Topological states of matter

Abstract Strong electron correlations have long been recognized as driving the emergence of novel phases of matter. A well recognized example is high-temperature superconductivity which cannot be understood in terms of the standard weak-coupling theory. The exotic properties that accompany the formation of the two-channel Kondo (2CK) effect, including the emergence of an unconventional metallic state in the low-energy limit, also originate from strong electron interactions. Despite its paradigmatic role for the formation of non-standard metal behavior, the stringent conditions required for its emergence have made the observation of the nonmagnetic, orbital 2CK effect in real quantum materials difficult, if not impossible. We report the observation of orbital one- and two-channel Kondo physics in the symmetry-enforced Dirac nodal line (DNL) metals IrO2 and RuO2 nanowires and show that the symmetries that enforce the existence of DNLs also promote the formation of nonmagnetic Kondo correlations. Rutile oxide nanostructures thus form a versatile quantum matter platform to engineer and explore intrinsic, interacting topological states of matter.

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Topological transitions in an oscillatory driven liquid crystal cell

Scientific Reports ◽

10.1038/s41598-020-75165-8 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Marcel G. Clerc ◽

Michał Kowalczyk ◽

Valeska Zambra

Keyword(s):

Liquid Crystal ◽

Topological States Of Matter ◽

Low Frequency ◽

Vortex State ◽

Liquid Crystal Cell ◽

Topological Transition ◽

Exotic States ◽

Crystal Cell ◽

Topological States ◽

Topological Transitions

Abstract Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose–Einstein condensates, superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. These topological states can persist out of thermodynamics equilibrium. Here we investigate topological states of matter in a system with injection and dissipation of energy by means of oscillatory forcing. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from a non-vortex state to a state in which vortices persist, topological transition. Depending on the period and the type of the forcing, the vortices self-organise, forming square lattices, glassy states, and disordered vortex structures. The bifurcation diagram is characterised experimentally. A continuous topological transition is observed for the sawtooth and square forcings. The scenario changes dramatically for sinusoidal forcing where the topological transition is discontinuous, which is accompanied by serial transitions between square and glassy vortex lattices. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Numerical simulations show topological transitions and the emergence of square vortex lattice. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states.

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Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals

Nature Communications ◽

10.1038/s41467-019-13861-4 ◽

2020 ◽

Vol 11 (1) ◽

Cited By ~ 14

Author(s):

Xiujuan Zhang ◽

Zhi-Kang Lin ◽

Hai-Xiao Wang ◽

Zhan Xiong ◽

Yuan Tian ◽

...

Keyword(s):

Band Gap ◽

Topological States Of Matter ◽

Quantum Spin ◽

Band Gaps ◽

Quantum Spin Hall Effect ◽

Classical Systems ◽

Topological Materials ◽

And Topology ◽

Topological States ◽

Symmetry Protected

AbstractSymmetry and topology are two fundamental aspects of many quantum states of matter. Recently new topological materials, higher-order topological insulators, were discovered, featuring bulk–edge–corner correspondence that goes beyond the conventional topological paradigms. Here we discover experimentally that the nonsymmorphic p4g acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, whereas the second band gap exhibits quadrupole topology with anomalous Wannier bands. Such a topological hierarchy allows us to observe experimentally distinct, multiplexed topological phenomena and to reveal a topological transition triggered by the geometry transition from the p4g group to the C4v group, which demonstrates elegantly the fundamental interplay between symmetry and topology. Our study demonstrates that classical systems with controllable geometry can serve as powerful simulators for the discovery of novel topological states of matter and their phase transitions.

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Novel topological states of nodal points and nodal rings in 2D planar octagon TiB4

Nanoscale ◽

10.1039/d0nr08015b ◽

2021 ◽

Vol 13 (5) ◽

pp. 3194-3200

Author(s):

Weizhen Meng ◽

Wei Liu ◽

Xiaoming Zhang ◽

Ying Liu ◽

Xuefang Dai ◽

...

Keyword(s):

2D Materials ◽

Topological States Of Matter ◽

Two Dimensional ◽

Nodal Points ◽

Potential Applications ◽

Topological States

Topological states of matter in two-dimensional (2D) materials have received increasing attention due to their potential applications in nanoscale spintronics.

