arXiv subjects

Junyeong Ahn

Publications and source records attributed to Junyeong Ahn.

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arXiv2022

Riemannian geometry of resonant optical responses

The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects. However, it has been challenging to relate quantum geometry to resonant optical responses. The main obstacle is that optical transitions involve a pair of states, while existing geometrical properties are defined for a single state. As a result, a concrete geometric understanding of optical responses has so far been limited to two-level systems, where the Hilbert space is completely determined by a single state and its orthogonal complement. Here, we construct a general theory of Riemannian geometry for resonant optical processes by identifying transition dipole moment matrix elements as tangent vectors. This theory applies to arbitrarily high-order responses, suggesting that optical responses can generally be thought of as manifestations of the Riemannian geometry of quantum states. We use our theory to show that third-order photovoltaic Hall effects are related to the Riemann curvature tensor and demonstrate an experimentally accessible regime where they dominate the response.

cond-mat.mes-hall↗

arXiv2022

Rare-earth monopnoctides -- family of antiferromagnets hosting magnetic Fermi arcs

Since the discovery of topological insulators a lot of research effort has been devoted to magnetic topological materials, in which non-trivial spin properties can be controlled by magnetic fields, culminating in a wealth of fundamental phenomena and possible applications. The main focus was on ferromagnetic materials that can host Weyl fermions and therefore spin textured Fermi arcs. The recent discovery of Fermi arcs and new magnetic bands splitting in antiferromagnet (AFM) NdBi has opened up new avenues for exploration. Here we show that these uncharted effects are not restricted to this specific compound, but rather emerge in CeBi, NdBi, and NdSb when they undergo paramagnetic to AFM transition. Our data show that the Fermi arcs in NdSb have 2-fold symmetry, leading to strong anisotropy that may enhance effects of spin textures on transport properties. Our findings thus demonstrate that the RBi and RSb series are materials that host magnetic Fermi arcs and may be a potential platform for modern spintronics.

cond-mat.other↗

arXiv2022

Emergence of Fermi arcs and novel magnetic splitting in an antiferromagnet

The Fermi arcs are signatures of exotic states in solids because they defy conventional concept of Fermi surfaces as closed contours in momentum space. Fermi arcs were first discovered in cuprates, and caused by the pseudogap. Weyl semimetals provided another way to generate Fermi arcs by breaking either the time reversal symmetry (TRS) or inversion symmetry of a 3D Dirac semimetal, which can result in a Weyl semimetal with pairs of Weyl nodes that have opposite chirality. The bulk-boundary correspondence associated with the Chern number leads to the emergence of Fermi arcs on the boundary. Here, we present experimental evidence that pairs of magnetically split hole- and electron-like Fermi arcs emerge below the Neel temperature, in the antiferromagnetic (AFM) state of cubic NdBi due to a novel band splitting effect. Whereas TRS is broken by the AFM order, both inversion and nonsymmorphic TRS are preserved in the bulk, precluding the possibility of a Weyl semimetal. The observed magnetic splitting is highly unusual, as it creates bands of opposing curvature, that changes with temperature and follows the antiferromagnetic order parameter. This is completely different from previously reported cases of magnetic splittings such as traditional Zeeman and Rashba, where the curvature of the bands is preserved. Therefore, our finding represents a new Fermionic state created by new type of magnetic band splitting in the presence of a long-range AFM order that are not readily explained by existing theoretical ideas.

cond-mat.str-el↗

arXiv2021

Superconductivity-induced spectral weight transfer due to quantum geometry

Optical spectral weight transfer associated with the onset of superconductivity at high energy scales compared with the superconducting gap has been observed in several systems such as high-$T_c$ cuprates. While there are still debates on the origin of this phenomenon, a consensus is that it is due to strong correlation effects beyond the BCS theory. Here we show that there is another route to a nonzero spectral weight transfer based on the quantum geometry of the conduction band in multiband systems. We discuss applying this idea to the cuprates and twisted multilayer graphene.

cond-mat.supr-con↗

arXiv2021

Many-body selection rule for quasiparticle pair creations in centrosymmetric superconductors

