Theorists Keep Finding Paths to Superconductivity When Analyzing LK99

Kings College of London and University of Colorado researchers looked at LK99 by going beyond density function theory analysis with a different analytic approach. They looked at electron and hole doping, within the QSGW (quasiparticle self-consistent GW ) framework. They conclude that while LK99 might or might not be superconducting, it has interesting properties that could be a path to superconductivity. The LK99 class of systems is a unique playground to explore the transition from band- to Mott-insulator to multideterminantal nature of weakly doped Mott physics. LK99 variants are doing very interesting things with effects that are strongly associated with superconductors or potential superconductors.

Are the LK99 doubters and haters saying that this theoretically highly interesting substance something that a bunch of sloppy researchers or fraudulent researchers just happened to get lucky with?

Two surprising results emerge from QSGW that are not found in density-functional theory.

1. Doping Changes the Electronic Properties and States of LK99 A Lot
The first is the marked change in splitting between Pb states in the conduction band and the O-derived valence band states with doping. This can be understood as a change in the screening as the system becomes metallic.

The close relation between bandgaps in sp bonded semiconductors and the long-range form of the screened coulomb interactions has been established for some time and the effect of changes in screening on the band structure in such systems systems has been also been reported. What is unique in the present case is that bandgaps with two different origins coexist: one of another of semiconductor character (Pb-O) which is sensitive to doping and another of Mott character (Cu-O) which is not.

2. Two spin states in which Cu can be aligned parallel or antiparallel to the host

The second remarkable finding is the coexistence of two spin states, with the Cu aligned either parallel or antiparallel to the host. The presence of an atomic-like d state in a semiconducting conduction band is also seen in Cu-doped ZnO. But in the present case flat bands with low kinetic energy allow a moment to be induced on the sp subspace that would not occur in Cu-doped ZnO, and the coexistence of two subspaces with different spin channels is new. In the QSGW approach, the quasiparticlization procedure demands a single Slater determinant; thus the alignment of the two kinds of spins emerges as two distinct solutions. While it was possible to stabilize two distinct spin configurations, there was a strong tendency to flip between them as self-consistency proceeded. This indicates that the spin configurations are nearly degenerate in energy. Self-consistency is clearly essential here: such a result would be problematic with conventional forms of GW, e.g. one-shot GW based on DFT. The crucial role of self-consistency has been discussed recently for several other insulating systems.

The near-degeneracy of distinct ground states in a oneparticle description suggests that the true ground state cannot be described by a single-determinant; and moreover correlations from spin fluctuations between the Cu local moment and delocalized environment are likely to be very strong. This does not by itself indicate a strong propensity for superconductivity, but it does suggest a novel path to strong correlations, which may result in superconductivity. We believe, irrespective of whether room-temperature superconductivity is realized in these classes of materials or not, the fact that Pb10(PO4)6O is a band insulator, Pb9Cu(PO4)6O is a Mott insulator and the electron- and hole-doped Pb9Cu(PO4)6O can not be described by a single Slater determinant, makes these class of systems a unique playground to explore the transition from band- to Mott-insulator to multideterminantal nature of weakly doped Mott physics.

QSGW stands for “Quasiparticle Self-Consistent GW” and is a computational method commonly used to study the electronic structure and properties of solid materials, including properties related to superconductivity. In materials science, the GW method is a modification of density functional theory (DFT ) aimed at more accurately describing the electronic structure of materials. QSGW is a variant of the GW approach that incorporates the concept of quasiparticles in its calculations, which refers to the collective excitation of electrons in a material under interaction. This method is often more accurate in describing strongly correlated electron systems and calculating the excitation energy levels, spectral properties, and electron affinity of materials.

Methods
They apply quasiparticle self-consistent GW theory (QSGW ), which, in contrast to conventional GW methods, modifies the charge density and is determined
by a variational principle. Further, QSGWˆ is a diagrammatic extension of QSGW where the screened coulomb interaction W is computed including excitonic vertex corrections (ladder diagrams) by solving a Bethe–Salpeter equation (BSE) within Tamm-Dancoff approximation. Crucially, both our QSGW and QSGWˆ methods are fully self-consistent in both selfenergy Σ and the charge densit . G, Σ, and Wˆ are updated iteratively until all of them converge. Such approaches are parameter-free and have no starting point bias.

Multiple Slater determinants and strong spin-fluctuations as key ingredients of the electronic structure of electron- and hole-doped Pb10−xCux(PO4)6O

LK-99, with chemical formula Pb10−xCux(PO4)6O, was recently reported to be a room-temperature superconductor. While this claim has met with little support in a flurry of ensuing work, a variety of calculations (mostly based on density-functional theory) have demonstrated that the system possesses some unusual characteristics in the electronic structure, in particular flat bands. We have established previously that within DFT, the system is insulating with many characteristics resembling the classic cuprates, provided the structure is not constrained to the P3(143) symmetry nominally assigned to it. Here we describe the basic electronic structure of LK-99 within self-consistent many-body perturbative approach, quasiparticle self-consistent GW (QSGW) approximation and their diagrammatic extensions. QSGW predicts that pristine LK-99 is indeed a Mott/charge transfer insulator, with a bandgap gap in excess of 3eV, whether or not constrained to the P3(143) symmetry. The highest valence bands occur as a pair, and look similar to DFT bands. The lowest conduction band is an almost dispersionless state of largely Cu d character. When Pb9Cu(PO4)6O} is hole-doped, the valence bands modify only slightly, and a hole pocket appears. However, two solutions emerge: a high-moment solution with the Cu local moment aligned parallel to neighbors, and a low-moment solution with Cu aligned antiparallel to its environment. In the electron-doped case the conduction band structure changes significantly: states of mostly Pb character merge with the formerly dispersionless Cu d state, and high-spin and low spin solutions once again appear. Thus we conclude that with suitable doping, the ground state of the system is not adequately described by a band picture, and that strong correlations are likely.