Topological mechanics

Huber, Sebastian

doi:10.1038/nphys3801

Cited by 665 publications

(459 citation statements)

References 35 publications

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“…Although first studied in solid-state materials, there has been great progress in exploring QH physics also with ultracold atoms [5][6][7][8][9][10], photons [11][12][13], classical circuits [14,15] and mechanical systems [16][17][18], where the magnetic field effects must be engineered artificially [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Synthetic dimensions for cold atoms from shaking a harmonic trap

2017

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We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time-modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realisation of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.

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Section: Introductionmentioning

confidence: 99%

Synthetic dimensions for cold atoms from shaking a harmonic trap

2017

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“…As learned from electrons, the QH and QAH effects are characterized by a topological invariant called Chern number of the first class, which is defined as an integration of the Berry curvature over the Brillouin zone and can be nonzero only for broken TRS [12]. Nontrivial topological states with nonzero Chern number have been well established for photons [13][14][15] and recently reported for phonons, acoustic or mechanical systems [16][17][18][19][20][21][22][23][24][25][26][27]. As demonstrated by these previous works, topological quantities (like Berry curvature, Berry phase and Chern number) are independent of particle statistics and can be defined for phonons as for electrons.…”

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confidence: 99%

“…As demonstrated by these previous works, topological quantities (like Berry curvature, Berry phase and Chern number) are independent of particle statistics and can be defined for phonons as for electrons. The phononic states with nonzero Chern number give the Q(A)H-like edge states of phonons, which are topologically protected to be gapless, one-way and immune to backscattering [16][17][18][19][20][21][22][23][24][25][26][27].…”

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confidence: 99%

Model for topological phononics and phonon diode

Liu¹,

Xu²,

Zhang³

et al. 2017

Phys. Rev. B

148

156

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The quantum anomalous Hall effect, an exotic topological state first theoretically predicted by Haldane and recently experimentally observed, has attracted enormous interest for low-power-consumption electronics. In this work, we derived a Schrödinger-like equation of phonons, where topology-related quantities, time reversal symmetry and its breaking can be naturally introduced similar as for electrons. Furthermore, we proposed a phononic analog of the Haldane model, which gives the novel quantum (anomalous) Halllike phonon states characterized by one-way gapless edge modes immune to scattering. The topologically nontrivial phonon states are useful not only for conducting phonons without dissipation but also for designing highly efficient phononic devices, like an ideal phonon diode, which could find important applications in future phononics.

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“…Recently, new mechanical systems with emergent functionalities, so-called mechanical metamaterials, have been inspired by topological insulators, in which only the surface boundaries can behave as conductors [69]. Small mechanically asymmetric building blocks are combined, and it is now possible to create materials with unusual order and machine-like functionalities (e.g., using 3D printers) [70,71].…”

Section: Discussionmentioning

confidence: 99%

Snap-buckling in asymmetrically constrained elastic strips

Sano

Wada

2018

Phys. Rev. E

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When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking and forms a cylindrical arc, a phenomenon well known as Euler buckling. When this cylindrical section is pushed in the other direction, the bending direction can suddenly reverse. This instability is called snap-through buckling and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constraints break the intrinsic symmetry of the strip, generating rich exotic mechanical behaviors including largely hysteretic but reproducible force responses and switch-like discontinuous shape changes. We establish the set of exact analytical solutions that fully explain all of our major experimental and numerical findings. Asymmetric boundary conditions arise naturally in diverse situations when a thin object is in contact with a solid surface at one end, but their profound consequences for the buckling mechanics have been largely overlooked to date. The idea of introducing asymmetry through boundary conditions would yield new insight into complex and programmable functionalities in material and industrial design.

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Topological mechanics

Abstract: Electronic topological insulators have inspired the design of new mechanical systems that could soon find real-life applications.

Cited by 665 publications

References 35 publications

Synthetic dimensions for cold atoms from shaking a harmonic trap

Synthetic dimensions for cold atoms from shaking a harmonic trap

Model for topological phononics and phonon diode

Snap-buckling in asymmetrically constrained elastic strips

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