We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ...ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.
Lattice geometry, topological electron behaviour and the competition between different possible ground states all play a role in determining the properties of materials with a kagome lattice ...structure. In particular, the compounds KV3Sb5, CsV3Sb5 and RbV3Sb5 all feature a kagome net of vanadium atoms. These materials have recently been shown to exhibit superconductivity at low temperature and an unusual charge order at high temperature, revealing a connection to the underlying topological nature of the band structure. We highlight these discoveries, place them in the context of wider research efforts in topological physics and superconductivity, and discuss the open problems for this field.Superconductivity and ordered states formed by interactions—both of which could be unconventional—have recently been observed in a family of kagome materials.
Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1–4. A charge-density-wave-like order with orbital currents has been proposed for achieving the ...quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.An unconventional chiral charge order is observed in a kagome superconductor by scanning tunnelling microscopy. This charge order has unusual magnetic tunability and intertwines with electronic topology.
Exceptional topological insulators Denner, M Michael; Skurativska, Anastasiia; Schindler, Frank ...
Nature communications,
09/2021, Letnik:
12, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the ...three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, ...but protected modes at corners or hinges. Here, we explore symmetry-protected topological phases in strongly interacting many-body systems with this generalized bulk-boundary correspondence. We introduce several exactly solvable bosonic lattice models as candidates for interacting higher-order symmetry-protected topological (HOSPT) phases protected by spatial symmetries, and develop a topological field theory that captures the nontrivial nature of the gapless corner and hinge modes. We show how, for rotational symmetry, this field theory leads to a natural relationship between HOSPT phases and conventional SPT phases with an enlarged internal symmetry group. We also explore the connection between bosonic and fermionic HOSPT phases in the presence of strong interactions, and comment on the implications of this connection for the classification of interacting fermionic HOSPT phases. Finally, we explore how gauging internal symmetries of these phases leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations and geometrical defects related to the spatial symmetry.
Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, ...topological quantum chemistry, and the method of symmetry-based indicators. Despite having a symmetric, exponentially localized Wannier representation, each Wannier function cannot be completely localized to a single primitive unit cell in the bulk. Such multicellular topology is shown to be neither stable nor fragile, but delicate; i.e., the topology can be nullified by adding trivial bands to either valence or conduction band.
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological ...crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.
We expand the phase diagram of two-dimensional, nonsymmorphic crystals at integer fillings that do not guarantee gaplessness. In addition to the trivial, gapped phase that is expected, we find that ...band inversion leads to a class of topological, gapless phases. These topological phases are exemplified by the monolayers of MTe2 (M=W,Mo ) if spin-orbit coupling is neglected. We characterize the Dirac band touching of these topological metals by the Wilson loop of the non-Abelian Berry gauge field. Furthermore, we develop a criterion for the proximity of these topological metals to 2D and 3D Z2 topological insulators when spin-orbit coupling is included; our criterion is based on nonsymmorphic symmetry eigenvalues, and may be used to identify topological materials without inversion symmetry. An additional feature of the Dirac cone in monolayer MTe2 is that it tilts over in a Lifshitz transition to produce electron and hole pockets—a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently reported, nonsaturating magnetoresistance in WTe2 , as well as its circular dichroism in photoemission. We complement our analysis and first-principles band structure calculations with an ab-initio-derived tight-binding model for the WTe2 monolayer.
Entanglement properties are routinely used to characterize phases of quantum matter in theoretical computations. For example, the spectrum of the reduced density matrix, or so-called "entanglement ...spectrum", has become a widely used diagnostic for universal topological properties of quantum phases. However, while being convenient to calculate theoretically, it is notoriously hard to measure in experiments. Here, we use the IBM quantum computer to make the first ever measurement of the entanglement spectrum of a symmetry-protected topological state. We are able to distinguish its entanglement spectrum from those we measure for trivial and long-range ordered states.
Electronic systems with flat bands are predicted to be a fertile ground for hosting emergent phenomena including unconventional magnetism and superconductivity1–15, but materials that manifest this ...feature are rare. Here, we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co3Sn2S2 (refs. 16–20). We observe a pronounced peak at the Fermi level, which we identify as arising from the kinetically frustrated kagome flat band. On increasing the magnetic field up to ±8 T, this state exhibits an anomalous magnetization-polarized many-body Zeeman shift, dominated by an orbital moment that is opposite to the field direction. Such negative magnetism is induced by spin–orbit-coupling quantum phase effects21–25 tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of a kagome magnet where the low-energy physics can be dominated by the spin–orbit-coupled flat band.The authors show that a magnetic material with kagome lattice planes hosts a flat band near the Fermi level. Electrons in this band exhibit ‘negative magnetism’ due to the Berry curvature.
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