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Register a new userPhonon helicity and Nieh-Yan Anomaly in the Kramers-Weyl semimetals of Chiral Crystals
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Chao-Xing Liu
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Nieh-Yan anomaly describes the non-conservation of chiral charges induced by the coupling between Dirac fermions and torsion fields. Since the torsion field is beyond general relativity, this effect remains hypothetical and its relevance to our universe is unclear in the context of high-energy physics. In this work, we propose that the phonons can induce a torsion field for the Kramers-Weyl fermions through electron-phonon interaction in a non-magnetic chiral crystal, thus leading to the occurrence of the Nieh-Yan anomaly in this condensed matter system. As a consequence, the Nieh-Yan term can strongly influence the phonon dynamics and lead to the helicity of acoustic phonons, namely, two transverse phonon modes mix with each other to form a circular polarization with a non-zero angular momentum at a finite phonon momentum and the phonon angular momentum reverses its sign for opposite momenta due to time reversal symmetry. The phonon helicity can be probed through measuring the total phonon angular momentum driven by a temperature gradient.
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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 $Lambda$, with canonical dimensions of momentum. Comparison of the anomaly equation and the hydrodynamic equations suggests that the value of the cut-off parameter $Lambda$ is determined by the normal state Fermi liquid and non-relativistic uniaxial symmetry of the $p$-wave superfluid or superconductor.
Recently, the existence of massless chiral (Weyl) fermions has been postulated in a class of semi-metals with a non-trivial energy dispersion.These materials are now commonly dubbed Weyl semi-metals (WSM).One predicted property of Weyl fermions is the chiral or Adler-Bell-Jackiw anomaly, a chirality imbalance in the presence of parallel magnetic and electric fields. In WSM, it is expected to induce a negative longitudinal magnetoresistance (NMR), the chiral magnetic effect.Here, we present experimental evidence that the observation of the chiral magnetic effect can be hindered by an effect called current jetting. This effect also leads to a strong apparent NMR, but it is characterized by a highly non-uniform current distribution inside the sample. It appears in materials possessing a large field-induced anisotropy of the resistivity tensor, such as almost compensated high-mobility semimetals due to the orbital effect.In case of a non-homogeneous current injection, the potential distribution is strongly distorted in the sample.As a consequence, an experimentally measured potential difference is not proportional to the intrinsic resistance.Our results on the MR of the WSM candidate materials NbP, NbAs, TaAs, TaP exhibit distinct signatures of an inhomogeneous current distribution, such as a field-induced zero resistance and a strong dependence of the `measured resistance on the position, shape, and type of the voltage and current contacts on the sample. A misalignment between the current and the magnetic-field directions can even induce a negative resistance. Finite-element simulations of the potential distribution inside the sample, using typical resistance anisotropies, are in good agreement with the experimental findings. Our study demonstrates that great care must be taken before interpreting measurements of a NMR as evidence for the chiral anomaly in putative Weyl semimetals.
Chiral anomaly induced negative magnetoresistance (NMR) has been widely used as a critical transport evidence on the existence of Weyl fermions in topological semimetals. In this mini review, we discuss the general observation of the NMR phenomena in non-centrosymmetric NbP and NbAs. We show that NMR can be contributed by intrinsic chiral anomaly of Weyl fermions and/or extrinsic effects, such as superimposition of Hall signals, field-dependent inhomogeneous current flow in the bulk, i.e. current jetting, and weak localization (WL) of coexistent trivial carriers. Such WL controlled NMR is heavily dependent on sample quality, and is characterized by pronounced crossover from positive to negative MR growth at elevated temperatures, as a result of the competition between the phase coherence time and the spin-orbital scattering constant of the bulk trivial pockets. Thus, the correlation of NMR and chiral anomaly needs to be scrutinized, without the support of other complimentary techniques. Due to the lifting of spin degeneracy, the spin orientations of Weyl fermions are either parallel or antiparallel to the momentum, a unique physical property known as helicity. The conservation of helicity provides strong protection for the transport of Weyl fermions, which can only be effectively scattered by magnetic impurities. Chemical doping of magnetic and non-magnetic impurities are thus more convincing in probing the existence of Weyl fermions than the NMR method.
We show that Weyl semimetals exhibit a mixed axial-torsional anomaly in the presence of axial torsion, a concept exclusive of these materials with no known natural fundamental interpretation in terms of the geometry of spacetime. This anomaly implies a nonconservation of the axial current---the difference in current of left- and right-handed chiral fermions---when the torsion of the spacetime in which the Weyl fermions move couples with opposite sign to different chiralities. The anomaly is activated by driving transverse sound waves through a Weyl semimetal with a spatially varying tilted dispersion, which can be engineered by applying strain. This leads to sizable alternating current in presence of a magnetic field that provides a clear-cut experimental signature of our predictions.
In this paper, the chiral Hall effect of strained Weyl semimetals without any external magnetic field is proposed. Electron-phonon coupling emerges in the low-energy fermionic sector through a pseudogauge potential. We show that, by using chiral kinetic theory, the chiral Hall effect appears as a response to a real time-varying electric field in the presence of structural distortion and it causes spatial chirality and charges separation in a Weyl system. We also show that the coupling of the electrons to acoustic phonons as a gapless excitation leads to emerging an optical absorption peak at $omega=omega_{el}$, where $omega_{el}$ is defined as a characteristic frequency associated with the pseudomagnetic field. We also propose the strain-induced planar Hall effect as another transport signature of the chiral-anomaly equation.
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