Designer Curved-Space Geometry for Relativistic Fermions in Weyl Metamaterials

Westström, Alex; Ojanen, Teemu

doi:10.1103/physrevx.7.041026

Cited by 58 publications

(76 citation statements)

References 57 publications

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“…66. Related recent work discusses emergent tetrads, gauge fields and anomaly terms in Weyl SFs [67,68] and semimetals [69][70][71][72][73][74], without the framework of emergent conservation laws and geometry.…”

Section: Pacs Numbersmentioning

confidence: 99%

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Nissinen

2020

Phys. Rev. Lett.

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Momentum transport is anomalous in chiral p + ip superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin-connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticles and they satisfy the conservation laws associated with local Lorentz symmetry, restricted to the plane of uniaxial anisotropy of the superfluid (or -conductor). Moreover, we show that the anomalous Galilean momentum conservation is a consequence of the gravitational Nieh-Yan (NY) chiral anomaly the Weyl fermions experience on the background geometry. Notably, the NY anomaly coefficient features a non-universal ultraviolet cut-off scale Λ, with canonical dimensions of momentum. Comparison of the anomaly equation and the hydrodynamic equations suggests that the value of the cut-off parameter Λ is determined by the normal state Fermi liquid and non-relativistic uniaxial symmetry of the p-wave superfluid or superconductor. PACS numbers:Introduction. -Topological phases can be classified in terms of quantum anomalies that are robust to interactions and other perturbations [1-3]. Protected emergent quasi-relativistic fermi excitations coupled to gauge fields and geometry arise as dictated by topology and anomaly inflow [4][5][6]. In particular gapless fermions with Weyl spectrum and chiral anomalies are a recent prominent example [7][8][9][10][11][12][13][14][15][16]. On the other hand, topological phases and their coupling to geometry (and gravity) is currently a rapidly advancing subject. The well-established results concern the Hall viscosity [17] and chiral central charge [18][19][20] related to gravitational anomalies [21][22][23] and thermal transport in quantum Hall systems, topological superfluids (SFs) and superconductors (SCs), as well as semimetals [24-48, 66, 72, 83], the case of SFs and SCs being especially important due to the lack of conserved charge. Any purported topological response of geometrical origin is necessary more subtle than that based on gauge fields with conserved charges due to the inherent dichotomy between topology and geometry.Topologically protected Weyl quasiparticles arise also in three-dimensional chiral p-wave SFs and SCs [5,49]. As any chiral fermion in three dimensions, they suffer from the chiral anomaly in the presence of non-trivial background fields, now as an anomaly where momentum is transferred from the order parameter fluctuations to the quasiparticles [49-55],

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Section: Pacs Numbersmentioning

confidence: 99%

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Nissinen

2020

Phys. Rev. Lett.

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“…As established in Refs. [9,10], smoothly varying magnetization will give rise to a lowenergy description in terms of locally varying frame fields. As discussed in the present work, the effective geometry encoded in frame fields admit non-vanishing torsion.…”

Section: Introduction-mentioning

confidence: 99%

“…Following the general method introduced in Refs. [9,10], we block diagonalize the parent Hamiltonian [for details, see the supplemental information (SI)]. This leads to an effective Weyl Hamiltonian,…”

Section: Introduction-mentioning

confidence: 99%

Topological magnetotorsional effect in Weyl semimetals

Liang

Ojanen

2020

Phys. Rev. Research

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In this work we introduce a thermal magnetotorsional effect (TME) as a novel topological response in magnetic Weyl semimetals. We predict that magnetization gradients perpendicular to the Weyl node separation give rise to temperature gradients depending only on the local positions of the Weyl nodes. The TME is a consequence of magnetization-induced effective torsional spacetime geometry and the finite temperature Nieh-Yan anomaly. Similarly to anomalous Hall effect and chiral anomaly, the TME has a universal material-independent form. We predict that the TME can be observed in magnetic Weyl semimetal EuCd2As2.

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“…In translationally invariant systems the two-fold band-touching in Weyl semimetals can be associated with a conserved Berry charge which is topologically protected. Moreover, even in the presence of spatially varying perturbations the low-energy properties can be understood in terms of Weyl particles experiencing artificial gravity and gauge fields [23]. The condensed-matter setting allows for remarkable opportunities in engineering synthetic gauge fields and geometries that mimic and generalize the phenomenology of high-energy physics [16,[24][25][26][27][28][29][30][31][32][33][34].…”

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confidence: 99%

Curved spacetime theory of inhomogeneous Weyl materials

Liang

Ojanen

2019

Phys. Rev. Research

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We show how the universal low-energy properties of Weyl semimetals with spatially varying timereversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-spacetime geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.arXiv:1906.07540v1 [cond-mat.mes-hall]

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Designer Curved-Space Geometry for Relativistic Fermions in Weyl Metamaterials

Cited by 58 publications

References 57 publications

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Topological magnetotorsional effect in Weyl semimetals

Curved spacetime theory of inhomogeneous Weyl materials

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