Jun‐Won Rhim

We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the flat band cannot be defined. This singularity precludes the compact localized states from forming a comple

We investigate Landau level structures of semimetals with nodal ring dispersions. When the magnetic field is applied parallel to the plane in which the ring lies, there exist almost nondispersive Landau levels at the Fermi level (${E}_{F}=0$) as a function of the momentum along the field direction inside the ring. We show that the Landau levels at each momentum along the field direction can be described by the Hamiltonian for the graphene bilayer with fictitious interlayer couplings under a tilt

The Zak phase $\ensuremath{\gamma}$, the generalization of the Berry phase to Bloch wave functions in solids, is often used to characterize inversion-symmetric one-dimensional (1D) topological insulators. Due to its dependence on the real-space origin and unit cell, however, there is an ambiguity in its use in a bulk-boundary correspondence. Here, we extract an origin-independent part of $\ensuremath{\gamma}$, the so-called intercellular Zak phase ${\ensuremath{\gamma}}^{\mathrm{inter}}$, and sh

The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has in certain scenarios even been shown to fail, depending on the boundary profiles of the terminated system. Here, we introduce bulk numbers that capture the exact number of in-gap modes, without any such subtleties in one spatial dimension. Similarly, based on

We theoretically study the spin stiffness of graphene and graphene nanoribbon based on the Hubbard-type Hamiltonian. Using the Hartree-Fock method with the inclusion of the adiabatic spin twist, we have obtained the effective energy functional and investigated the magnetic excitations of the two-dimensional graphene and zigzag graphene nanoribbon (ZGNR). We have analyzed the spin stiffness of the system with varying temperature and the strength of on-site Coulomb repulsion. For ZGNR, we have als

Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfly, for an electron moving in lattice under magnetic field. Connected with the $n=0$ Landau level, the central band of the Hofstadter butterfly is especially interesting in the honeycomb lattice. While the entire Hofstadter butterfly can be in principle obtained by solving Harper's

Abstract The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band syst

Electronic structures of the zigzag bilayer graphite nanoribbons(Z-BGNR) with various ribbon width $N$ are studied within the tight binding approximation. Neglecting the inter-layer hopping amplitude $\gamma_4$, which is an order of magnitude smaller than the other inter-layer hopping parameters $\gamma_1$ and $\gamma_3$, there exist two fixed Fermi points $\pm k^*$ independent of the ribbon width with the peculiar energy dispersion near $k^*$ as $\ve (k) \sim \pm (k-k^*)^N$. By investigating th

Abstract A singular flat band (SFB), a distinct class of the flat band, has been shown to exhibit various intriguing material properties characterized by the quantum distance. We present a general construction scheme for a tight-binding model hosting an SFB, where the quantum distance profile can be controlled. We first introduce how to build a compact localized state (CLS), endowing the flat band with a band-touching point and a specific value of the maximum quantum distance. Then, we develop a

There has been tremendous recent progress in realizing topological insulator initiated by the proposal of Kane and Mele for the graphene system. They have suggested that the odd ${Z}_{2}$ index for the graphene manifests the spin-filtered edge states for the graphene nanoribbons, which lead to the quantum spin Hall effect (QSHE). Here, we investigate the role of the spin-orbit interaction both for the zigzag and armchair nanoribbons with special care in the edge geometry. For the pristine zigzag

Motivated by recent experiments on ${\mathrm{Pr}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, we provide a theory of quantum oscillations in the Luttinger model with quadratic band touching, modeled for the spin-orbit-coupled conduction electrons in pyrochlore iridates. The magneto- and Hall resistivities are computed for electron- and hole-doped systems, and the corresponding Shubnikov--de Haas (SdH) signals are investigated. The SdH signals are characterized by aperiodic behaviors that originate fr

In condensed matter physics, the Kagome lattice and its inherent flat bands have attracted considerable attention for their prediction and observation to host a variety of exotic physical phenomena. Despite extensive efforts to fabricate thin films of Kagome materials aimed at modulating flat bands through electrostatic gating or strain manipulation, progress has been limited. Here, we report the observation of a d-orbital hybridized Kagome-derived flat band in Ag/Si(111) <mml:math xmlns:mml="ht

Abstract In recent years, the spin Hall effect has received great attention because of its potential application in spintronics and quantum information processing and storage. However, this effect is usually studied under the external homogeneous electric field. Understanding how the inhomogeneous electric field affects the spin Hall effect is still lacking. Here, we investigate a two-dimensional two-band time-reversal symmetric system and give an expression for the intrinsic spin Hall conductiv

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 sym