arXiv subjects

Bohm-Jung Yang

Publications and source records attributed to Bohm-Jung Yang.

At least 73 records · Page 4Linked to original sources

arXiv2019

Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems

We study the homotopy classification of symmetry representations to describe the bulk topological invariants protected by the combined operation of a two-fold rotation $C_{2z}$ and time-reversal $T$ symmetries. We define topological invariants as obstructions to having smooth Bloch wave functions compatible with a momentum-independent symmetry representation. When the Bloch wave functions are required to be smooth, the information on the band topology is contained in the symmetry representation. This implies that the $d$-dimensional homotopy class of the unitary matrix representation of the symmetry operator corresponds to the $d$-dimensional topological invariants. Here, we prove that the second Stiefel-Whitney number, a two-dimensional topological invariant protected by $C_{2z}T$, is the homotopy invariant that characterizes the second homotopy class of the matrix representation of $C_{2z}T$. As an application of our result, we show that the three-dimensional bulk topological invariant for the $C_{2z}T$-protected topological crystalline insulator proposed by C. Fang and L. Fu in Phys. Rev. B 91, 161105(R) (2015), which we call the 3D strong Stiefel Whitney insulator, is identical to the quantized magnetoelectric polarizability. The bulk-boundary correspondence associated with the quantized magnetoelectric polarizability shows that the 3D strong Stiefel-Whitney insulator has chiral hinges states as well as 2D massless surface Dirac fermions. This shows that the 3D strong Stiefel Whitney insulator has the characteristics of both the first order and the second order topological insulators, simultaneously, which is consistent with the recent classification of higher-order topological insulators protected by an order-two symmetry.

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arXiv2019

Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle

We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the Euler class. To prove this, we examine the generic band topology of two dimensional real fermions in systems with space-time inversion $I_{ST}$ symmetry. The Euler class is an integer topological invariant classifying real two band systems. We show that a two-band system with a nonzero Euler class cannot have an $I_{ST}$-symmetric Wannier representation. Moreover, a two-band system with the Euler class $e_{2}$ has band crossing points whose total winding number is equal to $-2e_2$. Thus the conventional Nielsen-Ninomiya theorem fails in systems with a nonzero Euler class. We propose that the topological phase transition between two insulators carrying distinct Euler classes can be described in terms of the pair creation and annihilation of vortices accompanied by winding number changes across Dirac strings. When the number of bands is bigger than two, there is a $Z_{2}$ topological invariant classifying the band topology, that is, the second Stiefel Whitney class ($w_2$). Two bands with an even (odd) Euler class turn into a system with $w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the nontrivial second Stiefel-Whitney class remains robust against adding trivial bands, it does not impose a Wannier obstruction when the number of bands is bigger than two. However, when the resulting multi-band system with the nontrivial second Stiefel-Whitney class is supplemented by additional chiral symmetry, a nontrivial second-order topology and the associated corner charges are guaranteed.

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arXiv2019

Stiefel-Whitney classes and topological phases in band theory

In this article, we review the recent progress in the study of topological phases in systems with space-time inversion symmetry $I_{\text{ST}}$. $I_{\text{ST}}$ is an anti-unitary symmetry which is local in momentum space and satisfies $I_{\text{ST}}^2=1$ such as $PT$ or $C_{2}T$ symmetry where $P$, $T$, $C_2$ indicate inversion, time-reversal, and two-fold rotation symmetries, respectively. Under $I_{\text{ST}}$, the Hamiltonian and the Bloch wave function can be constrained to be real-valued, which makes the Berry curvature and the Chern number to vanish. In this class of systems, gapped band structures of real wave functions can be topologically distinguished by Stiefel-Whitney numbers instead. The first and second Stiefel-Whitney numbers $w_1$ and $w_2$, respectively, are the corresponding invariants in 1D and 2D, which are equivalent to the quantized Berry phase and the $Z_2$ monopole charge, respectively. We first describe the topological phases characterized by the first Stiefel-Whitney number, including 1D topological insulators with quantized charge polarization, 2D Dirac semimetals, and 3D nodal line semimetals. Next we review how the second Stiefel-Whitney class characterizes the 3D nodal line semimetals carrying a $Z_{2}$ monopole charge. In particular, we explain how the second Stiefel-Whitney number $w_2$, the $Z_{2}$ monopole charge, and the linking number between nodal lines are related. Finally, we review the properties of 2D and 3D topological insulators characterized by the nontrivial second Stiefel Whitney class.

