arXiv subjects

Bohm-Jung Yang

Publications and source records attributed to Bohm-Jung Yang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Quantum geometric bound for saturated ferromagnetism

Despite its abundance in nature, predicting the occurrence of ferromagnetism in the ground state is possible only under very limited conditions such as in a flat band system with repulsive interaction or in a band with a single hole under infinitely large Coulomb repulsion, etc. Here, we propose a general condition to achieve saturated ferromagnetism based on the quantum geometry of electronic wave functions in itinerant electron systems. By analyzing the spin excitations of multi-band repulsive Hubbard models with an integer band filling, relevant to either ferromagnetic insulators or semimetals, we show that quantum geometry stabilizes the Goldstone mode in the strongly correlated limit. Our theory indicates the stability of ferromagnetism in a large class of insulators and semimetals other than the previously studied flat band systems and their variants. Moreover, we rigorously prove that saturated ferromagnetism is forbidden in any system with trivial quantum geometry, which includes every half-filled system. We believe that our findings reveal a profound connection between quantum geometry and ferromagnetism, which can be extended to various symmetry-broken ground states in itinerant electronic systems.

cond-mat.str-el↗

arXiv2024

Unconventional topological phase transition of the Hopf insulator

The topological phase transition between two band insulators is mediated by a gapless state whose low-energy band structure normally contains sufficient information for describing the topology change. In this work, we show that there is a class of topological insulators whose topological phase transition cannot be explained by this conventional paradigm. Taking the Hopf insulator as a representative example, we show that the change of the Hopf invariant requires the information of wave functions as well as the gapless band structure simultaneously. More explicitly, the description of the Hopf invariant change requires us to trace not only the trajectory of Weyl points but also the evolution of the preimages for two distinct eigenstates. We show that such an unconventional topological phase transition originates from the fact that the Hopf invariant is well-defined when all the lower dimensional topological invariants are trivial, which in turn allows us to lift the classifying space of occupied state projectors to the corresponding universal 2-covering space of wave functions. Generalizing our theory to inversion-symmetric 10-fold Altland-Zirnbauer symmetry classes, we provide a complete list of symmetry classes, all of which turn out to have delicate band topology related to the Hopf invariant, where similar unconventional topological phase transitions can appear.

cond-mat.mes-hall↗

arXiv2024

Euler band topology in spin-orbit coupled magnetic systems

The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are extremely rare. Here, we show that in a quantum spin Hall insulator with two-fold rotation $C_{2z}$ about the $z$-axis, a pair of bands with nontrivial $\mathbb{Z}_2$ invariant turn into magnetic Euler bands under in-plane Zeeman field or in-plane ferromagnetic ordering. The resulting magnetic insulator generally carries a nontrivial second Stiefel-Whitney invariant. In particular, when the topmost pair of occupied bands carry a nonzero Euler number, the corresponding magnetic insulator can be called a magnetic Euler insulator. Moreover, the topological phase transition between a trivial magnetic insulator and a magnetic Stiefel-Whitney or Euler insulator is mediated by a stable topological semimetal phase in which Dirac nodes carrying non-Abelian topological charges exhibit braiding processes across the transition. Using the first-principles calculations, we propose various candidate materials hosting magnetic Euler bands. We especially show that ZrTe$_5$ bilayers under in-plane ferromagnetism are a candidate system for magnetic Stiefel-Whitney insulators in which the non-Abelian braiding-induced topological phase transitions can occur under pressure.

cond-mat.mes-hall↗

arXiv2024

Nodal fermions in a strongly spin-orbit coupled frustrated pyrochlore superconductor

The pyrochlore lattice, a three-dimensional network of corner-sharing tetrahedra, is a promising material playground for correlated topological phases arising from the interplay between spin-orbit coupling (SOC) and electron-electron interactions. Due to its geometrically frustrated lattice structure, exotic correlated states on the pyrochlore lattice have been extensively studied using various spin Hamiltonians in the localized limit. On the other hand, the topological properties of the electronic structure in the pyrochlore lattice have rarely been explored, due to the scarcity of pyrochlore materials in the itinerant paramagnetic limit. Here, we explore the topological electronic band structure of pyrochlore superconductor RbBi$_{2}$ using angle-resolved photoemission spectroscopy. Thanks to the strong SOC of the Bi pyrochlore network, we experimentally confirm the existence of three-dimensional (3D) massless Dirac fermions enforced by nonsymmorphic symmetry, as well as a 3D quadratic band crossing protected by cubic crystalline symmetry. Furthermore, we identify an additional 3D linear Dirac dispersion associated with band inversion protected by threefold rotation symmetry. These observations reveal the rich non-trivial band topology of itinerant pyrochlore lattice systems in the strong SOC regime. Through manipulation of electron correlations and SOC of the frustrated pyrochlore lattices, this material platform is a natural host for exotic phases of matter, including the fractionalized quantum spin Hall effect in the topological Mott insulator phase, as well as axion electrodynamics in the axion insulator phase.

