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 inversionISTsymmetry. 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 anIST-symmetric Wannier representation. Moreover, a two-band system with the Euler classe2has band crossing points whose total winding number is equal to2e2. 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 aZ2topological invariant classifying the band topology, that is, the second Stiefel Whitney class (w2). Two bands with an even (odd) Euler class turn into a system withw2=0(w2=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 multiband 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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A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D ...Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant.
Topological acoustic triple point Park, Sungjoon; Hwang, Yoonseok; Choi, Hong Chul ...
Nature communications,
11/2021, Volume:
12, Issue:
1
Journal Article
Peer reviewed
Open access
Acoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu-Goldstone theorem. Here, we show that this ...triple point can carry a topological charge Formula: see text that is a property of three-band systems with space-time-inversion symmetry. The charge Formula: see text can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes. We call triple points with nontrivial Formula: see text the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when O
or T
groups protect it. The charge Formula: see text constrains the nodal structure and wavefunction texture around TATP, and can induce anomalous thermal transport of phonons and orbital Hall effect of electrons. Gapless points protected by the Nambu-Goldstone theorem form a new platform to study the topology of band degeneracies.
We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying Z2 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 the π Berry phase, in which a single nodal line can exist, the nodal lines with Z2 monopole charges should always exist in pairs. We show that a pair of nodal lines with Z2 monopole charges is created by a double band inversion process and that the resulting nodal lines are always linked by another nodal line formed between the two topmost occupied bands. It is shown that both the linking structure and the Z2 monopole charge are the manifestation of the nontrivial band topology characterized by the 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 insulator in the absence of Berry phase. Based on this, we propose that pair creation and annihilation of nodal lines with Z2 monopole charges can mediate a topological phase transition between a normal insulator and a three-dimensional weak Stiefel-Whitney insulator. Moreover, using first-principles calculations, we predict ABC-stacked graphdiyne as a nodal line semimetal (NLSM) with Z2 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 Z2 monopole charges under a T-breaking perturbation.
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The spin Hall effect is the transverse flow of the electron spin in response to an external electric field. Similarly, the temperature gradient in magnets can drive a transverse flow of the magnon ...spin, which provides a thermal alternative for spin manipulation. Recently, phonon angular momentum (PAM), the angular momentum of atoms resulting from their orbital motion around their equilibrium positions, has garnered attention as a quantity analogous to the magnon spin. Here, we report that the temperature gradient generally induces a transverse flow of PAM, which we term the phonon angular momentum Hall effect (PAMHE). The PAMHE arises whenever there are transverse and longitudinal acoustic phonons, and it is therefore ubiquitous in condensed matter systems. As a consequence of the PAMHE, PAM accumulates at the crystal edges. When the atoms in the crystal carry a non-zero Born effective charge, the edge PAM induces edge magnetization, which can be observed through optical measurement.
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We theoretically study the intrinsic thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows in-plane ...Dzyaloshinskii–Moriya interaction between the nearest neighbors, which does not affect the linear spin wave theory. However, the Dzyaloshinskii–Moriya interaction induces large Berry curvature in the magnetoelastic excitations through the magnon–phonon interaction (MPI) to produce thermal Hall current. Furthermore, the magnetoelastic excitations transport spin, which is inherited from the magnons. Therefore, spin Nernst current accompanies the thermal Hall current. Because the MPI does not conserve the spin, we examine the spatial distribution of spin induced by a thermal gradient in the system having a stripe geometry. We find that spin is accumulated at the edges, reflecting the spin Nernst current. We also find that the total spin of the systemand, therefore, the magnetizationis changed, because of the thermal gradient and MPI.
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Abstract
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.
Because of the recent development of thin film and artificial superstructure growth techniques, it is possible to control the dimensionality of the system, smoothly between two and three dimensions. ...In this Letter we unveil the dimensional crossover of emergent topological phenomena in correlated topological materials. In particular, by focusing on the thin film of pyrochlore iridate antiferromagnets grown along the 111 direction, we demonstrate that the thin film can have a giant anomalous Hall conductance, proportional to the thickness of the film, even though there is no Hall effect in 3D bulk material. Moreover, in the case of ultrathin films, a quantized anomalous Hall conductance can be observed, despite the fact that the system is an antiferromagnet. In addition, we uncover the emergence of a new topological phase, the nontrivial topological properties of which are hidden in the bulk insulator and manifest only in thin films. This shows that the thin film of correlated topological materials is a new platform to search for unexplored novel topological phenomena.
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Correlated topological phases (CTPs) with interplay between topology and electronic correlations have attracted tremendous interest in condensed matter physics. Therein, correlated Weyl semimetals ...(WSMs) are rare in nature and, thus, have so far been less investigated experimentally. In particular, the experimental realization of the interacting WSM state with logarithmic Fermi velocity renormalization has not been achieved yet. Here, experimental evidence of a correlated magnetic WSM state with logarithmic renormalization in strained pyrochlore iridate Pr2Ir2O7 (PIO) which is a paramagnetic Luttinger semimetal in bulk, is reported. Benefitting from epitaxial strain, “bulk‐absent” all‐in–all‐out antiferromagnetic ordering can be stabilized in PIO film, which breaks time‐reversal symmetry and leads to a magnetic WSM state. With further analysis of the experimental data and renormalization group calculations, an interacting Weyl liquid state with logarithmically renormalized Fermi velocity, similar to that in graphene, is found, dressed by long‐range Coulomb interactions. This work highlights the interplay of strain, magnetism, and topology with electronic correlations, and paves the way for strain‐engineering of CTPs in pyrochlore iridates.
A novel correlated magnetic Weyl semimetal state with logarithmic renormalization is experimentally realized in the high‐quality strained film of Pr2Ir2O7. Strain‐induced all‐in–all‐out antiferromagnetic ordering breaks time‐reversal symmetry and leads to the magnetic Weyl semimetal state. Combing the experimental results and renormalization group calculations, an interacting Weyl semimetal state with logarithmic Fermi velocity renormalization is reported, dressed by long‐range Coulomb interactions.
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