Orbital-selective Peierls phase in the metallic dimerized chain ${\mathrm{MoOCl}}_{2}$

Letter

Orbital-selective Peierls phase in the metallic dimerized chain ${MoOCl}_{2}$

Yang Zhang, Ling-Fang Lin, Adriana Moreo, and Elbio Dagotto

Phys. Rev. B 104, L060102 – Published 9 August 2021

Abstract

Using ab initio density functional theory, here we systematically study the monolayer ${MoOCl}_{2}$ with a $4 d^{2}$ electronic configuration. Our main result is that an orbital-selective Peierls phase (OSPP) develops in ${MoOCl}_{2}$ , resulting in the dimerization of the Mo chain along the $b$ axis. Specifically, the Mo- $d_{x y}$ orbitals form robust molecular-orbital states inducing localized $d_{x y}$ singlet dimers, while the Mo- $d_{x z / y z}$ orbitals remain delocalized and itinerant. Our study shows that ${MoOCl}_{2}$ is globally metallic, with the Mo- $d_{x y}$ orbital bonding-antibonding splittings opening a gap and the Mo- $d_{x z / y z}$ orbitals contributing to the metallic conductivity. Overall, the results resemble the recently much discussed orbital-selective Mott phase but with the localized band induced by a Peierls distortion instead of Hubbard interactions. Finally, we also qualitatively discuss the possibility of OSPP in the $3 d^{2}$ configuration, as in ${CrOCl}_{2}$ .

Received 18 May 2021
Revised 5 July 2021
Accepted 28 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L060102

Physics Subject Headings (PhySH)

Orbital order Peierls transition Phase transitions

1-dimensional systems Strongly correlated systems

Density functional theory First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yang Zhang ¹, Ling-Fang Lin ¹, Adriana Moreo ^1,2, and Elbio Dagotto^1,2

¹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
²Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

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Vol. 104, Iss. 6 — 1 August 2021

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Figure 1
(a) and (b) Two possible electronic configurations in a dimer. Here we use two electrons in two orbitals per site, as an example. (a) Both orbitals form bonding-antibonding molecular-orbital states, resulting in an insulating phase (the sketched local density-of-states is localized). (b) The $γ = 1$ orbital forms strong molecular orbitals, while $γ = 2$ remains decoupled (the sketched local density-of-states has coexisting localized and itinerant features). (c) Schematic energy splitting of TM's $d$ orbitals with the $d^{2}$ configuration ( $Q_{3} < 0$ ) in the presence of the Hund rule. (d) Schematic three hoppings in one dimer for the $d^{2}$ configuration when three $t_{2 g}$ orbitals are active. (e)–(g) Possible lattice structures for real materials in the OSPP metallic phase. $O_{T}$ and $O_{P}$ indicate the oxygen atoms at the top or in-plane of the ${TMO}_{6}$ octahedron. Using the same level of detail of (d) would complicate (e) unnecessarily, thus in (e) each orbital is only sketched in a qualitative manner. (e) A two-dimensional sketch of a possible crystal structure with the TM-O-TM chain along the $a$ axis and ${TMO}_{2}$ chain along the $b$ axis, respectively. (f) Sketch of a ${TMO}_{2}$ chain. Due to the strong overlap of $d_{x y}$ orbitals along the $b$ axis, it could form a singlet dimer with $d d σ$ bonding. (g) Sketch of a TM-O-TM chain. The $d_{x z / y z}$ and O- $2 p$ orbitals form a $π^{*}$ state along the $a$ axis, inducing metallic conductivity along this axis. For better clarity we changed the lattice vectors of the conventional ${TMO}_{6}$ octahedral structure to the lattice axes of ${MoOCl}_{2}$ .
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Figure 2
(a) Schematic crystal structure of the ${MoOCl}_{2}$ conventional cell (magenta = Mo; green = Cl; red = O) for dimerized and undistorted phases, respectively. (b) and (c) Projected band structures of the monolayer ${MoOCl}_{2}$ for the nonmagnetic state: in (b) we use the undistorted phase (without Mo-Mo dimer) and in (c) the dimerized phase (with Mo-Mo dimer). The Fermi level is shown with dashed lines. The weight of each molybdenum orbital is represented by the circles' sizes. The coordinates of the high-symmetry points in the plane Brillouin zone are $Γ = (0, 0, 0)$ , $X = (0.5, 0, 0)$ , $S = (0.5, 0.5, 0)$ , $Y = (0, 0.5, 0)$ .
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Figure 3
(a)–(c) Wannier function of the Mo $t_{2 g}$ orbitals in the dimerized phase. (a) $d_{x z}$ orbital. (b) $d_{y z}$ orbital. (c) $d_{x y}$ orbital. It illustrates the alternating $d d σ$ -bonding and $d d σ^{*}$ -antibonding states along the $b$ axis. (d) Fermi surface. (e) Calculated energy barriers for the switching path from the undistorted to dimerized phases, based on a simple linear interpolation of the $Y^{1 +}$ mode by fixing the crystal constants of the dimerized phase. Inset: Electron localization function for the monolayer ${MoOCl}_{2}$ corresponding to the undistorted and dimerized phases, in the $a − b$ plane.
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Figure 4
(a) Projected density-of-states of the Mo- $d$ orbitals of monolayer ${MoOCl}_{2}$ with Mo-Mo dimerization for two spin configurations. (a) AFM arrangement of $d_{x z / y z}$ and spin-singlet state of $d_{x y}$ . (b) FM arrangement of $d_{x z / y z}$ and spin-singlet state of $d_{x y}$ . The five Mo $4 d$ orbitals are distinguished by different colors. We used $LSDA + U$ with Liechtenstein format ( $U = 3$ eV and $J_{H} = 0.6$ eV) on Mo sites.
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Figure 5
(a) and (b) Projected band structures of the monolayer dimerized ${CrOCl}_{2}$ phase for (a) nonmagnetic (GGA) and (b) AFM $(GGA + U)$ states, respectively. The weight of each Mo orbital is represented by the size of the circles. (c) and (d) Density-of-states of the Cr- $3 d$ orbitals of monolayer ${CrOCl}_{2}$ with Cr-Cr dimer, projected for one Cr atom. (c) AFM state. (d) FM state. The five Mo $3 d$ orbitals are distinguished by different colors. We used $LSDA + U$ with Liechtenstein format ( $U = 4$ eV and $J_{H} = 0.8$ eV) on Cr site.
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Physical Review B

covering condensed matter and materials physics

Orbital-selective Peierls phase in the metallic dimerized chain ${MoOCl}_{2}$

Yang Zhang, Ling-Fang Lin, Adriana Moreo, and Elbio Dagotto

Phys. Rev. B 104, L060102 – Published 9 August 2021

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Physical Review B

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Orbital-selective Peierls phase in the metallic dimerized chain MoOCl2

Yang Zhang, Ling-Fang Lin, Adriana Moreo, and Elbio Dagotto

Phys. Rev. B 104, L060102 – Published 9 August 2021

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Orbital-selective Peierls phase in the metallic dimerized chain ${MoOCl}_{2}$