cond-mat.mtrl-sci↗

arXiv2023

Quantum geometric bound and ideal condition for Euler band topology

Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in two-dimensional systems with space-time inversion $I_{ST}$ symmetry satisfying $I^2_{ST}=+1$. As $I_{ST}$ symmetry imposes the reality of the wave function with vanishing Berry curvature, the well-known inequality between the quantum metric and the Berry curvature is not meaningful in this class of systems. We find that the non-abelian quantum geometric tensor of two real bands exhibits an intriguing inequality between the off-diagonal Berry curvature and the quantum metric, which in turn gives the inequality between the quantum volume and the Euler invariant. Moreover, we show that the saturation condition of the inequality is deeply related to the ideal condition for Euler bands, which provides a criterion for the stability of fractional topological phases in interacting Euler bands. Our findings demonstrate the potential of the quantum geometry as a powerful tool for characterizing symmetry-protected topological states and their interaction effect.

cond-mat.mes-hall↗

arXiv2023

Quantum Valley and Sub-valley Hall Effect in the Large Angle Twisted Bilayer Graphene

We study the quantum valley Hall effect and related domain wall modes in twisted bilayer graphene at a large commensurate angle. Due to the quantum valley and sub-valley Hall effect, a small deviation from the commensurate angle generates two-dimensional conducting network patterns composed of one-dimensional domain wall conducting channels, which can induce non-Fermi liquid transport behavior within an accessible temperature range. The domain wall modes can be manipulated by using the layer shifting and external electric fields which, in turn, leads to the sub-valley Haldane and Semenoff masses on the domain wall modes. The large-angle twisted bilayer graphene and related materials can be a new setup to harness the quantum valley and sub-valley Hall effect with enhanced tunability.

cond-mat.mes-hall↗

arXiv2023

Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Non-Collinear Antiferromagnets

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in non-collinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that a non-collinear magnetic ordering in a metal can generate a momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to non-collinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the non-collinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

cond-mat.supr-con↗

arXiv2023

Quantum Geometry and Landau Levels of Quadratic Band Crossings

We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband coupling parameters on the wave function geometry of general QBCPs, we demonstrate that the interband coupling parameters can be entirely determined by the projected elliptic image of the wave functions on the Bloch sphere, which can be characterized by three parameters, i.e., the major $d_1$ and minor $d_2$ diameters of the ellipse, and one angular parameter $ϕ$ describing the orientation of the ellipse. These parameters govern the geometric properties of the system such as the Berry phase and modified LL spectra. Explicitly, by comparing the LL spectra of two quadratic band models with and without interband couplings, we show that the product of $d_1$ and $d_2$ determines the constant shift in LL energy while their ratio governs the initial LL energies near a QBCP. Also, by examining the influence of the rotation and time-reversal symmetries on the wave function geometry, we construct a minimal continuum model which exhibits various wave function geometries. We calculate the LL spectra of this model and discuss how interband couplings give LL structure for dispersive bands as well as nearly flat bands.

cond-mat.mes-hall↗

arXiv2023

Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators

Topological crystalline insulators (TCIs) can host anomalous surface states which inherits the characteristics of crystalline symmetry that protects the bulk topology. Especially, the diversity of magnetic crystalline symmetries indicates the potential for novel magnetic TCIs with distinct surface characteristics. Here, we propose a topological magnetic Dirac insulator (TMDI), whose two-dimensional surface hosts fourfold-degenerate Dirac fermions protected by either the $p'_c4mm$ or $p4'g'm$ magnetic wallpaper group. The bulk topology of TMDIs is protected by diagonal mirror symmetries, which give chiral dispersion of surface Dirac fermions and mirror-protected hinge modes. We propose candidate materials for TMDIs including Nd$_4$Te$_8$Cl$_4$O$_{20}$ and DyB$_4$ based on first-principles calculations, and construct a general scheme for searching TMDIs using the space group of paramagnetic parent states. Our theoretical discovery of TMDIs will facilitate future research on magnetic TCIs and illustrate a distinct way to achieve anomalous surface states in magnetic crystals.

