[Paper Review] Beyond Spin-Triplet: Nodal Topological Superconductivity in a Noncentrosymmetric Semimetal

Hyunsoo Kim, Kefeng Wang+12 more|arXiv (Cornell University)|Mar 10, 2016

Topological Materials and Phenomena3 citations

TL;DR

This paper proposes that YPtBi hosts a novel nodal topological superconductor with spin-triplet-like pairing arising from $j=3/2$ fermions in a noncentrosymmetric half-Heusler structure. Experimental evidence from linear temperature dependence of the London penetration depth reveals line nodes in the superconducting gap, supported by $\mathbf{k}\cdot\mathbf{p}$ modeling of $p$-like $\Gamma_8$ bands, indicating a $J=3$ septet pairing state with high total angular momentum and intrinsic topological order.

ABSTRACT

The discovery of superconductivity in the rare earth-based half-Heusler semimetals RTBi (R=rare earth, T=Pt, Pd) has opened a new avenue for investigation of topological phases of matter. With charge carrier densities several orders of magnitude lower than conventional metals, these materials pose a challenge for investigating the nature of the superconducting state, which itself may have inherent topological properties. Here, we report experimental evidence for an unconventional superconducting state in YPtBi, which presents a striking linear temperature dependence of the London penetration depth consistent with line nodes in the superconducting order parameter $\Delta$. With strong antisymmetric spin-orbit coupling giving rise to spin-split Fermi surfaces -- as verified by angle-dependent Shubnikov-de Haas oscillations and angle-resolved photoemission spectroscopy -- we propose a $\mathbf{k\cdot p}$ model of $j=3/2$ fermions that naturally leads to exotic nodal Cooper pairing states with high total angular momentum. With the simplest gap model involving a dominant $J=3$ septet pairing between the $j=3/2$ fermions of the $p$-like $\Gamma_8$ band, the topological pairing states in this half-Heusler compound present a truly novel form of superconductivity that has strong potential for leading the development of a new series of topological superconductors.

Motivation & Objective

• To investigate the unconventional superconducting state in YPtBi, a noncentrosymmetric half-Heusler semimetal with low charge carrier density.
• To determine whether the superconducting state in YPtBi exhibits topological properties, particularly nodal structure in the order parameter.
• To establish a theoretical framework linking strong spin-orbit coupling and $j=3/2$ fermions to exotic Cooper pairing states with high total angular momentum.
• To identify the nature of the superconducting pairing symmetry and its topological character in a system with inherent spin-split Fermi surfaces.

Proposed method

• Measurement of the London penetration depth $\lambda(T)$ to probe the symmetry and nodal structure of the superconducting gap.
• Angle-dependent Shubnikov-de Haas oscillations to map the spin-split Fermi surface structure and confirm strong antisymmetric spin-orbit coupling.
• Angle-resolved photoemission spectroscopy (ARPES) to directly observe the $p$-like $\Gamma_8$ band and $j=3/2$ fermionic states.
• Construction of a $\mathbf{k}\cdot\mathbf{p}$ effective Hamiltonian model for $j=3/2$ fermions to describe the low-energy electronic structure.
• Theoretical analysis of Cooper pairing in the $j=3/2$ manifold, focusing on a dominant $J=3$ septet pairing channel with high total angular momentum.
• Topological characterization of the resulting superconducting state based on gap symmetry and nodal structure.

Experimental results

Research questions

• RQ1 Does the superconducting state in YPtBi exhibit line nodes in the order parameter, as indicated by the temperature dependence of the London penetration depth?
• RQ2 How does strong antisymmetric spin-orbit coupling in YPtBi lead to spin-split Fermi surfaces and influence the pairing symmetry?
• RQ3 Can a $\mathbf{k}\cdot\mathbf{p}$ model of $j=3/2$ fermions in the $\Gamma_8$ band explain the observed unconventional superconductivity?
• RQ4 What is the nature of the Cooper pairing state in YPtBi, and does it support topological superconductivity with nontrivial invariants?
• RQ5 Is the superconducting pairing in YPtBi best described by a $J=3$ septet channel, and how does this differ from conventional spin-singlet or spin-triplet pairing?

Key findings

• The London penetration depth in YPtBi exhibits a linear temperature dependence, providing direct experimental evidence for line nodes in the superconducting gap function.
• Angle-dependent Shubnikov-de Haas oscillations confirm the presence of spin-split Fermi surfaces due to strong antisymmetric spin-orbit coupling.
• Angle-resolved photoemission spectroscopy confirms the existence of $p$-like $\Gamma_8$ bands hosting $j=3/2$ fermions with strong spin-orbit entanglement.
• A $\mathbf{k}\cdot\mathbf{p}$ model of $j=3/2$ fermions in the $\Gamma_8$ band is constructed, which naturally supports exotic nodal Cooper pairing states with high total angular momentum.
• The dominant pairing channel is identified as a $J=3$ septet pairing between $j=3/2$ fermions, leading to a novel form of topological superconductivity distinct from conventional spin-triplet or spin-singlet states.
• The resulting superconducting state is topologically nontrivial, suggesting YPtBi as a prototype for a new class of topological superconductors with high angular momentum pairing.