Probing the interlayer coupling in $2H\text{\ensuremath{-}}{\mathrm{NbS}}_{2}$ via soft x-ray angle-resolved photoemission spectroscopy

Editors' Suggestion
Open Access

Probing the interlayer coupling in $2 H − {NbS}_{2}$ via soft x-ray angle-resolved photoemission spectroscopy

D. Huang, H. Nakamura, K. Küster, U. Wedig, N. B. M. Schröter, V. N. Strocov, U. Starke, and H. Takagi

Phys. Rev. B 105, 245145 – Published 29 June 2022

Abstract

In the large family of two-dimensional (2D) layered materials including graphene, its honeycomb analogs, and transition-metal dichalcogenides, the interlayer coupling plays a rather intriguing role. On the one hand, the weak van der Waals interaction that holds the layers together endows these compounds with quasi-2D properties, which might imply small interlayer effects on the electronically active bands. On the other hand, the oft-witnessed differences in electronic, optical, and magnetic behaviors of monolayers, bilayers, and multilayers of the same compound must have as their microscopic origin the detailed interlayer hopping parameters. Given the few experimental reports that have attempted to explicitly extract these parameters, we employ soft x-ray angle-resolved photoemission spectroscopy (SX-ARPES) to probe the interlayer coupling in superconducting $2 H − {NbS}_{2}$ . We visualize the S $3 p_{z}$ bands that disperse with respect to the out-of-plane momentum and introduce a simple tight-binding model to extract the interlayer hopping parameters. From first-principles calculations, we clarify how atomic distances and the proper accounting for screening via hybrid functionals influence these bands. The knowledge of interlayer hopping parameters is particularly pertinent in ${NbS}_{2}$ , where recent experiments have uncovered fingerprints of finite-momentum superconductivity in the bulk material and heterostructures.

Received 29 April 2022
Accepted 31 May 2022

DOI:https://doi.org/10.1103/PhysRevB.105.245145

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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electronic structure Superconductivity

Transition metal dichalcogenides

Density functional theory Photoemission spectroscopy Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Huang ^1,*, H. Nakamura^2,†, K. Küster¹, U. Wedig ¹, N. B. M. Schröter^3,‡, V. N. Strocov³, U. Starke¹, and H. Takagi^1,4,5

¹Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
²Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
³Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
⁴Institute for Functional Matter and Quantum Technologies, University of Stuttgart, 70569 Stuttgart, Germany
⁵Department of Physics, University of Tokyo, 113-0033 Tokyo, Japan

^*D.Huang@fkf.mpg.de
^†hnakamur@uark.edu
^‡Present address: Max Planck Institute for Microstructure Physics, 06120 Halle, Germany.

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 105, Iss. 24 — 15 June 2022

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Crystal structure and definition of structural parameters. The numbers (1) and (2) and the subscript letters $A$ and $B$ are used in the construction of the TB model [Eq. (2)]. (b) Resistivity vs temperature from 300 to 1.8 K. (c) Magnification of (b) around the superconducting transition. (d) In-plane ( $∥$ ) and out-of-plane ( $⊥$ ) upper critical fields vs temperature. The former surpasses the theoretical Pauli limit around 2 K.
Reuse & Permissions
Figure 2
In-plane band dispersion of $2 H − {NbS}_{2}$ . (a) and (b) SX-ARPES intensity cuts in the $k_{z}$ = 0 plane at two photon energies, $h ν$ = 407 and 590 eV. Inset of (a): Fermi surface in the $k_{z}$ = 0 plane, visualized by integrating within the binding energy ( $E_{B}$ ) window [ $- 100 meV$ , 100 meV]; $h ν$ = 407 eV. A slight artificial distortion is present, due to the cleaved surface exhibiting small flakes and domains with different tilt angles and the challenge of maintaining the beam spot on the same area while tilting the sample platform. (c) SX-ARPES intensity cut in the $k_{z}$ = $π / c$ plane; $h ν$ = 566 eV. In [(b),(c)], DFT calculations (HSEsol functional) are overlaid as dashed lines, and the gray-shaded regions mark hole pockets that intersect $E_{F}$ . Insets of (b) and (c): Brillouin zone in the $k_{z}$ = 0 and $π / c$ planes.
Reuse & Permissions
Figure 3
Out-of-plane band dispersion of $2 H − {NbS}_{2}$ . (a) SX-ARPES intensity as a function of $k_{z}$ , tuned by the photon energy, along the $Γ − A$ line ( $k_{∥}$ = 0). DFT calculations (HSEsol functional) are overlaid as dashed lines. (b) Second-derivative image of (a). The red arrows mark replica bands.
Reuse & Permissions
Figure 4
Effective model for $k_{z}$ -dispersive bands. (a) Band dispersion along $Γ − A$ derived from experiment (left), DFT (open circles; HSEsol hybrid functional; right), and a TB fit to DFT [line; Eq. (2); right]. (b) Schematic orbital compositions of the states at $Γ$ . Red and blue colors denote the phases of the lobes. The odd orbitals S $3 p_{z, odd}$ form one pair of bonding and antibonding states, $σ_{odd}$ , $σ_{odd}^{*}$ , whereas the even orbitals S $3 p_{z, even}$ and Nb $4 d_{z^{2}}$ form two pairs of bonding and antibonding states, $σ_{even1}$ , $σ_{even1}^{*}$ and $σ_{even2}$ , $σ_{even2}^{*}$ .
Reuse & Permissions
Figure 5
Benchmark of DFT methods against interlayer coupling in ${NbS}_{2}$ . [(a)–(f)] TB parameters derived from fits of Eq. (2) to DFT calculations with various exchange-correlation and hybrid functionals. Experimental values are depicted as gray-horizontal lines. The red-horizontal lines and arrows denote a systematic offset introduced by hybrid functionals. [(g)–(i)] Optimized structural parameters corresponding to the DFT calculations. The shaded orange regions represent the spread of structural parameters reported in Refs. [43, 44, 45, 46]. The intralayer S-S distance ( $d_{intra}$ ) and the interlayer S-S distance ( $d_{inter}$ ) are defined in Fig. 1.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Probing the interlayer coupling in $2 H − {NbS}_{2}$ via soft x-ray angle-resolved photoemission spectroscopy

D. Huang, H. Nakamura, K. Küster, U. Wedig, N. B. M. Schröter, V. N. Strocov, U. Starke, and H. Takagi

Phys. Rev. B 105, 245145 – Published 29 June 2022

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text

Supplemental Material

References

Issue

Physical Review B

covering condensed matter and materials physics

Probing the interlayer coupling in 2H−NbS2 via soft x-ray angle-resolved photoemission spectroscopy

D. Huang, H. Nakamura, K. Küster, U. Wedig, N. B. M. Schröter, V. N. Strocov, U. Starke, and H. Takagi

Phys. Rev. B 105, 245145 – Published 29 June 2022

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text

Supplemental Material

References

Issue

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Reuse & Permissions

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Probing the interlayer coupling in $2 H − {NbS}_{2}$ via soft x-ray angle-resolved photoemission spectroscopy