cond-mat.mes-hall↗

arXiv2023

Real Hopf Insulator

Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy invariant and the related band topology of three-dimensional (3D) real-valued Hamiltonians with two occupied and two unoccupied bands. Such a real Hamiltonian generally appears in $\mathcal{PT}$ symmetric spinless fermion systems where $\mathcal{P}$ and $\mathcal{T}$ indicate the inversion and time-reversal symmetries, respectively. We show that the 3D band topology of the system is characterized by two independent Hopf invariants when the lower-dimensional band topology is trivial. Thus, the corresponding 3D band insulator with nonzero Hopf invariants can be called a real Hopf insulator (RHI). In sharp contrast to all the other topological insulators discovered up to now, the topological invariants of RHI can be defined only when the fixed number of both the occupied and unoccupied states are simultaneously considered. Thus, the RHI belongs to the category of delicate topological insulators proposed recently. We show that finite-size systems with slab geometry support surface states with nonzero Chern numbers in a $\mathcal{PT}$-symmetric manner independent of the Fermi level position, and establish the bulk-boundary correspondence. We also discuss the bulk-boundary correspondence of rotation symmetric RHIs using the returning Thouless pump.

cond-mat.mes-hall↗

arXiv2023

Correlated normal state fermiology and topological superconductivity in UTe2

UTe2 is a promising candidate for spin-triplet superconductors, in which a paramagnetic normal state becomes superconducting due to spin fluctuations. The subsequent discovery of various unusual superconducting properties has promoted the use of UTe2 as an exciting playground to study unconventional superconductivity, but fathoming the normal state fermiology and its influence on the superconductivity still requires further investigation. Here, we theoretically show that electron correlation induces a dramatic change in the normal state fermiology with an emergent correlated Fermi surface (FS) driven by Kondo resonance at low temperatures. This emergent correlated FS can account for various unconventional superconducting properties in a unified way. In particular, the geometry of the correlated FS can naturally host topological superconductivity in the presence of odd-parity pairings, which become the leading instability due to strong ferromagnetic spin fluctuations. Moreover, two pairs of odd-parity channels appear as accidentally degenerate solutions, which can naturally explain the multicomponent superconductivity with broken time-reversal symmetry. Interestingly, the resulting time-reversal breaking superconducting state is a Weyl superconductor in which Weyl points migrate along the correlated FS as the relative magnitude of nearly degenerate pairing solutions varies. We believe that the correlated normal state fermiology we discovered provides a unified platform to describe the unconventional superconductivity in UTe2.

cond-mat.supr-con↗

arXiv2023

Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field

In this work, we show that a buckled honeycomb lattice can host a boundary-obstructed topological superconductor (BOTS) in the presence of f-wave spin-triplet pairing (fSTP). The underlying buckled structure allows for the manipulation of both chemical potential and sublattice potential using a double gate setup. Although a finite sublattice potential can stabilize the fSTP with a possible higher-order band topology, because it also breaks the relevant symmetry, the stability of the corner modes is not guaranteed. Here we show that the fSTP on the honeycomb lattice gives BOTS under nonzero sublattice potential, thus the corner modes can survive as long as the boundary is gapped. Also, by examining the large sublattice potential limit where the honeycomb lattice can be decomposed into two triangular lattices, we show that the boundary modes in the normal state are the quintessential ingredient leading to the BOTS. Thus the effective boundary Hamiltonian becomes nothing but the Hamiltonian for Kitaev chains, which eventually gives the corner modes of the BOTS.

cond-mat.supr-con↗

arXiv2022

Theory of transverse magnetization in spin-orbit coupled antiferromagnets

Some antiferromagnets under a magnetic field develop magnetization perpendicular to the field as well as more conventional ones parallel to the field. So far, the transverse magnetization (TM) has been attributed to either spin canting effect or the presence of cluster magnetic multipolar ordering. However, a general theory of TM based on microscopic understanding is still missing. Here, we construct a general microscopic theory of TM in antiferromagnets with cluster magnetic multipolar ordering by considering classical spin Hamiltonians with spin anisotropy that arises from the spin-orbit coupling. First, from general symmetry analysis, we show that TM can appear only when all crystalline symmetries are broken other than the antiunitary mirror, antiunitary two-fold rotation, and inversion symmetries. Moreover, by analyzing spin Hamiltonians, we show that TM always appears when the degenerate ground state manifold of the spin Hamiltonian is discrete. On the other hand, when the degenerate ground state manifold is continuous, TM generally does not appear except when the magnetic field direction and the spin configuration satisfy specific geometric conditions under single-ion anisotropy. Finally, we show that TM can induce anomalous planar Hall Effect, a unique transport phenomenon that can be used to probe multipolar antiferromagnetic structures. We believe that our theory provides a useful guideline for understanding the anomalous magnetic responses of the antiferromagnets with complex magnetic structures.

