Optical probes of two-component pairing states in transition metal dichalcogenides

TL;DR

This work addresses the problem of identifying the superconducting pairing symmetry in transition metal dichalcogenides, focusing on the two-component E' channel that can realize nematic or chiral ground states under Ising SOC. It adopts a multiband BdG framework for H-phase TMDs and computes the linear optical conductivity via the Kubo formalism, predicting symmetry-based fingerprints: a diagonal conductivity anisotropy $σ_{xx}-σ_{yy}$ for nematic order and a finite optical Hall conductivity $σ_{xy}^H$ for chiral order. The key findings are that realistic meV-scale gaps yield measurable signatures, with $Δσ/σ$ of order $10^{-5}$ in the nematic case and Kerr rotations $θ_K$ of order $10^{-5}$–$10^{-4}$ rad in the chiral case, plus high-frequency features tied to Van Hove singularities. These results provide a practical optical-diagnostic route to distinguish nematic and chiral $E'$ superconductivity in TMDs, and are potentially applicable to NbSe$_2$, TaS$_2$, and CrBr$_3$/NbSe$_2$ systems in current or near-future experiments.

Abstract

Signatures of unconventional superconductivity have been recently observed in certain transition metal dichalcogenides (TMDs), including 4H$_b$-TaS$_2$ and monolayer 2H-NbSe$_2$. While the pairing channel remains unknown, it has been argued that spin fluctuations can stabilize pairing in the two-component $E'$ channel, a $p$-wave spin-triplet state which could be consistent with some of the reported signatures. Exploiting the particular multi-orbital character of the Fermi surface and the presence of Ising spin-orbit coupling, which enable finite optical conductivity in the clean limit, in this work we predict clear-cut optical signatures to detect and distinguish the chiral and nematic ground states of the $E'$ pairing. We quantify how nematic $E'$ states produce a diagonal anisotropy $σ_{xx}\!\neq\!σ_{yy}$ due to the broken threefold symmetry ($C_3$), while chiral $E'$ states yield a finite optical Hall conductivity $σ_{xy}^H$ due to broken time-reversal symmetry, and find both signals could be detected in current experiments. For instance, for realistic gaps in the meV range, we predict a relative anisotropy $Δσ/σ\sim10^{-5}$ in the nematic states, and a polar Kerr rotation of $θ_K\!\sim\!10^{-5}$ rad in the chiral states. These symmetry fingerprints provide a practical route to distinguish nematic and chiral superconducting order in TMD superconductors.

Figures (8)

• Figure 1: H-polytype of TMDs. (a) Crystalline structure of a single H-layer, corresponding to an ABA stacking of hexagonal lattices. (b) Band structure of the normal state of the H layer of TaS$_2$. (c) Optical conductivity in the normal state of TaS$_2$ shown in the range where it is nonzero.
• Figure 2: Band structure of the BdG Hamiltonian in Eq. \ref{['eqn:bdg_hamiltonian']} for 4Hb-TaS$_2$ with the superconducting pairings (a) $\Delta_{p_x}$, (b) $\Delta_{p_y}$, and (c) $\Delta_{p+ip}$ for $\Delta=0.1$ eV. The dark (light) gray shading marks the minimal (maximal) gap along high-symmetry directions. Insets show the gap magnitude across the Brillouin zone; light colors indicate smaller gaps and insets mark the paths used in the main panels. The dotted-dashed line in (c) marks the energy associated with the van Hove singularity that produces the secondary peak in the absorptive components $\mathrm{Re}\sigma_{xx}$ and $\mathrm{Im}\sigma^H_{xy}$.
• Figure 3: Anisotropy of the absorptive part of the optical conductivity at low (main figures) and high (inset) frequencies for the nematic phases $\Delta_{p_x}$ and $\Delta_{p_y}$ with $\Delta=0.1$ eV.
• Figure 4: Hall response in the chiral state. We compare the anti-symmetric and symmetric absorptive components of the optical conducitivty, $\mathrm{Im}\sigma^H_{xy}$ and ${\rm Re}\sigma_{xx}$, respectively, for $\Delta_{p+ip}$ at $\Delta=0.1$ eV at low (main) and high (inset) frequencies. The shadowed region indicates the span of the gap across the Brillouin Zone.
• Figure 5: Brillouin Zone-resolved absorptive part of the optical conductivity ${\rm Re}\sigma_{xx}$ (left column) and ${\rm Im}\sigma^H_{xy}$ (right) column integrated between $\omega=1.3\Delta$ and $\omega=1.8\Delta$ (upper row) corresponding to the low-energy peak in the response in Fig. \ref{['fig:hall_conductivity_pip']}, and $\omega=3\Delta$ and $\omega=4\Delta$ (lower row) corresponding to the secondary peak in the response in Fig. \ref{['fig:hall_conductivity_pip']}.