Four-dimensional topological lattices through connectivity

Price, Hannah M.

doi:10.1103/physrevb.101.205141

Cited by 20 publications

(10 citation statements)

References 63 publications

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“…This is a peculiar topological effect associated to the existence of quantized topological currents in four-dimensional (4D) semimetals. This effect could be measured in quantum-engineered settings using a synthetic dimension [52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

2020

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Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. In this work, we introduce a model describing a semimetal in four spatial dimensions, whose nodal points act like tensor monopoles in momentum space. This system is shown to exhibit monopole-to-monopole phase transitions, as signaled by a change in the value of the topological Dixmier-Douady invariant as well as by the associated surface states on its boundary. We use this model to reveal an intriguing "4D parity magnetic effect," which stems from a parity-type anomaly. In this effect, topological currents are induced upon time modulating the separation between the fictitious monopoles in the presence of a magnetic perturbation. Besides its theoretical implications in both condensed matter and quantum field theory, the peculiar four-dimensional (4D) magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.

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Section: Introductionmentioning

confidence: 99%

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

2020

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“…In those circuits, topological zero modes manifest themselves through a divergent impedance which we call topolectrical resonances. Finally, but not least, electronic circuits provide possibilities to simulate nodal lines and drumhead states beyond three dimensions, in an analogous way as simulating topological insulators in Class AI with electronic circuits in four dimensions [181,182].…”

Section: B Phononic Crystalsmentioning

confidence: 99%

Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems

Park¹,

Gao²,

Zhang³

et al. 2022

Preprint

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Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in momentum space, remain less explored. Here, we explain the theoretical concept of topological nodal lines and review recent and ongoing progress using artificial materials. The review includes recent demonstrations of non-Abelian topological charges of nodal lines in momentum space and examples of nodal lines realized in photonic and other systems. Finally, we will address the challenges involved in both experimental demonstration and theoretical understanding of topological nodal lines.

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“…( 1) can be realized by using the four hyperfine ground states of rubidium-87 atoms coupled with radio-frequency and microwave fields [27]. Electric circuits [28][29][30] can also be used to implement the four-band Hamiltonian. Now we consider how to extract the quantum metric in our degenerate system.…”

Section: Such a Matrix Can Be Decomposed Into The Product Of A Matrixmentioning

confidence: 99%

Revealing Chern number from quantum metric

Zhang

2021

Preprint

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Chern number is usually characterized by Berry curvature. Here, we give the general relation between Berry curvature and quantum metric, which indicates that the Chern number is also encoded in quantum metric as well as the surface area of Brillouin zone on the hypersphere embedded in Euclidean parameter space. We find that there is a corresponding relationship between the quantum metric and the metric on such a hypersphere. We show how the vacuum field equation with a "cosmological constant" emerge naturally from our system. Besides, we give a protocol to measure the quantum metric in the degenerate system.

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Four-dimensional topological lattices through connectivity

Cited by 20 publications

References 63 publications

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems

Revealing Chern number from quantum metric

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