Protection of Ising spin-orbit coupling in bulk misfit superconductors

Letter

Protection of Ising spin-orbit coupling in bulk misfit superconductors

Tomas Samuely, Darshana Wickramaratne, Martin Gmitra, Thomas Jaouen, Ondrej Šofranko, Dominik Volavka, Marek Kuzmiak, Jozef Haniš, Pavol Szabó, Claude Monney, Geoffroy Kremer, Patrick Le Fèvre, François Bertran, Tristan Cren, Shunsuke Sasaki, Laurent Cario, Matteo Calandra, Igor I. Mazin, and Peter Samuely

Phys. Rev. B 108, L220501 – Published 4 December 2023

Abstract

Ising superconductivity is present due to the combined effect of broken-inversion symmetry and spin-orbit coupling that locks the spins out of plane, features that are associated with two-dimensional materials. We show that bulk misfit superconductors, ${(LaSe)}_{1.14} (Nb {Se}_{2})$ and ${(LaSe)}_{1.14} {(Nb {Se}_{2})}_{2}$ , comprising monolayers and bilayers of $Nb {Se}_{2}$ , exhibit unexpectedly strong Ising protection with a Pauli-limit violation comparable to monolayer $Nb {Se}_{2}$ . We establish these misfit compounds as Ising superconductors using complementary experimental methods in combination with first-principles calculations. A concerted effect of charge-transfer, defects, reduction of interlayer hopping, and stacking enables Ising superconductivity in these compounds and therefore provides a possible pathway to design of bulk superconductors that are resilient to magnetic fields.

Received 18 September 2023
Accepted 13 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.L220501

Physics Subject Headings (PhySH)

Doping effects Hall effect Meissner effect Spin-orbit coupling Spin-triplet pairing Superconductivity

Angle-resolved photoemission spectroscopy Density functional theory Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tomas Samuely^1,*, Darshana Wickramaratne ², Martin Gmitra ^1,3, Thomas Jaouen⁴, Ondrej Šofranko¹, Dominik Volavka ¹, Marek Kuzmiak ³, Jozef Haniš ¹, Pavol Szabó³, Claude Monney⁵, Geoffroy Kremer^5,6, Patrick Le Fèvre⁷, François Bertran⁷, Tristan Cren⁸, Shunsuke Sasaki ⁹, Laurent Cario⁹, Matteo Calandra¹⁰, Igor I. Mazin^11,†, and Peter Samuely ³

¹Institute of Physics, Faculty of Science, Pavol Jozef Šafárik University in Košice, 04001 Košice, Slovakia
²Center for Computational Materials Science, U.S. Naval Research Laboratory, Washington, DC 20375, USA
³Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences, 04001 Košice, Slovakia
⁴Univ Rennes, CNRS, (IPR Institut de Physique de Rennes) - UMR 6251, F-35000 Rennes, France
⁵Département de Physique and Fribourg Center for Nanomaterials, Université de Fribourg, Fribourg CH-1700, Switzerland
⁶Institut Jean Lamour, UMR 7198, CNRS-Université de Lorraine, Campus ARTEM, 2 allée André Guinier, BP 50840, 54011 Nancy, France
⁷SOLEIL synchrotron, L’Orme des Merisiers, Départementale 128, F-91190 Saint-Aubin, France
⁸Institut des NanoSciences de Paris, Sorbonne Université and CNRS-UMR 7588, Paris 75005, France
⁹Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, F-44000 Nantes, France
¹⁰Dipartimento di Fisica, Università di Trento, via Sommarive 14, I-38123 Povo, Italy
¹¹Department of Physics and Astronomy and Quantum Science and Engineering Center, George Mason University, Fairfax, Virginia 22030, USA

