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, Volume:
12, Issue:
1
Journal Article
Peer reviewed
Open access
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.
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.
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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.
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