Engineering Two-Dimensional Nodal Semimetals in Functionalized Biphenylene by Fluorine Adatoms.

We propose a band engineering scheme on the biphenylene network, a newly synthesized carbon allotrope. We illustrate that the electronic structure of the biphenylene network can be significantly altered by controlling conditions affecting the symmetry and destructive interference of wave functions through periodic fluorination. First, we investigate the mechanism for the appearance of a type-II Dirac fermion in a pristine biphenylene network. We show that the essential ingredients are mirror symmetries and stabilization of the compact localized eigenstates via destructive interference. While the former is used for the band-crossing point along high symmetry lines, the latter induces highly inclined Dirac dispersions. Subsequently, we demonstrate the transformation of the biphenylene network's type-II Dirac semimetal phase into various Dirac phases such as type-I Dirac, gapped type-II Dirac, and nodal line semimetals through the deliberate disruption of mirror symmetry or modulation of destructive interference by varying the concentration of fluorine atoms.

Tunable Colossal Anomalous Hall Conductivity in Half-Metallic Material Induced by d-Wave-Like Spin-Orbit Gap.

The anomalous Hall conductivity (AHC) in magnetic materials, resulting from inverted band topology, has emerged as a key adjustable function in spin-torque devices and advanced magnetic sensors. Among systems with near-half-metallicity and broken time-reversal symmetry, cobalt disulfide (CoS2) has proven to be a material capable of significantly enhancing its AHC. In this study, the AHC of CoS2 is empirically assessed by manipulating the chemical potential through Fe- (hole) and Ni- (electron) doping. The primary mechanism underlying the colossal AHC is identified through the application of density functional theory and tight-binding analyses. The main source of this substantial AHC is traced to four spin-polarized massive Dirac dispersions in the kz = 0 plane of the Brillouin zone, located slightly below the Fermi level. In Co0.95Fe0.05S2, the AHC, which is directly proportional to the momentum-space integral of the Berry curvature (BC), reached a record-breaking value of 2507 Ω-1cm-1. This is because the BCs of the four Dirac dispersions all exhibit the same sign, a consequence of the d-wave-like spin-orbit coupling among spin-polarized eg orbitals.

Geometric characterization of anomalous Landau levels of isolated flat bands.

According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.

Quantum distance and anomalous Landau levels of flat bands.

Semiclassical quantization of electronic states under a magnetic field, as proposed by Onsager, describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field1-5. Even in graphene with relativistic energy dispersion, Onsager's rule correctly describes the π Berry phase, as well as the unusual Landau level spectrum of Dirac particles6,7. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. Here we show that the semiclassical quantization rule breaks down for a class of dispersionless flat bands called 'singular flat bands'8. The singular flat band has a band crossing with another dispersive band that is enforced by the band-flatness condition, and shows anomalous magnetic responses. The Landau levels of a singular flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field, and exhibit an unusual 1/n dependence on the Landau level index n, which results in diverging orbital magnetic susceptibility. The total energy spread of the Landau levels of a singular flat band is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert-Schmidt quantum distance. We show that there is a universal and simple relationship between the total Landau level spread of a flat band and the maximum Hilbert-Schmidt quantum distance, which can be verified in various candidate materials. The results indicate that the anomalous Landau level spectrum of flat bands is promising for the direct measurement of the quantum geometry of wavefunctions in condensed matter.

Direct Observation of Flatband Loop States Arising from Nontrivial Real-Space Topology.

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.

Determination of the band parameters of bulk 2H-MX2 (M = Mo, W; X = S, Se) by angle-resolved photoemission spectroscopy.

Monolayer MX2 (M = Mo, W; X = S, Se) has recently been drawn much attention due to their application possibility as well as the novel valley physics. On the other hand, it is also important to understand the electronic structures of bulk MX2 for material applications since it is very challenging to grow large size uniform and sustainable monolayer MX2. We performed angle-resolved photoemission spectroscopy and tight binding calculations to investigate the electronic structures of bulk 2H-MX2. We could extract all the important electronic band parameters for bulk 2H-MX2, including the band gap, direct band gap size at K (-K) point and spin splitting size. Upon comparing the parameters for bulk 2H-MX2 (our work) with mono- and multi-layer MX2 (published), we found that stacked layers, substrates for thin films, and carrier concentration significantly affect the parameters, especially the band gap size. The origin of such effect is discussed in terms of the screening effect.

Quantitative analysis on electric dipole energy in Rashba band splitting.

We report on quantitative comparison between the electric dipole energy and the Rashba band splitting in model systems of Bi and Sb triangular monolayers under a perpendicular electric field. We used both first-principles and tight binding calculations on p-orbitals with spin-orbit coupling. First-principles calculation shows Rashba band splitting in both systems. It also shows asymmetric charge distributions in the Rashba split bands which are induced by the orbital angular momentum. We calculated the electric dipole energies from coupling of the asymmetric charge distribution and external electric field, and compared it to the Rashba splitting. Remarkably, the total split energy is found to come mostly from the difference in the electric dipole energy for both Bi and Sb systems. A perturbative approach for long wave length limit starting from tight binding calculation also supports that the Rashba band splitting originates mostly from the electric dipole energy difference in the strong atomic spin-orbit coupling regime.