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arXiv2019

Two-dimensional Peierls instability via zone boundary Dirac line nodes in layered perovskite oxides

Interplay of Fermi surface topology and electron correlation is the quintessential ingredient underlying spontaneous symmetry breaking in itinerant electronic systems. In one-dimensional (1D) systems at half-filling, the inherent Fermi surface nesting makes the translationally invariant metallic state unstable, which is known as Peierls instability. Extending the scope of Peierls instability to two (2D) or three dimensions (3D), however, is not straightforward, since the Fermi surface in higher dimensions is generally not nested. In this work, we show that a perfectly nested Fermi surface can be realized in a class of 2D perovskite oxides, giving rise to 2D Peierls instability. Here the central role is played by the zone boundary Dirac line node (DLN) protected by two orthogonal glide mirrors induced by the rotation of oxygen octahedra. Especially, at a critical angle of the octahedron rotation, the zone-boundary DLN flattens, leading to logarithmically diverging susceptibility. We propose the 2D Peierls instability driven by dispersionless DLN as a principle mechanism for spontaneous symmetry breaking in various layered perovskite oxides including the antiferromagnetism of Sr$_2$IrO$_4$. As a clear signature of the 2D Peierls instability, we predict that the magnetic domain wall in Sr$_2$IrO$_4$ hosts localized soliton modes.

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arXiv2019

Topological Magnetoelastic Excitations in Non-Collinear Antiferromagnets

We study the topological property of the magnetoelastic excitation in non-collinear antiferromagnets. As a toy model, we consider the magnon-phonon coupling in a triangular antiferromagnet with a $120^\circ$ Nèel order. We find that in the presence of out-of-plane external magnetic field, the magnon-polaron bands, which arise from hybridization of magnons and phonons, can carry Chern number, even though the individual magnon and phonon bands are topologically trivial. Large Berry curvature is induced from the anti-crossing regions between the magnon and phonon bands, which renormalizes the thermal Hall conductivity of phonon bands. To compute the Berry curvature and Chern number of magnon-polarons, we give a simple algorithm to diagonalize magnetoelastic Hamiltonian without diagonalizing the phonon Hamiltonian, by mapping the problem to the diagonalization of bosonic Bogoliubov-de-Gennes (BdG) Hamiltonian. This is necessary because the contribution to the Berry curvature from phonon cannot be properly captured if we compute the Berry curvature from magnetoelastic Hamiltonian whose phonon sector has been already diagonalized.

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arXiv2019

Crystalline topological Dirac semimetal phase in rutile structure $β'$-PtO$_2$

Based on first-principles calculations and symmetry analysis, we propose that a transition metal rutile oxide, in particular $β'$-PtO$_2$, can host a three-dimensional topological Dirac semimetal phase. We find that $β'$-PtO$_2$ possesses a linked nodal rings structure when spin-orbit coupling is neglected. Incorporating spin-orbit coupling gaps the nodal rings, while preserving a single pair of three-dimensional Dirac points protected by a screw rotation symmetry. This Dirac point is created by a band inversion of two $d$ bands, which is a realization of a DSM phase in correlated electron systems. Moreover, a mirror plane in the momentum space carries a nontrivial mirror Chern number $n_M = -2$, which distinguishes $β'$-PtO$_2$ from the Dirac semimetals known so far, such as Na$_3$Bi and Cd$_3$As$_2$. If we apply a perturbation that breaks the rotation symmetry and preserves the mirror symmetry, the Dirac points are gapped and the system becomes a topological crystalline insulator.

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arXiv2019

Classification of flat bands according to the band-crossing singularity of Bloch wave functions

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 complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a nonsingular flat band has no singularity, and thus forms a vector bundle. A nonsingular flat band can be completely isolated from other bands while preserving the perfect flatness. All one-dimensional flat bands belong to the nonsingular class. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the flat band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in flat bands.

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arXiv2018

Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges

We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying $Z_{2}$ monopole charges, which can be realized in three-dimensional systems invariant under the combination of inversion $P$ and time reversal $T$ when spin-orbit coupling is negligible. In contrast to the well-known $PT$-symmetric nodal lines protected only by $π$ Berry phase in which a single nodal line can exist, the nodal lines with $Z_{2}$ monopole charges should always exist in pairs. We show that a pair of nodal lines with $Z_{2}$ monopole charges is created by a {\it double band inversion} (DBI) process, and that the resulting nodal lines are always {\it linked by another nodal line} formed between the two topmost occupied bands. It is shown that both the linking structure and the $Z_{2}$ monopole charge are the manifestation of the nontrivial band topology characterized by the {\it second Stiefel-Whitney class}, which can be read off from the Wilson loop spectrum. We show that the second Stiefel-Whitney class can serve as a well-defined topological invariant of a $PT$-invariant two-dimensional (2D) insulator in the absence of Berry phase. Based on this, we propose that pair creation and annihilation of nodal lines with $Z_{2}$ monopole charges can mediate a topological phase transition between a normal insulator and a three-dimensional weak Stiefel-Whitney insulator (3D weak SWI). Moreover, using first-principles calculations, we predict ABC-stacked graphdiyne as a nodal line semimetal (NLSM) with $Z_{2}$ monopole charges having the linking structure. Finally, we develop a formula for computing the second Stiefel-Whitney class based on parity eigenvalues at inversion invariant momenta, which is used to prove the quantized bulk magnetoelectric response of NLSMs with $Z_2$ monopole charges under a $T$-breaking perturbation.

