[Paper Review] Tunneling spectroscopy of few-monolayer NbSe$_2$ in high magnetic field: Ising protection and triplet superconductivity

Marko Kuzmanović, Tom Dvir+11 more|arXiv (Cornell University)|Apr 1, 2021

Physics of Superconductivity and Magnetism1 references4 citations

TL;DR

This study uses high-field tunneling spectroscopy on few-monolayer NbSe₂ to demonstrate robust superconductivity beyond the Pauli limit, attributing it to Ising protection and the emergence of equal-spin triplet superconductivity (ESTS). The data show a field-dependent superconducting gap that persists up to 30 T in bilayer NbSe₂, inconsistent with standard Ising theory but well explained by a model including ESTS coupling to the singlet order parameter via in-plane magnetic fields.

ABSTRACT

In conventional Bardeen-Cooper-Scrieffer (BCS) superconductors, Cooper pairs of electrons of opposite spin (i.e. singlet structure) form the ground state. Equal spin triplet pairs (ESTPs), as in superfluid $^3$He, are of great interest for superconducting spintronics and topological superconductivity, yet remain elusive. Recently, odd-parity ESTPs were predicted to arise in (few-)monolayer superconducting NbSe$_2$, from the non-colinearity between the out-of-plane Ising spin-orbit field (due to the lack of inversion symmetry in monolayer NbSe$_2$) and an applied in-plane magnetic field. These ESTPs couple to the singlet order parameter at finite field. Using van der Waals tunnel junctions, we perform spectroscopy of superconducting NbSe$_2$ flakes, of 2--25 monolayer thickness, measuring the quasiparticle density of states (DOS) as a function of applied in-plane magnetic field up to 33T. In flakes $\lesssim$ 15 monolayers thick the DOS has a single superconducting gap. In these thin samples, the magnetic field acts primarily on the spin (vs orbital) degree of freedom of the electrons, and superconductivity is further protected by the Ising field. The superconducting energy gap, extracted from our tunnelling spectra, decreases as a function of the applied magnetic field. However, in bilayer NbSe$_2$, close to the critical field (up to 30T, much larger than the Pauli limit), superconductivity appears to be more robust than expected from Ising protection alone. Our data can be explained by the above-mentioned ESTPs.

Motivation & Objective

• To investigate the origin of enhanced superconducting critical fields in few-monolayer NbSe₂ under high in-plane magnetic fields.
• To determine whether Ising spin-orbit coupling and equal-spin triplet pairing (ESTS) explain the observed robustness beyond the Pauli limit.
• To distinguish between singlet superconductivity with Ising protection and a scenario involving intrinsic ESTS order parameters.
• To quantitatively assess the role of spin-orbit coupling and triplet pairing using tunneling spectroscopy data up to 33 T.
• To test theoretical models of Ising protection and Abrikosov-Gor'kov-type suppression against experimental data.

Proposed method

• Performed van der Waals tunnel junctions on exfoliated NbSe₂ flakes with thicknesses of 2–25 monolayers.
• Conducted quasiparticle density of states (DOS) measurements via tunneling spectroscopy in magnetic fields up to 33 T.
• Applied in-plane magnetic fields to probe the interplay between spin-orbit coupling and superconductivity.
• Fitted the measured DOS to extract the superconducting gap as a function of magnetic field, comparing with Ising and ESTS models.
• Used theoretical models including Ising protection, Abrikosov-Gor'kov theory, and Ising+ESTS coupling to interpret the data.
• Accounted for disorder and inter-valley scattering effects in model fitting, with error bars derived from statistical analysis of fits.

Experimental results

Research questions

• RQ1 Can Ising protection alone explain the observed suppression of the superconducting gap in few-monolayer NbSe₂ under high in-plane magnetic fields?
• RQ2 Does the persistence of superconductivity beyond the Pauli limit in bilayer NbSe₂ indicate the presence of equal-spin triplet pairing?
• RQ3 How does the inclusion of an equal-spin triplet component in the order parameter improve the fit to experimental tunneling spectra compared to standard Ising theory?
• RQ4 What is the role of spin-orbit coupling strength and inter-valley scattering in determining the critical field behavior?
• RQ5 Is the observed field dependence of the gap consistent with a microscopic mechanism involving singlet-triplet coupling via in-plane magnetic fields?

Key findings

• In flakes ≤15 monolayers thick, the quasiparticle density of states shows a single superconducting gap that decreases with increasing in-plane magnetic field.
• The superconducting gap in bilayer NbSe₂ persists up to ~30 T, significantly exceeding the Pauli limit and indicating enhanced robustness beyond standard Ising protection.
• The data are inconsistent with pure Ising theory or Abrikosov-Gor'kov models, which fail to reproduce the observed gap evolution, especially the 'linear' intermediate-field behavior.
• The best fit to the data is achieved by a model that includes both Ising protection and an equal-spin triplet component of the order parameter, with $E_{SO} = 9.62T_{cs}$ and $T_{ct} = 0.05T_{cs}$ for the bilayer.
• The extracted spin-orbit coupling energy $E_{SO}$ is consistent with ARPES measurements, suggesting $E_{SO} ightarrow 14.45T_{cs}$ for bilayer NbSe₂ ($T_{cs} = 2.6$ K), and $E_{SO} = 2.21T_{cs}$ for 6-monolayer ($T_{cs} = 5.4$ K).
• Theoretical models including only singlet pairing and K/K’–Γ coupling fail to fit the data, reinforcing the necessity of including triplet pairing for a quantitative description.