When metal becomes superconducting, new optical excitation channels are created by particle-hole mixing. These excitation channels contribute negligibly to optical responses in most superconductors, but they can be relevant in ultra-strong-coupling superconductors that are close to the Bose-Einstein condensate regime. Recently, selection rules for these excitations have been formulated based on single-particle anti-unitary symmetries in the mean-field theory. While being potentially useful for studying optical properties of ultra-strong-coupling superconductors, they had fundamental limitations because significant quantum fluctuations invalidate mean-field approaches. Here, we use many-body states to formulate an optical selection rule that does not rely on the mean-field approximation. In this approach, the physical meaning of the previous selection rules becomes clearer as they are simply recast as the selection rule for many-body inversion eigenstates, not involving anti-unitary symmetries. This selection rule applies not only to the Bogoliubov quasiparticles of Fermi liquids but also to non-Fermi-liquid quasiparticles and electrically charged bosonic excitations. We also study the Bogoliubov Fermi surfaces, whose topological stability is closely related to the selection rule. We provide a many-body formulation of their topological charges and show that the low-energy optical conductivity of the Bogoliubov Fermi surfaces depends crucially on their secondary topological charge. Finally, we discuss the implications of our results to the stability of the superconducting state.

cond-mat.supr-con↗

arXiv2021

Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry

Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundary. In conventional topological superconductors, Majorana in-gap states appear in the form of either localized zero-dimensional modes or propagating spin-1/2 fermions with a quasi-relativistic dispersion relation. Here we show that unconventional propagating Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states fall into three different categories: a spin-$S$ Majorana fermion with $(2S+1)$-fold degeneracy $(S\geq3/2)$, a Majorana Fermi line carrying two distinct topological charges, and a quartet of spin-1/2 Majorana fermions related by fourfold rotational symmetry. The spectral properties of the first two kinds, which go beyond the conventional spin-1/2 fermions, are unique to topological superconductors and have no counterpart in topological insulators. We show that the unconventional Majorana surface states can be obtained in the superconducting phase of doped $Z_2$ topological insulators or Dirac semimetals with rotational symmetry.

cond-mat.mes-hall↗

arXiv2021

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

cond-mat.supr-con↗

arXiv2020

Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals

We study the low-frequency properties of the bulk photovoltaic effect in topological semimetals. The bulk photovoltaic effect is a nonlinear optical effect that generates DC photocurrents under uniform irradiation, allowed by noncentrosymmetry. It is a promising mechanism for a terahertz photodetection based on topological semimetals. Here, we systematically investigate the low-frequency behavior of the second-order optical conductivity in point-node semimetals. Through symmetry and power-counting analysis, we show that Dirac and Weyl points with tilted cones show the leading low-frequency divergence. In particular, we find new divergent behaviors of the conductivity of Dirac and Weyl points under circularly polarized light, where the conductivity scales as $ω^{-2}$ and $ω^{-1}$ near the gap-closing point in two and three dimensions, respectively. We provide a further perspective on the low-frequency bulk photovoltaic effect by revealing the complete quantum geometric meaning of the second-order optical conductivity tensor. The bulk photovoltaic effect has two origins, which are the transition of electron position and the transition of electron velocity during the optical excitation, and the resulting photocurrents are respectively called the shift current and the injection current. Based on an analysis of two-band models, we show that the injection current is controlled by the quantum metric and Berry curvature, whereas the shift current is governed by the Christoffel symbols near the gap-closing points in semimetals. Finally, for further demonstrations of our theory beyond simple two-band models, we perform first-principles calculations on magnetic Dirac semimetal MnGeO$_3$and Weyl semimetal PrGeAl. Our work brings out new insights into the structure of nonlinear optical responses as well as for the design of semimetal-based terahertz photodetectors.

