[论文解读] Surface-localized topological superconductivity in nodal-loop materials: BdG analysis

Takeru Matsushima, Hiroki Tsuchiura|arXiv (Cornell University)|Feb 26, 2026

Topological Materials and Phenomena被引用 0

一句话总结

摘要：本文表明，在具有 drumhead 表面态的节点线半金属中，自洽 Bardeen–Cooper–Schrieffer（BdG）分析倾向于表面局域的手性 p 波超导性，强烈带隙化 drumhead 能带，而 d 波配对要弱得多。

ABSTRACT

We theoretically study surface superconductivity in a nodal-line semimetal by combining a minimal tight-binding model with a layer-resolved Bogoliubov-de Gennes approach. In the normal state, the model realizes a bulk nodal loop and an associated drumhead surface band in a slab geometry with open boundaries in the $z$ direction: the central layers reproduce the bulk-like density of states, whereas the surface layer exhibits a sharp zero-energy peak originating from the drumhead states. On top of this band structure we introduce chiral $p$-wave and $d_{x^2-y^2}$-wave superconducting channels and determine the layer-dependent gap amplitudes self-consistently. The chiral $p$-wave order parameter is strongly enhanced at the outermost layers and decays within only a few layers towards the interior, while the $d$-wave order parameter is more than an order of magnitude smaller on all layers. The quasiparticle dispersion and surface local density of states in the chiral $p$-wave state show that the drumhead band is efficiently gapped out and that the zero-energy peak in the normal surface spectrum is split into two coherence peaks, directly reflecting the induced superconducting gap. These results demonstrate that superconductivity driven by drumhead surface states is naturally biased toward a surface-localized chiral $p$-wave pairing symmetry and may offer qualitative guidance for interpreting surface-sensitive experiments on Pd-doped CaAgP.

研究动机与目标

• Motivate exploration of superconductivity emerging from drumhead surface states in nodal-line semimetals.
• Determine which pairing symmetry (chiral p-wave vs d-wave) is favored when superconductivity originates from drumhead surface states.
• Characterize how the superconducting gap, LDOS, and spatial profile depend on layer index in a slab geometry.
• Assess implications for surface-sensitive experiments on Pd-doped CaAgP by connecting drumhead states to observed superconductivity.

提出的方法

• Construct a minimal tight-binding nodal-line model on a cubic lattice with a nodal loop and drumhead surface states in a slab geometry along z.
• Formulate a Bogoliubov–de Gennes (BdG) Hamiltonian with H_BdG = H_0 + H_Δ and solve self-consistently for layer-dependent gaps Δ_0,n.
• Introduce two pairing channels with fixed form factors: chiral p-wave φ(k_parallel)=sin k_x + i sin k_y and d_{x^2−y^2}-wave φ(k_parallel)=cos k_x − cos k_y, using Γ to encode pairing in pseudospin space.
• Compute layer- and momentum-resolved Green’s functions to obtain LDOS D_n(k_parallel,E) and total LDOS D_n(E).
• Diagonalize H_BdG(k_parallel) to obtain quasiparticle spectra and use the self-consistent gap equation Δ_{0,n} = V ∑_{k_parallel} φ*(k_parallel) ∑_{ν>0} ∑_{σ,σ′} Γ_{σσ′} u_{nνσ}(k_parallel) v_{nνσ′}^*(k_parallel) tanh(E_ν(k_parallel)/2T).

实验结果

研究问题

• RQ1 Does superconductivity emerging from drumhead surface states favor a particular pairing symmetry (p-wave vs d-wave) in a nodal-line semimetal?
• RQ2 How do surface-localized drumhead states affect the layer dependence of the superconducting gap and the surface LDOS?
• RQ3 What is the impact of the drumhead states on the quasiparticle spectrum when a chiral p-wave or d-wave order is self-consistently established?
• RQ4 How sensitive is surface superconductivity to shifting the chemical potential away from the drumhead band?

主要发现

• The chiral p-wave order parameter is strongly enhanced at the outermost layers and decays within a few layers, indicating surface-localized superconductivity.
• The d-wave order parameter remains more than an order of magnitude smaller on all layers, making it much less favorable than the p-wave channel.
• In the chiral p-wave state, the drumhead surface band is gapped, and the zero-energy surface LDOS peak splits into two finite-energy coherence peaks, reflecting the induced surface superconducting gap.
• Superconductivity from drumhead states is biased toward surface-localized chiral p-wave pairing, with the interior slab remaining essentially normal at the considered parameters.
• Shifting the chemical potential away from zero suppresses the surface superconductivity, with Δ_0,n vanishing on inner layers for μ=0.2, indicating sensitivity to the drumhead band's occupancy.