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arXiv2018

Magnetic field induced topological semimetals near a quantum critical point of pyrochlore iridates

Motivated by the recent experimental observation of anomalous magneto-transport properties near the Mott quantum critical point (QCP) of pyrochlore iridates, we study the generic topological band structure near QCP in the presence of magnetic field. We have found that the competition between different energy scales can generate various topological semi-metal phases near QCP. Here the central role is played by the presence of a quadratic band crossing (QBC) with four-fold degeneracy in the paramagnetic band structure. Due to the large band degeneracy and strong spin-orbit coupling, the degenerate states at QBC can show an anisotropic Zeeman effect as well as the conventional isotropic Zeeman effect. Through the competition between three different magnetic energy scales including the exchange energy between Ir electrons and two Zeeman energies, various topological semimetals can be generated near QCP. Moreover, we have shown that these three magnetic energy scales can be controlled by modulating the magnetic multipole moment (MMM) of the cluster of spins in a unit cell, which can couple to the intrinsic MMM of the degenerate states at QBC. We propose the general topological band structure under magnetic field achievable near QCP, which would facilitate the experimental discovery of novel topological semimetal states in pyrochlore iridates.

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arXiv2018

Unconventional anomalous Hall effect from antiferromagnetic domain walls of Nd2Ir2O7 thin films

Ferroic domain walls (DWs) create different symmetries and ordered states compared with those in single-domain bulk materials. In particular, the DWs of an antiferromagnet (AFM) with non-coplanar spin structure have a distinct symmetry that cannot be realized in those of their ferromagnet counterparts. In this paper, we show that an unconventional anomalous Hall effect (AHE) can arise from the DWs of a non-coplanar AFM, Nd2Ir2O7. Bulk Nd2Ir2O7 has a cubic symmetry; thus, its Hall signal should be zero without an applied magnetic field. The DWs generated in this material break the two-fold rotational symmetry, which allows for finite anomalous Hall conductivity. A strong f-d exchange interaction between the Nd and Ir magnetic moments significantly influences antiferromagnetic domain switching. Our epitaxial Nd2Ir2O7 thin film showed a large enhancement of the AHE signal when the AFM domains switched, indicating that the AHE is mainly due to DWs. Our study highlights the symmetry broken interface of AFM materials as a new means of exploring topological effects and their relevant applications.

cond-mat.str-el↗

arXiv2017

Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus

We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ~0.6 eV. High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their moving along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by spacetime inversion symmetry, even in the presence of spin-orbit coupling. Our results establish black phosphorus in the inverted regime as a simple model system of 2D symmetry-protected (topological) Dirac semimetals, offering an unprecedented opportunity for the discovery of 2D Weyl semimetals.

cond-mat.mtrl-sci↗

arXiv2017

Classification of accidental band crossings and emergent semimetals in two-dimensional noncentrosymmetric systems

We classify all possible gap-closing procedures which can be achieved in two-dimensional time-reversal invariant noncentrosymmetric systems. For exhaustive classification, we examine the space group symmetries of all 49 layer groups lacking inversion taking into account spin-orbit coupling. Although a direct transition between two insulators is generally predicted to occur when a band crossing happens at a general point in the Brillouin zone, we find that a variety of stable semimetal phases with point or line nodes can also arise due to the band crossing in the presence of additional crystalline symmetries. Through our theoretical study, we provide, for the first time, the complete list of nodal semimetals created by a band inversion in two-dimensional noncentrosymmetric systems with time-reversal invariance. The transition from an insulator to a nodal semimetal can be grouped into three classes depending on the crystalline symmetry. Firstly, in systems with a two-fold rotation about the z-axis (normal to the system), a band inversion at a generic point generates a two-dimensional Weyl semimetal with point nodes. Secondly, when the band crossing happens on the line invariant under a two-fold rotation (mirror) symmetry with the rotation (normal) axis lying in the two-dimensional plane, a Weyl semimetal with point nodes can also be obtained. Finally, when the system has a mirror symmetry about the plane embracing the whole system, a semimetal with nodal lines can be created. Applying our theoretical framework, we identify various two-dimensional materials as candidate systems in which stable nodal semimetal phases can be induced via doping, applying electric field, or strain-engineering, etc.

