Vector and bidirector representations of magnetic point groups

Erb, K. C.; Hlinka, J.

doi:10.1080/01411594.2019.1695256

Cited by 12 publications

(8 citation statements)

References 15 publications

(21 reference statements)

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“…Specifically, the two-fold rotations with rotation vector in the xy plane and the mirror reflections with normal vector in the xy plane are multiplied by time reversal. The irreps are formally the same as for D 4h since the groups are isomorphic [38].…”

Section: Model Systemmentioning

confidence: 99%

Distortional weak-coupling instability of Bogoliubov Fermi surfaces

2021

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Centrosymmetric multiband superconductors which break time-reversal symmetry generically have two-dimensional nodes, i.e., Fermi surfaces of Bogoliubov quasiparticles. We show that the coupling of the electrons to the lattice always leads to a weak-coupling instability of such a state towards spontaneous breaking of inversion symmetry at low temperatures. This instability is driven by a Cooper logarithm in the internal energy but the order parameter is not superconducting but distortional. We present a comprehensive symmetry analysis and introduce a measure that allows to compare the strengths of competing distortional instabilities. Moreover, we discuss the instability using an effective single-band model. This framework reveals a duality mapping of the effective model which maps the distortional order parameter onto a superconducting one, providing a natural explanation for the Cooper logarithm and the weak-coupling nature of the instability. Finally, we consider the possibility of a pair-density wave state when inversion symmetry is broken. We find that it can indeed exist but does not affect the instability itself.

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Section: Model Systemmentioning

confidence: 99%

Distortional weak-coupling instability of Bogoliubov Fermi surfaces

2021

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“…The emergence of the Berry curvature dipole is identified by the discussions parallel to those of the magnetic ASOC because the spin and momentum-space Berry curvature have the same space-time symmetry (P-even and T -odd). The magnetically-tunable responses discussed above can be systematically identified with the help of magnetic symmetry analysis (Erb and Hlinka, 2020;Watanabe and Yanase, 2020;Yatsushiro et al, 2022) and are expected to be a key to rich spintronic phenomena based on antiferromagnetic materials.…”

Section: B Control Of Electronic Property With Pt -Symmetric Magnetic...mentioning

confidence: 99%

Photocurrent response in parity-time symmetric current-ordered states

Watanabe

Yanase

2021

Phys. Rev. B

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Parity-time-reversal symmetry (PT symmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T ), is a fundamental concept of physics and characterizes the functionality of materials as well as P and T symmetries. In particular, the PT -symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leaves PT symmetry intact, the simultaneous violation of P and T symmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagnetic P-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion. Contents I. Introduction II. Magnetic Parity Violation and Space-Time Symmetry A. Parity-time-reversal symmetry and parity violations B. Hidden Magnetic Degrees of Freedom in Crystals C. Multipolar degree of freedom of visible antiferromagnets III. Emergent Responses of PT -symmetric magnets A. Electric-Magnetic Classification of Response Function B. Magnetic Counterpart of Piezoelectric Effect C. Nonreciprocal Property of Electronic Transport and Optical Response 1. Nonreciprocal conductivity 2. Photocurrent generation IV. Availability of PT -symmetric Magnets and Physical Properties A. Switching the compensated magnets B. Control of electronic property with PT -symmetric magnetic order V.

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“…The functions f i (k) must transform like the σ i . The leading-order basis functions can be found in tables [54] or constructed by standard methods. A − has the two leading-order basis functions k x (3k 2 y − k 2 x ) and k y (3k 2 x − k 2 y ) and Eq.…”

Section: A Examplementioning

confidence: 99%

“…In this paper, we add to the systematization of band touchings by providing a classification of twofolddegenerate band-touching points and lines for the 122 magnetic point groups [48][49][50][51][52][53][54][55]. We here consider each magnetic point group as a subgroup of SU(2) ⊗ {e, Θ}, where Θ denotes the time-reversal operation.…”

Section: Introductionmentioning

confidence: 99%

Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles

Knoll,

Timm

2021

Preprint

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Symmetry-protected topological semimetals are at the focus of solid-state research due to their unconventional properties, for example regarding transport. By investigating local two-band Bloch Hamiltonians in the spin-1/2 basis for the 122 magnetic point groups, we classify twofold-degenerate band touchings such as Weyl points, robust nodal lines on axes and in mirror planes, and fragile nodal lines. We find that all magnetic point groups that lack the product of inversion and timereversal symmetries can give rise to topologically non-trivial band-touching points. Hence, such nodes are the rule rather than the exception and, moreover, do not require any complicated multiband physics. Our classification is applicable to every momentum in the Brillouin zone by considering the corresponding little group and provides a powerful tool to identify magnetic and non-magnetic topological semimetals.

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Vector and bidirector representations of magnetic point groups

Cited by 12 publications

References 15 publications

Distortional weak-coupling instability of Bogoliubov Fermi surfaces

Distortional weak-coupling instability of Bogoliubov Fermi surfaces

Photocurrent response in parity-time symmetric current-ordered states

Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles

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