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From the adiabatic theorem of quantum mechanics to topological states of matter

physica status solidi (RRL) - Rapid Research Letters ◽

10.1002/pssr.201206416 ◽

2013 ◽

Vol 7 (1-2) ◽

pp. 109-129 ◽

Cited By ~ 48

Author(s):

Jan Carl Budich ◽

Björn Trauzettel

Keyword(s):

Quantum Mechanics ◽

Topological States Of Matter ◽

Adiabatic Theorem ◽

Topological States

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Tensor Monopoles in superconducting systems

Quantum ◽

10.22331/q-2021-12-07-601 ◽

2021 ◽

Vol 5 ◽

pp. 601

Author(s):

H. Weisbrich ◽

M. Bestler ◽

W. Belzig

Keyword(s):

Topological Structure ◽

Gauge Theories ◽

Topological States Of Matter ◽

Three Dimensions ◽

Gauge Fields ◽

Quantum Geometry ◽

Central Concept ◽

Dirac Monopole ◽

Topological States ◽

Phase Differences

Topology in general but also topological objects such as monopoles are a central concept in physics. They are prime examples for the intriguing physics of gauge theories and topological states of matter. Vector monopoles are already frequently discussed such as the well-established Dirac monopole in three dimensions. Less known are tensor monopoles giving rise to tensor gauge fields. Here we report that tensor monopoles can potentially be realized in superconducting multi-terminal systems using the phase differences between superconductors as synthetic dimensions. In a first proposal we suggest a circuit of superconducting islands featuring charge states to realize a tensor monopole. As a second example we propose a triple dot system coupled to multiple superconductors that also gives rise to such a topological structure. All proposals can be implemented with current experimental means and the monopole readily be detected by measuring the quantum geometry.

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Coexisting Edge States and Gapless Bulk in Topological States of Matter

Physical Review Letters ◽

10.1103/physrevlett.114.136801 ◽

2015 ◽

Vol 114 (13) ◽

Cited By ~ 26

Author(s):

Yuval Baum ◽

Thore Posske ◽

Ion Cosma Fulga ◽

Björn Trauzettel ◽

Ady Stern

Keyword(s):

Topological States Of Matter ◽

Edge States ◽

Topological States

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Pressure-induced phase transitions and superconductivity in a quasi–1-dimensional topological crystalline insulator α-Bi4Br4

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1909276116 ◽

2019 ◽

Vol 116 (36) ◽

pp. 17696-17700 ◽

Cited By ~ 4

Author(s):

Xiang Li ◽

Dongyun Chen ◽

Meiling Jin ◽

Dashuai Ma ◽

Yanfeng Ge ◽

...

Keyword(s):

Phase Transitions ◽

Topological States Of Matter ◽

Rotational Symmetry ◽

Structural Phase ◽

Research Field ◽

X Ray Diffraction ◽

Insulator Metal Transition ◽

Topological States ◽

Symmetry Protected ◽

Topological Crystalline Insulator

Great progress has been achieved in the research field of topological states of matter during the past decade. Recently, a quasi–1-dimensional bismuth bromide, Bi4Br4, has been predicted to be a rotational symmetry-protected topological crystalline insulator; it would also exhibit more exotic topological properties under pressure. Here, we report a thorough study of phase transitions and superconductivity in a quasihydrostatically pressurized α-Bi4Br4 crystal by performing detailed measurements of electrical resistance, alternating current magnetic susceptibility, and in situ high-pressure single-crystal X-ray diffraction together with first principles calculations. We find a pressure-induced insulator–metal transition between ∼3.0 and 3.8 GPa where valence and conduction bands cross the Fermi level to form a set of small pockets of holes and electrons. With further increase of pressure, 2 superconductive transitions emerge. One shows a sharp resistance drop to 0 near 6.8 K at 3.8 GPa; the transition temperature gradually lowers with increasing pressure and completely vanishes above 12.0 GPa. Another transition sets in around 9.0 K at 5.5 GPa and persists up to the highest pressure of 45.0 GPa studied in this work. Intriguingly, we find that the first superconducting phase might coexist with a nontrivial rotational symmetry-protected topology in the pressure range of ∼3.8 to 4.3 GPa; the second one is associated with a structural phase transition from monoclinic C2/m to triclinic P-1 symmetry.

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