Flat bands with higher Chern number in pyrochlore slabs

Trescher, Maximilian; Bergholtz, Emil J.

doi:10.1103/physrevb.86.241111

Cited by 120 publications

(114 citation statements)

References 40 publications

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“…Although close to experimental limits, the resulting Casimir pressure at such a separation is still within observable bounds [36]. Alternatively, multiorbital [29] or multilayer materials [25,28] with possible larger gaps can bring the force even further within measurable values.…”

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confidence: 99%

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Repulsive Casimir Effect with Chern Insulators

Rodriguez-López

Grushin

2014

Phys. Rev. Lett.

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We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. We show that achieving repulsion is possible with thin films of Cr-doped ðBi; SbÞ 2 Te 3 , that were recently discovered to be Chern insulators with quantized Hall conductivity. DOI: 10.1103/PhysRevLett.112.056804 PACS numbers: 73.23.-b, 03.70.+k, 41.20.-q, 72.20.-i More than half a century after its theoretical prediction, the Casimir effect [1] still stands among the most intriguing quantum phenomena. The relatively recent quantitative experimental access to the physics of this effect [2], the force experienced by objects due to quantum vacuum fluctuations, has revealed that it is still far from being completely understood. Despite the development of useful calculating tools in terms of the scattering formalism [3,4], the possibility of achieving repulsion in vacuum between two material plates is still so far unreachable experimentally. Two dielectrics can repel when immersed in a medium with very specific optical properties [5,6] and no mirror-symmetric situation can give rise to repulsion [7,8]. These restrictions turn the search for repulsion in vacuum into a difficult challenge that can potentially solve stiction issues [2,9]. Earlier proposals include magnetic materials [10], metamaterials [11,12], engineered geometries [13], and quantum Hall effect (QHE) systems [14], where the latter was subsequently generalized to a QHE system made out of doped graphene sheets [15]. In [16,17], the concept of a topological Casimir effect was explored using three-dimensional topological insulators (TI) [18,19], which owing to their topological electromagnetic (EM) response, opened the way to a tunable repulsion. In these works, the finite frequency part of the topological response [20] arising from the EM response encoded in the θ term [21,22] was assumed to be the quantized zero frequency response for all frequencies, which is only valid for certain distance scales depending on material parameters.In this Letter, we propose to achieve and manipulate repulsion by exploring the Casimir force arising due to the topological nature of Chern insulators (CI). These general class of two dimensional materials have a quantized Hall conductivity in the absence of external magnetic field due to the nontrivial topological structure of the Bloch bands [18,19,23]. The Chern number C ∈ Z is the topological attribute of each band that, if finite, indicates a quantized contribution to the Hall conductivity at zero frequency σ xy ð0Þ ¼ Ce 2 =h. ...

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confidence: 99%

“…Our results point towards TI thin films and other systems with higher Chern numbers [25][26][27][28][29] as the most promising future route to realize and control Casimir repulsion.…”

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confidence: 99%

Repulsive Casimir Effect with Chern Insulators

Rodriguez-López

Grushin

2014

Phys. Rev. Lett.

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“…Up to now, extreme conditions including ultralow temperature (<2 K) are still required to observe the QAH effect. In addition, QAH insulators with |C| > 1 are not well explored and most of these studies are limited to toy model analysis [21][22][23].…”

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confidence: 99%

Atomically dispersed tungsten on metal halide monolayer as a ferromagnetic Chern insulator

et al. 2018

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“…to recently discovered fractional Chern insulators (FCIs) [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] because of the adiabatic continuity between Hofstadter and Chern insulator states [34][35][36]. Additionally, we study a one-dimensional lattice model for which our generalized Hofstadter model can be regarded as a two-dimensional ancestor.…”

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confidence: 99%

“…These states are expected to be similar to FCIs in topological flat bands, although the net magnetic field is nonzero in our model (a gauge transformation can be used to obtain a zero net magnetic field [34]). We adopt some commonly used criteria, such as the ground-state topological degeneracy, the spectral flow under twisted boundary conditions, and the particle-cut entanglement spectrum, to identify the ground states as FQH states [19][20][21][22][23][24][25][26][27][28][29][30][31].…”

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Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices

et al. 2013

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Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C| = 1 and |C| > 1 bands is confirmed which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.

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Flat bands with higher Chern number in pyrochlore slabs

Cited by 120 publications

References 40 publications

Repulsive Casimir Effect with Chern Insulators

Repulsive Casimir Effect with Chern Insulators

Atomically dispersed tungsten on metal halide monolayer as a ferromagnetic Chern insulator

Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices

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