cond-mat.mes-hall↗

arXiv2022

Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture

Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of gap-closing nodes at the Fermi energy ($E_F$) with other nodes below $E_F$. As the number of linked nodes can be changed only via pair-creation or pair-annihilation, a linked node is more stable and robust than ordinary nodes without linking. Here we propose a new type of a linked nodal structure between a nodal line (nodal surface) at $E_F$ with another nodal line (nodal surface) below $E_F$ in two-dimensional (three-dimensional) spinless fermion systems with $\mathcal{IT}$ symmetry where $\mathcal{I}$ and $\mathcal{T}$ indicate inversion and time-reversal symmetries, respectively. Because of additional chiral and rotational symmetries, in our system, a double band inversion creates a pair of linked nodes carrying the same topological charges, thus the pair are unremovable via a Lifshiftz transition, which is clearly distinct from the cases of the linked nodes reported previously. A realistic tight binding model and effective theory are developed for such a linking structure. Also, using density functional theory calculations, we propose a class of materials, composed of stacked bilayer graphene with Kekulé texture, as a candidate system hosting the new type of the linked nodal structure.

cond-mat.mtrl-sci↗

arXiv2022

Unsupervised learning of topological phase diagram using topological data analysis

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised learning of the topological phase diagrams. This is possible because the quantum distance can capture the shape of the space formed by the Bloch wavefunctions as we sweep over the Brillouin zone. Therefore, if we minimize the volume of the space formed by the wavefunction through a continuous deformation, the wavefunctions will end up forming distinct spaces which depend on the topology of the wavefunctions. Combining this observation with the topological data analysis, which provides tools such as the persistence diagram to capture the topology of the space formed by the wavefunctions, we can cluster together Hamiltonians that give rise to similar persistence diagrams after the deformation. By examining these clusters as well as representative persistence diagrams in the clusters, we can draw the phase diagram as well as distinguish between topologically trivial and nontrivial phases. Our proposal to minimize the volume can be interpreted as finding geodesics in 1D Brillouin zone, and minimal surfaces in 2D and higher-dimensional Brillouin zones. Using this interpretation, we can guarantee the convergence of the minimization under certain conditions, which is an outstanding feature of our algorithm. We demonstrate the working principles of our machine learning algorithm using various models.

cond-mat.mes-hall↗

arXiv2021

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.

cond-mat.mes-hall↗

arXiv2021

General construction of flat bands with and without band crossings based on wave function singularity

In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS) and also the singularity of the flat-band wave function obtained by a Fourier transform of the CLS (FT-CLS). In order to construct a flat-band model systematically using these ingredients, we first choose a CLS with a specific symmetry representation in a given lattice. Then, the singularity of FT-CLS indicates whether the resulting flat band exhibits a band crossing point or not. A tight-binding Hamiltonian with the flat band corresponding to the FT-CLS is obtained by introducing a set of basis molecular orbitals, which are orthogonal to the FT-CLS. Our construction scheme can be systematically applied to any lattice so that it provides a powerful theoretical framework to study exotic properties of both gapped and gapless flat bands arising from their wave function singularities.

cond-mat.mes-hall↗

arXiv2021

Flat bands with band crossings enforced by symmetry representation

Flat bands have band crossing points with other dispersive bands in many systems including the canonical flat band models in the Lieb and kagome lattices. Here we show that some of such band degeneracy points are unavoidable because of the symmetry representation (SR) of the flat band under unitary symmetry. We refer to such a band degeneracy point of flat bands as a SR-enforced band crossing. SR-enforced band crossing is distinct from the conventional band degeneracy protected by symmetry eigenvalues or topological charges in that its protection requires both specific symmetry representation and band flatness of the flat band, simultaneously. Even $n$-fold rotation $C_n$ ($n=2,3,4,6$) symmetry, which cannot protect band degeneracy without additional symmetries due to its abelian nature, can protect SR-enforced band crossings in flat band systems. In two-dimensional flat band systems with $C_n$ symmetry, when the degeneracy of a SR-enforced band crossing is lifted by a $C_n$ symmetry-preserving perturbation, we obtain a nearly flat Chern band. Our theory not only explains the origin of the band crossing points of FBs existing in various models, but also gives a strict no-go theorem for isolated FBs in a given lattice arising from the SR.

cond-mat.mes-hall↗