Superconducting states that break space-group symmetries of the underlying crystal can exhibit nontrivial spatial modulation of the order parameter. Previously, such remarkable states were intimately associated with the breaking of translational symmetry, giving rise to the density-wave orders, with wavelengths spanning several unit cells. However, a related basic concept has been long overlooked: when only intra-unit-cell symmetries of the space group are broken, the superconducting states can display a distinct type of nontrivial modulation preserving long-range lattice translation. Here, we refer to this new concept as the pair density modulation (PDM), and report the first observation of a PDM state in exfoliated thin flakes of iron-based superconductor FeTe$_{\text{0.55}}$Se$_{\text{0.45}}$. Using scanning tunneling microscopy, we discover robust superconducting gap modulation with the wavelength corresponding to the lattice periodicity and the amplitude exceeding 30% of the gap average. Importantly, we find that the observed modulation originates from the large difference in superconducting gaps on the two nominally equivalent iron sublattices. The experimental findings, backed up by model calculations, suggest that in contrast to the density-wave orders, the PDM state is driven by the interplay of sublattice symmetry breaking and a peculiar nematic distortion specific to the thin flakes. Our results establish new frontiers for exploring the intertwined orders in strong-correlated electronic systems and open a new chapter for iron-based superconductors.

Magic-angle twisted trilayer graphene (MATTG) exhibits a range of strongly correlated electronic phases that spontaneously break its underlying symmetries 1 , 2 . Here we investigate the correlated phases of MATTG using scanning tunnelling microscopy and identify marked signatures of interaction-driven spatial symmetry breaking. In low-strain samples, over a filling range of about two to three electrons or holes per moiré unit cell, we observe atomic-scale reconstruction of the graphene lattice that accompanies a correlated gap in the tunnelling spectrum. This short-scale restructuring appears as a Kekulé supercell—implying spontaneous inter-valley coherence between electrons—and persists in a wide range of magnetic fields and temperatures that coincide with the development of the gap. Large-scale maps covering several moiré unit cells further reveal a slow evolution of the Kekulé pattern, indicating that atomic-scale reconstruction coexists with translation symmetry breaking at a much longer moiré scale. We use auto-correlation and Fourier analyses to extract the intrinsic periodicity of these phases and find that they are consistent with the theoretically proposed incommensurate Kekulé spiral order 3 , 4 . Moreover, we find that the wavelength characterizing moiré-scale modulations monotonically decreases with hole doping away from half-filling of the bands and depends weakly on the magnetic field. Our results provide essential insights into the nature of the correlated phases of MATTG in the presence of strain and indicate that superconductivity can emerge from an inter-valley coherent parent state.

A compositional glass is a state with an unavoidable disorder in chemical compositions on each site, characterized by frustration and freezing of the compositional degrees of freedom at low temperature. From this state a full atomic long-range order is unachievable by a reasonable thermodynamic treatment. There is a similarity between a spin glass (a magnetic state with disorder in spin orientations) and a compositional glass (with disorder in site occupations by chemical elements): both have frustrated ground states and a frozen disorder at low temperatures T < Tf (here Tf is called the freezing temperature). While it is possible to perform a ground-state search in a compositional glass, the resulting set of the fully ordered structures does not adequately represent the real solid with an inherent atomic disorder. Compositional glasses constitute a class of materials, which is insufficiently understood, but is of high industrial importance. Some of the phases in the precipitated alloys (including steels, high-entropy alloys, and superalloys) might be compositional glasses, and their better understanding would facilitate materials design. Due to their strength at high operating temperatures, superalloys are used in combustion engines and particularly in jet turbine engines. Precipitation strengthening of nickel superalloys is an area of active research. Local phase transformations inside Ni3Al-based precipitates are of particular interest due to their impact on creep strength. In the Ni3(Al1−xTix)1 ternary system, the competing phases are Ni3Al-type L12 (γʹ) and Ni3Ti-type D024 (η), while D019 (χ) is higher in energy. These three phases differ by the stacking of atomic layers: locally, the last two look like the internal and external stacking faults in L12. We compute enthalpies of disordered and ordered Ni3(Al1−xTix)1 ternary structures, examine phase stability, investigate the ground states and competing structures, and predict that the Ti-rich Ni3(Al1−xTix)1 D024 phase is a compositional glass with the atomic disorder on the Al/Ti sublattice. To resolve apparent contradictions among the previous experiments and to confirm our prediction, we perform X-ray diffraction and scanning electron microscopy analysis of the cast Ni3(Ti0.917Al0.083)1 sample. Our measurements appear to confirm the ab initio computed results. Our results elucidate properties of compositional glasses and provide a better understanding of precipitation strengthening mechanisms in Ni superalloys.

Over the last decade, conditions for perfect state transfer in quantum spin chains have been discovered and their experimental realizations addressed, as have their extensions to more complex geometries of coupled cavity-emitter arrays. In this paper we further consider such studies and situations in which quantum state transfer can occur with high fidelity, even when the cavity-cavity coupling rates and cavity-emitter interaction rates are comparable. This is accomplished through the development and use of a Monte Carlo approach to the inverse eigenvalue problem, which allows the determination of coupling rates which optimize quantum state transfer fidelity and subsequent time evolution of the polariton wave function through exact diagonalization of the resulting Jaynes-Cummings-Hubbard Hamiltonian. The effect of inhomogeneous emitter locations is also evaluated. Our key results include the demonstration that our methodology can be used successfully to establish Hamiltonian parameters for high-fidelity state transfer in more general lattice geometries and excitation number sectors, and also a determination of the effects of fluctuations in those parameters about their optimal values.