[Paper Review] Momentum dependence of the superconducting gap and in-gap states in MgB2 multi-band superconductor

Daixiang Mou, Rui Jiang+4 more|arXiv (Cornell University)|Apr 23, 2015

Superconductivity in MgB2 and Alloys3 citations

TL;DR

This study uses tunable laser-based angle-resolved photoemission spectroscopy (ARPES) to investigate the momentum and temperature dependence of the superconducting gap in MgB2. It finds isotropic s-wave pairing symmetry with a gap magnitude of ~7 meV on σ bands and discovers a flat in-gap state at ~3 meV confined near the Fermi surface, suggesting possible impurity-induced bound states or interband scattering, though the origin remains unresolved.

ABSTRACT

We use tunable laser based Angle Resolved Photoemission Spectroscopy to study the electronic structure of the multi-band superconductor, MgB2. These results form the base line for detailed studies of superconductivity in multi-band systems. We find that the magnitude of the superconducting gap on both sigma bands follows a BCS-like variation with temperature with Delta0 ~7 meV. The value of the gap is isotropic within experimental uncertainty and in agreement with pure a s-wave pairing symmetry. We also observe in-gap states confined to kF of the sigma band that occur at some locations of the sample surface. The energy of this excitation, ~3 meV, is inconsistent with scattering from the pi band.

Motivation & Objective

• To systematically investigate the momentum and temperature dependence of the superconducting gap in MgB2’s σ bands using high-resolution ARPES.
• To determine whether the superconducting gap exhibits anisotropy, which would indicate non-s-wave pairing symmetry.
• To identify and characterize the origin of a previously unreported in-gap state observed below Tc at specific surface locations.
• To provide experimental baseline data for understanding multi-band superconductivity, particularly in relation to pairing symmetry and impurity effects.

Proposed method

• Employed tunable vacuum ultraviolet (VUV) laser-based ARPES with 1 meV energy resolution and 0.13° angular resolution to measure electronic structure.
• Conducted measurements at photon energy of 6.7 eV, corresponding to kz ≈ 0.22π/c, to access the Brillouin zone center and σ bands near Γ.
• Used symmetrized energy distribution curves (EDCs) to extract the superconducting gap and in-gap state positions as a function of temperature.
• Performed temperature-dependent ARPES on cleaved MgB2 single crystals (Tc ≈ 39 K) at base pressure < 8×10⁻¹¹ Torr to minimize surface contamination.
• Compared experimental gap evolution with BCS theory predictions to assess pairing symmetry.
• Mapped the momentum distribution of the in-gap state, focusing on its localization near the Fermi surface (kF).

Experimental results

Research questions

• RQ1 Does the superconducting gap on the σ bands of MgB2 exhibit momentum-dependent anisotropy, indicating non-s-wave pairing?
• RQ2 How does the superconducting gap magnitude vary with temperature, and does it follow BCS-like behavior?
• RQ3 What is the origin of the in-gap state observed at ~3 meV below Tc, and why is it only visible at certain surface locations?
• RQ4 Is the in-gap state related to interband scattering, impurity bound states, or surface-specific electronic inhomogeneity?
• RQ5 Can the observed in-gap state be explained by conventional nonmagnetic impurities or requires a magnetic scattering potential?

Key findings

• The superconducting gap on both σ bands exhibits isotropic momentum dependence, with Δ₀ ≈ 7 meV, providing direct experimental evidence for s-wave pairing symmetry in MgB2.
• The temperature dependence of the gap follows a BCS-like behavior, confirming the conventional BCS nature of superconductivity in MgB2.
• A flat in-gap state at ~3 meV binding energy is observed below Tc, with intensity predominantly localized near the Fermi surface (kF) in momentum space.
• The energy of the in-gap state (~3 meV) is inconsistent with the known π-band gap (~1.5 meV), ruling out simple scattering from the π band.
• The in-gap state’s energy and temperature dependence are consistent with a BCS-like evolution, suggesting a strong link to superconductivity.
• The state is only observed at specific surface locations, with no correlation to visible surface defects, and is unlikely due to momentum mixing or instrumental artifacts.