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arXiv2017

Unconventional topological phase transition in two-dimensional systems with space-time inversion symmetry

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and two-fold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional two-fold rotation symmetry is mediated by an emergent stable two-dimensional Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and two-fold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair-creation/pair-annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D $Z_{2}$ topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase since the quantum well, lacking inversion symmetry intrinsically, has two-fold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

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arXiv2016

Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals

Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Here we show that a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling.

cond-mat.mtrl-sci↗

arXiv2015

Recent progress on correlated electron systems with strong spin-orbit coupling

Emergence of novel quantum ground states in correlated electron systems with strong spin-orbit coupling has been a recent subject of intensive studies. While it has been realized that spin-orbit coupling can provide non-trivial band topology in weakly interacting electron systems, as in topological insulators and semi-metals, the role of electron-electron interaction in strongly spin-orbit coupled systems has not been fully understood. The availability of new materials with significant electron correlation and strong spin-orbit coupling now makes such investigations possible. Many of these materials contain 5d or 4d transition metal elements; the prominent examples are iridium oxides or iridates. In this review, we succinctly discuss recent theoretical and experimental progress on this subject. After providing a brief overview, we focus on pyrochlore iridates and three-dimensional honeycomb iridates. In pyrochlore iridates, we discuss the quantum criticality of the bulk and surface states, and the relevance of the surface/boundary states in a number of topological and magnetic ground states, both in the bulk and thin film configurations. Experimental signatures of these boundary and bulk states are discussed. Domain wall formation and strongly-direction-dependent magneto-transport are also discussed. Regarding the three-dimensional honeycomb iridates, we consider possible quantum spin liquid phases and unusual magnetic orders in theoretical models with strongly bond-dependent interactions. These theoretical ideas and results are discussed in light of recent resonant X-ray scattering experiments on three-dimensional honeycomb iridates. We also contrast these results with the situation in two-dimensional honeycomb iridates. We conclude with the outlook on other related systems.

cond-mat.str-el↗

arXiv2015

Topological charges of three-dimensional Dirac semimetals with rotation symmetry

In general, the stability of a band crossing point indicates the presence of a quantized topological number associated with it. In particular, the recent discovery of three-dimensional Dirac semimetals in Na$_{3}$Bi and Cd$_{3}$As$_{2}$ demonstrates that a Dirac point with four-fold degeneracy can be stable as long as certain crystalline symmetries are supplemented in addition to the time-reversal and inversion symmetries. However, the topological charges associated with Na$_{3}$Bi and Cd$_{3}$As$_{2}$ are not clarified yet. In this work, we identify the topological charge of three-dimensional Dirac points. It is found that although the simultaneous presence of the time-reversal and inversion symmetries forces the net chiral charge to vanish, a Dirac point can carry another quantized topological charge when an additional rotation symmetry is considered. Two different classes of Dirac semimetals are identified depending on the nature of the rotation symmetries. First, the conventional symmorphic rotational symmetry which commutes with the inversion gives rise to the class I Dirac semimetals having a pair of Dirac points on the rotation axes. Since the topological charges of each pair of Dirac points have the opposite sign, a pair-creation or a pair-annihilation is required to change the number of Dirac points in the momentum space. On the other hand, the class II Dirac semimetals possess a single isolated Dirac point at a time-reversal invariant momentum, which is protected by a screw rotation. The non-symmorphic nature of screw rotations allows the anti-commutation relation between the rotation and inversion symmetries, which enables to circumvent the doubling of the number of Dirac points and create a single Dirac point at the Brillouin zone boundary.

cond-mat.mes-hall↗

arXiv2015

Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and Newtonian dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO$_2$/VO$_2$ superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-$N$ expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue $Z$ at energy $E$ scales as $Z \propto E^a$ with $a >0$, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, $Z \propto (|\log E|)^{-b}$ with universal $b = 3/2$.

cond-mat.str-el↗

arXiv2014

Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems

Topological phase transitions in condensed matters accompany emerging singularities of the electronic wave function, often manifested by gap-closing points in the momentum space. In conventional topological insulators in three dimensions (3D), the low energy theory near the gap-closing point can be described by relativistic Dirac fermions coupled to the long range Coulomb interaction, hence the quantum critical point of topological phase transitions provides a promising platform to test the novel predictions of quantum electrodynamics. Here we show that a new class of quantum critical phenomena emanates in topological materials breaking either the inversion symmetry or the time-reversal symmetry. At the quantum critical point, the theory is described by the emerging low energy fermions, dubbed the anisotropic Weyl fermions, which show both the relativistic and Newtonian dynamics simultaneously. The interplay between the anisotropic dispersion and the Coulomb interaction brings about a new screening phenomena distinct from the conventional Thomas-Fermi screening in metals and logarithmic screening in Dirac fermions.

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