Coexistence of Rashba and Ising Spin-Singlet Pairings in Two-Dimensional IrTe$_{2}$

TL;DR

This work demonstrates a band-selective coexistence of Rashba-like in-plane and Ising-like out-of-plane spin-singlet Cooper pairings in a strain-stabilized 2D IrTe$_2$ monolayer. By combining density-functional theory with a symmetry-constrained ${f k}ot{f p}$ model and spin-fluctuation mediated pairing, the authors show that distinct Fermi-surface sheets host uncoupled odd-parity pairing channels protected by inversion and crystal symmetry. The inner sheets favor Rashba-based spin textures, while the outer sheet supports Ising-type pairing, allowing for multichannel superconductivity with potential spin-filtered transport and anisotropic upper critical fields. These results establish a symmetry-based route to multichannel superconductivity in 2D transition-metal dichalcogenides and suggest tunability via strain, carrier density, and electric fields.

Abstract

Symmetry offers a useful approach to unfold the intertwined degrees of freedom. Thus it paves the way to resolve coexisting quantum orders into distinct symmetry sectors. Motivated by the recent observation of superconductivity in nano-flaked IrTe$_2$, we investigate the superconductivity in strain-stabilized two-dimensional (2D) limit of IrTe$_2$ by combining density-functional theory with mean-field solution of spin-fluctuation mediated pairing interaction on a symmetry-constrained ${\bf k}\cdot{\bf p}$ model. The spin-orbit coupled band structure shows $Γ$-centred Fermi sheets with coexistence of band-selective Rashba-like (in-plane) and Ising-like (out-of-plane) superconductivity. Remarkably, the superconducting gaps are odd in spin, orbital, and momentum channels despite the presence of global inversion symmetry. Fermi surface topologies and little-group symmetry enforce distinct irreducible representations to the Rashba and Ising channels, forbidding their mixing. Our findings open up a symmetry-based route to multichannel superconductivity in 2D transition-metal dichalcogenides with unique functionalities.

Figures (8)

• Figure 1: (a) Crystal structure of bulk IrTe$_2$. The black circle represents the inversion center of the structure. The monolayer IrTe$_2$ blocks (marked as dotted boxes) are stacked along the vertical $c$-axis. (b) Crystal structure of monolayer IrTe$_2$. Differently colored stars indicate inversion-symmetric atomic partners, while the black circle represents the inversion center. (c) Calculated energy cost in separating the monolayer blocks as function of interlayer distance, $d$. The converged value of the energy cost at large $d$ provides the estimate of cleavage energy. The inset pictorially illustrates the transition from bulk to monolayer. (d) Phonon spectrum of the monolayer under 1$\%$ tensile biaxial strain. The unstrained monolayer is found to be dynamically unstable, as indicated by the presence of unstable phonon frequencies in the spectrum shown in the inset.
• Figure 2: (a) Energy level positions of Te-$p$ and Ir-$t_{2g}$ in IrTe$_2$. (b) Te-$p_x$ Wannier function centered at Te site (marked as green ball) within a cage of Ir (marked as red ball) and Te. Plotted is constant value surface with yellow and magenta denoting two opposite signs of the function. (c) Left: Orbital-projected GGA band structure of the IrTe$_2$ monolayer along the high-symmetry path M–$\Gamma$–K–M. The Fermi level is set to zero. Colors denote orbital characters: Te-$p_x$ (green), Te-$p_y$ (blue), Te-$p_z$ (magenta), and Ir-$d$ (red). Zoomed-in views of the band structure near the Fermi level, highlighting degenerate Te $p_x/p_y$ bands at $\Gamma$ point is shown as inset. Right, top: Zoomed-in views of the band structure near the Fermi level upon inclusion of SOC, which splits Te $p_x/p_y$ bands at $\Gamma$ point. Right, bottom: GGA+SOC low energy band structure in $k_x$-$k_y$ plane.
• Figure 3: (a)–(c) Projection of spin expectation values on the Fermi surface, obtained from the DFT calculations. (d)-(f) The same, but obtained from the $k \cdot p$ model Hamiltonian. The strength of the spin expectation values is indicated by the color band shown in (c) and (f).
• Figure 4: (a) RPA spin susceptibility $\chi_s({\bf q})$ and (b) pairing eigenvectors $\Delta_{\nu}({\bf k})$ visualized on the FS. The two concentric circular FSs are formed by degenerate bands 1 and 2, while the outer one is formed by degenerate bands 3 and 4.
• Figure S1: (a) Displacement vector corresponding to the imaginary (negative) phonon mode. (b) Variation of the free energy as a function of time $t$ at $T = 300\ \mathrm{K}$ for IrTe$_2$ monolayer respectively.