Mixed Axial-Torsional Anomaly in Weyl Semimetals

Ferreirós, Yago; Kedem, Yaron; Bergholtz, Emil J.; Bardarson, Jensen. H.

doi:10.1103/physrevlett.122.056601

Cited by 58 publications

(61 citation statements)

References 86 publications

(110 reference statements)

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“…We note that the early papers [10][11][12] and [5,49] treat the anomaly in terms of an axial gauge field ∼ ±p Fl and the tetrad e a µ , leading to the requirement Λ = 0 in saturating the anomaly [81], in contrast to [67,68]. This is distinct from the emergent spacetime (14) or considerations of other systems, where such fields contribute only to a single anomaly [69,70,72].…”

Section: Pacs Numbersmentioning

confidence: 98%

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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: 98%

“…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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“…They can emerge from dislocations [2][3][4][5], temperature gradient [6][7][8][9] and background rotation. Especially, in the Dirac and Weyl semimetals, due to their gapless spectrum and strong spin-orbit coupling [10,11], torsion has led to rich physical phenomena, for example, chiral zero modes trapped in dislocations [12,13], the chiral torsional magnetic effect [14] and other viscoelastic responses [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Nieh-Yan anomaly: Torsional Landau levels, central charge, and anomalous thermal Hall effect

2020

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The Nieh-Yan anomaly is the anomalous breakdown of the chiral U(1) symmetry caused by the interaction between torsion and fermions. We study this anomaly from the point of view of torsional Landau levels. It was found that the torsional Landau levels are gapless, while their contributions to the chiral anomaly are canceled, except those from the lowest torsional Landau levels. Hence, the dimension is effectively reduced from (3+1)d to (1+1)d. We further show that the coefficient of the Nieh-Yan anomaly is the free energy density in (1+1)d. Especially, at finite temperature, the thermal Nieh-Yan anomaly is proportional to the central charge. The anomalous thermal Hall conductance in Weyl semimetals is then shown to be proportional to the central charge, which is the experimental fingerprint of the thermal Nieh-Yan anomaly. * zeminh2@illinois.edu[1] F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys. 48, 393 (1976).

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“…(4) has far-reaching physical consequences. Here we focus on the torsion-induced effects which have attracted significant attention recently [3,[5][6][7][8][24][25][26][27][28][29][30][31][32][33][34]. It has been shown that the torsion gives a contribution to the chiral anomaly [2] through the Nieh-Yan term [35], which in the absence of spin connection reads…”

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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Mixed Axial-Torsional Anomaly in Weyl Semimetals

Cited by 58 publications

References 86 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

Nieh-Yan anomaly: Torsional Landau levels, central charge, and anomalous thermal Hall effect

Topological magnetotorsional effect in Weyl semimetals

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