^*tomas.samuely@upjs.sk
^†imazin2@gmu.edu

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Issue

Vol. 108, Iss. 22 — 1 December 2023

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Images

Figure 1
Crystal structure of (a) 1T1H and (b) 1T2H. Dashed rectangles represent unit cell in $b c$ plane. (c) Topography of three atomic terraces of 1T1H, H surface in middle and ½-T surfaces adjacent to H surface. White arrow indicates area where scanning tip disrupted unstable ½-T layer. (d) (Top) Schematic illustration of how T layer of 1T1H can be cleaved into two ½-T layers. (Bottom) Height profile along green line in (c), imposed on illustrated atomic structure of H and T layers. Vertical size of illustrated atomic structure is to scale while horizontal size is exaggerated for clarity. Height profile reveals step size between $Nb {Se}_{2}$ , and ½-T layer terrace is $3 Å$ , i.e., half size of full T layer. (e) Topography of cleaved ½-T layer of 1T1H revealing imperfect tetragonal lattice. Large white spot corresponds to residue of removed top ½-T surface and dark spots correspond to vacancy sites. (f) Topography of H layer of 1T1H with hexagonal lattice after removing unstable ½-T layer by continuously sweeping area with STM tip. Periodicity of imaged T and H lattices is also visible in fast Fourier transform of (e) and (f) along with more intricate details stemming from misfit properties, described in Supplemental Material [18]. Scalebars in (c), (e), and (f) represent 5 nm.
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Figure 2
(a) Hall coefficients of 1T1H (red dots) and 1T2H (black squares). (b) Projections of energy-dispersive x-ray spectroscopic analyses for ${La}_{x} {Se}_{1.14} Nb {Se}_{2}$ crystals in La–Nb–Se ternary diagram (atomic percentages). Red dots are mean analyses of each crystal, while green star represents mean value for seven crystals. Black line represent theoretical compositions calculated between vacancy-rich $(x = 1)$ and vacancy-free $(x = 1.14)$ poles. Mean experimental composition lies on this line and evidences amount of La vacancies around 11.1%. More details in Supplemental Material [18].
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Figure 3
(a) ARPES map along $K^{'} - Γ - K$ high-symmetry line of hexagonal Brillouin zone of $2 H - Nb {Se}_{2}$ . $h ν = 106 eV$ . (b) ARPES map along $\bar{K^{'}} - \bar{Γ} - \bar{K}$ of 1T2H $[{(LaSe)}_{1.14} {(Nb {Se}_{2})}_{2}]$ . (c), (d) ARPES maps along $\bar{K^{'}} - \bar{Γ} - \bar{K}$ and $\bar{Γ} - \bar{M} - \bar{Γ}$ of 1T1H $[{(LaSe)}_{1.14} (Nb {Se}_{2})]$ . $h ν = 150 eV$ for both misfits. (e), (f) Out-of-plane momentum ( $k_{z}$ ) dispersions at $k_{y} = 0 Å^{- 1}$ and $E_{F}$ for $Nb {Se}_{2}$ and 1T2H. $h ν = 100 - 160 eV$ and $h ν = 20 - 60 eV$ for $2 H - Nb {Se}_{2}$ and 1T2H, respectively. Inner potential of 17.6 eV [24] and work function value of 5.9 eV [25] were used for converting photon energies into $k_{z}$ values within free-electron final-state approximation. Integer and half-integer values of $k_{z}$ correspond to $Γ$ points in $2 H - Nb {Se}_{2}$ (out-of-plane lattice parameter $c = 12.5 Å$ ) [26]. (g), (h) Fermi surfaces of 1T2H (g) and 1T1H (h) with overlaid hexagonal surface Brillouin zones of $2 H - Nb {Se}_{2}$ and associated $\bar{Γ}, \bar{K}, \bar{K^{'}}$ , and $\bar{M}$ high-symmetry points.
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Figure 4
Electronic structures unfolded onto hexagonal Brillouin zone along high-symmetry lines. (a) Band structure for supercell calculations of bare monolayer of $Nb {Se}_{2}$ (b) 1T2H and (c) 1T1H with 12.5% La vacancies.
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