding LEED patterns ( $E_{p} = 121 eV$ ). (d),(e) Comparison of large-energy scale ARPES intensity maps with band structures obtained from DFT slab calculations along the $\bar{M} − \bar{Γ} − \bar{M}$ and $\bar{Γ} − \bar{M} − \bar{Γ}$ directions of the surface Brillouin zone (BZ) for both pristine (left-hand side) and K-covered (right-hand side) surfaces in the CDW phase. The horizontal black arrows indicate the QWS (see text). The color scales from white to dark blue indicate the spectral weights obtained using the unfolding procedure (see SM). $h ν = 21.2 eV$ , $T = 40 K$ . (f) 3D BZ of $1 T − {TiSe}_{2}$ . Also shown is one CDW $q$ vector, $q_{C D W}$ . The $k_{x}$ axis depicted by the black arrow is the $\bar{Γ} − \bar{M}$ direction of the surface BZ. (g) Side view of the $1 T − {TiSe}_{2}$ six-layer slab with a $2 \times 4 K$ adlayer on the surface. The light blue isosurface refers to the missing charge and the yellow isosurface to the gained charge for a $0.0014 e^{-} / a_{0}^{3}$ level, where $a_{0}$ is the Bohr radius.
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Figure 2
(a) Band-bending potential extracted from DFT (see text and SM). (b) Near- $E_{F}$ enlargement of the surface layer-projected DFT-calculated band structure along $\bar{Γ} − \bar{M} − \bar{Γ}$ of the 0.125 ML K-covered slab. The color scale from white to dark blue indicates the spectral weights obtained using the unfolding procedure (see SM). (c) ARPES intensity map at $\bar{M}$ of a 0.14 ML K-covered surface. $h ν = 21.2 eV$ , $T = 40 K$ . (d) Same as (b) along $\bar{M} − \bar{Γ} − \bar{M}$ . The red arrows indicate the surface CDW gaps. (e) Same as (c) at $\bar{Γ}$ . (f) Laser-ARPES intensity map taken at $\bar{Γ}$ of a 0.33 ML K-covered surface. The red arrow indicates the surface CDW gap. $h ν = 6.3 eV$ , $T = 40 K$ .
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Figure 3
(a) FS at $\bar{M}$ for increasing $n_{2 DEG}$ . $h ν = 21.2 eV$ , $T = 40 K$ . (b) Corresponding ARPES intensity maps. The near- $E_{F}$ dispersions calculated within the effective Hamiltonian model of four interacting bands are also superimposed. (c) PS-calculated near-surface band bendings (black lines), eigenenergies $E_{d z^{2}, 1}^{0}$ (red-dashed lines), and modulus squared of the eigenfunctions $| ϕ_{d z^{2}, 1}^{0} (z) |^{2}$ (blue areas) of the first QWS as a function of $n_{2 DEG}$ . The surface potential values, $V_{S}$ , are also indicated. (d) Evolution of the BEs of the Mexican hat (green bands) and backfolding (orange bands) taken with respect to $E_{d z^{2}, 1}^{0}$ as a function of $n_{2 DEG}$ . Sketches of the bands configuration in the unperturbed CDW phase and surface-confined semimetallic normal state are also shown. (e) $Δ$ as a function of $n_{2 DEG}$ . The red-dashed line is a mean-field-like fitting with $Δ (n_{2 DEG}) = Δ_{0} (1 - n_{2 DEG} / n_{c})^{1 / 2} + Δ_{off}$ with $Δ_{0} = 88 \pm 24 meV$ , $Δ_{off} = 26 \pm 15 meV$ , and $n_{c} = 0.156 \pm 0.024 e^{-} / u . c .$ .
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Physical Review Letters

Carrier-Density Control of the Quantum-Confined 1T−TiSe2 Charge Density Wave

T. Jaouen, A. Pulkkinen, M. Rumo, G. Kremer, B. Salzmann, C. W. Nicholson, M.-L. Mottas, E. Giannini, S. Tricot, P. Schieffer, B. Hildebrand, and C. Monney

Phys. Rev. Lett. 130, 226401 – Published 31 May 2023

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Carrier-Density Control of the Quantum-Confined $1 T − {TiSe}_{2}$ Charge Density Wave