cond-mat.mes-hall↗

arXiv2020

Higher-Order Topological Superconductivity of Spin-Polarized Fermions

We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulae for the topological invariants characterizing higher-order topology of centrosymmetric superconductors. Based on the formulae, we systematically classify all possible band structures of ferromagnetic metals that can induce inversion-protected higher-order topological superconductivity. Among them, doped ferromagnetic nodal semimetals are identified as the most promising normal state platform for higher-order topological superconductivity. In two dimensions, we show that odd-parity pairing of doped Dirac semimetals induces a second-order topological superconductor. In three dimensions, odd-parity pairing of doped nodal line semimetals generates a nodal line topological superconductor with monopole charges. On the other hand, odd-parity pairing of doped monopole nodal line semimetals induces a three-dimensional third-order topological superconductor. Our theory shows that the combination of superconductivity and ferromagnetic nodal semimetals opens up a new avenue for future topological quantum computations using Majorana zero modes.

cond-mat.mes-hall↗

arXiv2020

Two-dimensional higher-order topology in monolayer graphdiyne

Based on first-principles calculations and tight-binding model analysis, we propose monolayer graphdiyne as a candidate material for a two-dimensional higher-order topological insulator protected by inversion symmetry. Despite the absence of chiral symmetry, the higher-order topology of monolayer graphdiyne is manifested in the filling anomaly and charge accumulation at two corners. Although its low energy band structure can be properly described by the tight-binding Hamiltonian constructed by using only the $p_z$ orbital of each atom, the corresponding bulk band topology is trivial. The nontrivial bulk topology can be correctly captured only when the contribution from the core levels derived from $p_{x,y}$ and $s$ orbitals are included, which is further confirmed by the Wilson loop calculations. We also show that the higher-order band topology of a monolayer graphdyine gives rise to the nontrivial band topology of the corresponding three-dimensional material, ABC-stacked graphdiyne, which hosts monopole nodal lines and hinge states.

cond-mat.mtrl-sci↗

arXiv2019

Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop

We study the bulk and boundary properties of fragile topological insulators (TIs) protected by inversion symmetry, mostly focusing on the class A of the Altland-Zirnbauer classification. First, we propose an efficient method for diagnosing fragile band topology by using the symmetry data in momentum space. Using this method, we show that among all the possible parity configurations of inversion-symmetric insulators, at least 17 percent of them have fragile topology in 2D while fragile TIs are less than 3 percent in 3D. Second, we study the bulk-boundary correspondence of fragile TIs protected by inversion symmetry. In particular, we generalize the notion of $d$-dimensional ($d$D) $k$th-order TIs, which is normally defined for $0 d$, and show that they all have fragile topology. In terms of the Dirac Hamiltonian, a $d$D $k$th-order TI has $(k-1)$ boundary mass terms. We show that a minimal fragile TI with the filling anomaly can be considered as the $d$D $(d+1)$th-order TI, and all the other $d$D $k$th-order TIs with $k>(d+1)$ can be constructed by stacking $d$D $(d+1)$th-order TIs. Although $d$D $(d+1)$th-order TIs have no in-gap states, the boundary mass terms carry an odd winding number along the boundary, which induces localized charges on the boundary at the positions where the boundary mass terms change abruptly. In the cases with $k>(d+1)$, we show that the net parity of the system with boundaries can distinguish topological insulators and trivial insulators. Also, by studying the (nested) Wilson loop spectra, we determine the minimal number of bands to resolve the Wannier obstruction, which is consistent with the prediction from our diagnosis method of fragile topology. Finally, we show that a $(d+1)$D $(k-1)$th-order TI can be obtained by an adiabatic pumping of $d$D $k$th-order TI, which generalizes the previous study of the 2D 3rd-order TI.

cond-mat.mes-hall↗

arXiv2019

Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics

The hallmark of symmetry-protected topological (SPT) phases is the existence of anomalous boundary states, which can only be realized with the corresponding bulk system. In this work, we show that for every Hermitian anomalous boundary mode of the ten Altland-Zirnbauer classes, a non-Hermitian counterpart can be constructed, whose long time dynamics provides a realization of the anomalous boundary state. We prove that the non-Hermitian counterpart is characterized by a point-gap topological invariant, and furthermore, that the invariant exactly matches that of the corresponding Hermitian anomalous boundary mode. We thus establish a correspondence between the topological classifications of $(d+1)$-dimensional gapped Hermitian systems and $d$-dimensional point-gapped non-Hermitian systems. We illustrate this general result with a number of examples in different dimensions. This work provides a new perspective on point-gap topological invariants in non-Hermitian systems.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