scholarly journals Tensor Monopoles in superconducting systems

Quantum ◽  
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.

scholarly journals Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Bruno Mera ◽  
Anwei Zhang ◽  
Nathan Goldman
Keyword(s):  
Quantum Physics ◽  
Berry Phase ◽  
Broad Class ◽  
Topological States Of Matter ◽  
Quantum Geometry ◽  
Special Cases ◽  
Chern Numbers ◽  
Spatial Dimensions ◽  
Topological States ◽  
Engineered Systems

Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles:~the Fubini-Study metric, which introduces a notion of distance between quantum states defined over a parameter space, and the Berry curvature associated with Berry-phase effects and topological band structures. In fact, recent studies have revealed direct relations between these two important quantities, suggesting that topological properties can, in special cases, be deduced from the quantum metric. In this work, we establish general and exact relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. In particular, we demonstrate that topological indices (Chern numbers or winding numbers) are bounded by the quantum volume determined by the quantum metric. Our theoretical framework, which builds on the Clifford algebra of Dirac matrices, is applicable to topological insulators and semimetals of arbitrary spatial dimensions, with or without chiral symmetry. This work clarifies the role of the Fubini-Study metric in topological states of matter, suggesting unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.

scholarly journals Experimental measurement of the quantum geometric tensor using coupled qubits in diamond

2019 ◽  
Vol 7 (2) ◽  
pp. 254-260 ◽  
Author(s):  
Min Yu ◽  
Pengcheng Yang ◽  
Musang Gong ◽  
Qingyun Cao ◽  
Qiuyu Lu ◽  
...  
Keyword(s):  
Experimental Measurement ◽  
Topological States Of Matter ◽  
Topological Defects ◽  
Quantum Geometry ◽  
And Topology ◽  
Wide Range ◽  
Nv Center ◽  
Topological States ◽  
Physical Phenomena ◽  
Complete Quantum

Abstract Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.

scholarly journals Towards the manipulation of topological states of matter: a perspective from electron transport

2018 ◽  
Vol 63 (9) ◽  
pp. 580-594 ◽  
Author(s):  
Cheng Zhang ◽  
Hai-Zhou Lu ◽  
Shun-Qing Shen ◽  
Yong P. Chen ◽  
Faxian Xiu
Keyword(s):  
Electron Transport ◽  
Topological States Of Matter ◽  
Topological States

On the topological structure of the vacuum in SU(2) and SU(3) lattice gauge theories

1983 ◽  
Vol 128 (5) ◽  
pp. 309-315 ◽  
Author(s):  
K. Ishikawa ◽  
G. Schierholz ◽  
H. Schneider ◽  
M. Teper
Keyword(s):  
Topological Structure ◽  
Gauge Theories ◽  
Lattice Gauge ◽  
Lattice Gauge Theories

scholarly journals Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO2 and RuO2

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Sheng-Shiuan Yeh ◽  
Ta-Kang Su ◽  
An-Shao Lien ◽  
Farzaneh Zamani ◽  
Johann Kroha ◽  
...  
Keyword(s):  
Kondo Effect ◽  
High Temperature Superconductivity ◽  
Topological States Of Matter ◽  
Nodal Line ◽  
Metallic State ◽  
Strong Electron ◽  
Quantum Matter ◽  
Kondo Physics ◽  
Topological States ◽  
Weak Coupling Theory

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.

scholarly journals Topological transitions in an oscillatory driven liquid crystal cell

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.

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

2020 ◽  
Vol 11 (1) ◽  
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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