Prof. J. C. Seamus Davis

Abstract:

The quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTIs) when a Dirac mass gap opens in the spectrum of the topological surface states (SSs). Unaccountably, although the mean mass gap can exceed 28 meV (or ∼320 K), the QAH effect is frequently only detectable at temperatures below 1 K. Using atomic-resolution Landau level spectroscopic imaging, we compare the electronic structure of the archetypal FMTI Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ to that of its nonmagnetic parent (Bi_0.1Sb_0.9)₂Te₃, to explore the cause. In (Bi_0.1Sb_0.9)₂Te₃, we find spatially random variations of the Dirac energy. Statistically equivalent Dirac energy variations are detected in Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ with concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS electronic disorder conspire to drastically suppress the minimum mass gap to below 100 μeV for nanoscale regions separated by <1 μm. This fundamentally limits the fully quantized anomalous Hall effect in Sb₂Te₃-based FMTI materials to very low temperatures.

Abstract:

The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states [Formula: see text] is predicted at the terminal BiO surface of Bi₂Sr₂CaCu₂O₈ and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of [Formula: see text], the modulations of the coherence peak energy [Formula: see text] and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space [Formula: see text] Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi₂Sr₂CaCu₂O₈ does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.

Abstract:

The defining characteristic^1,2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)^3,4. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling⁵, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi₂Sr₂CaCu₂O_8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a₀)(1/8, 0) and Q ≈ (2π/a₀)(0, 1/8) (where a₀ is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state^6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi₂Sr₂CaCu₂O_8+δ.