Session N25: Dirac and Weyl Semimetals: Theory 2

Polarization jumps across Weyl semimetal phase in two-dimensional materials

The electric polarization in insulating systems is described by the Berry phase of Bloch states according to the modern theory of polarization. The polarization changes continuously and smoothly as we change a parameter of the system as long as the system remains insulating. In this talk, we present our recent discovery of the jump of polarization in two-dimensional materials when the system goes across the Weyl semimetal phase, which is protected by a symmetry. For two-dimensional Weyl semimetals, a parameter M is introduced to break the symmetry and make the system insulating. We compare values of polarization in two limits M→0⁺ and M→0^- and see that there is a finite jump of polarization. This jump of polarization is described by the newly introduced “Weyl dipole” representing how the Weyl points with monopole charges are displaced in the reciprocal space [1]. We also discuss another scenario where a Weyl semimetal phase appears at transitions between normal insulator to topological insulator phases. In such cases, Weyl points do not appear in pairs generally but a finite jump of polarization still exists. We clarify how to modify the discussion above to describe these jumps.   

Author not Attending

Low dimensional crystals, including quasi-two-dimensional (2D) layered crystals and quasi-one-dimensional (1D) rod-like crystals, exhibit different properties from conventional three-dimensional crystals. In this work, we systematically study the emergent particles in 529 magnetic layer groups (MLGs) and 394 magnetic rod groups (MRGs). Based on restricting the co-representations of the magnetic space group to a subgroup, we construct the k·p Hamiltonians and identify all possible emergent particles, including spinful and spinless, essential, and accidental particles in 529 MLGs and 394 MRGs. We find that there are six kinds of emergent particles in MLGs and three kinds of emergent particles in MRGs. Moreover, we show the correspondence between MLGs (MRGs) and magnetic space groups. We hope this work will facilitate search and design low dimensional materials.   

Discovering and Engineering two-dimensional Weyl phonons from First principles

Topological properties in phononic systems have attracted great attention in the past decade, as phonons differ fundamentally from electrons in many aspects. Phonon Weyl points (WPs) and Weyl nodal lines(WNLs), as typical topological features in 3D systems, have been widely predicted and studied in different compounds. In 2D systems, although dirac nodes in phonon dispersions are well-studied in hexagonal lattices (for example graphene), Weyl phonons did not receive equal attention. The lack of the third free variable k_z imposes symmetry conditions on the existence of WPs in 2D, and materials realizations of electronic Weyls points in systems such as monolayer FeB₂ and Cr₂C are predicted only recently. In this study we extend the concept of 2D Weyl electrons to 2D Weyl phonons. We use DFT to calculate phonon band structures to explore type-I/type-II WPs and WNLs for a series of 2D hexagonal materials with inversion symmetry breaking. By tuning crystal structures, we engineer the phonon band structures, thus transform WPs and WNLs.   

Nonlinear axion dynamics in topological Weyl semimetal

The concept of Weyl fermions was first hypothesized in the context of high energy physics to describe massless chiral fermions, but has since been applied to describe quasiparticle excitations in condensed matter materials with topologically-enforced band-crossings. These particles naturally have an additional chiral symmetry which enriches transport, e.g. presence of Fermi arcs. However, the chiral anomaly serves to break this symmetry, which leads to a static axion response, characterized by topological magnetoelectric effects such as the chiral magnetic effect or anomalous Hall effect.

The situation becomes more complex when chiral symmetry is spontaneously broken by the introduction of charge density wave (CDW) order. The Goldstone mode of the CDW then acts as a dynamical axion mode, and may possess a signature in e.g. negative longitudinal magnetoresistance. However, to date identifying this collective mode has posed a serious experimental and theoretical challenge.  Therefore, we present a new route towards detecting the axion mode based on a nonlinear optical response of the magnetoelectric interaction. We propose signatures based on the frequency and polarization dependence in these spectroscopies which can conclusively identify this elusive collective mode. Finally, various material candidates and signatures are considered, as well as possible complications and constraints.   

Topological photonics and unidirectional surface plasmon polaritons in a Weyl semimetal

The axion effect in the dielectric function of Weyl semimetals (WSM) gives rise to topological photonic bands with non-zero Chern number. On the surface of WSM, unidirectional surface plasmon polaritons (SPPs) emerge as a consequence of the topological photonic bands. We found that this  SPP can mediate two qubits with decay time much longer than SPP in conventional metals.

    

Phonon-Mediated Hydrodynamic Transport in Weyl Semimetals

In light of recent experimental and numerical analyses, we study through a simple microscopic model the role that electron-electron interactions mediated by virtual phonons can play in inducing a hydrodynamic regime in Weyl semimetals. The electric and thermal conductivities are obtained and, similarly to interactions with real phonons, they display a different scaling with temperature (T) depending on whether T lies above of below the Bloch-Grünesen temperature (T_BG). For T > T_BG the virtual phonons act on-shell, and a modified temperature-independent Lorenz ratio is obtained. At low temperatures T < T_BG, the system manifests a T² behavior for the electric and thermal scattering times. In addition, it is seen that chirality-violating interactions play a crucial role in inducing electric current relaxation through Baber scattering. We put our theory in context of experimental results.   

Magnetic breakdown spectrum of a Kramers–Weyl semimetal

We calculate the Landau levels of a Kramers–Weyl semimetal thin slab in a perpendicular magnetic field B. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in 1/B. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as 1/B-periodic magnetoconductance oscillations, at weaker fields and higher temperatures than the Shubnikov–de Haas oscillations due to Landau level quantization. No such spectrum appears in a generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant momenta is essential.   

Topological resonace in graphen-like materials

In topological materials, interacting with short and strong optical pulses, electrons can accumulate a topological phase during the pulse. Such phase can compensate the dynamic phase resulting in topological resonance, which is visible as a large inter-band transfer of electron population. We study theoretically the topological resonance in materials of the gapped multilayer graphene type. We show that the resonance can be observed only in the systems with finite bandgap. For monolayer graphene, the topological resonance can occur only in the field of an elliptically polarized pulse while for multilayer graphene, the resonance  can also be realized in a linearly polarized pulse.

    

Heesch Weyl Fermions in inadmissible chiral antiferromagnets

Symmetry plays a vital role in determining the topological properties of a material. Recently, the topological nature of the Kramers degeneracy at time-reversal-invariant momenta (TRIMs) as the Kramers Weyl node was revealed for the nonmagnetic chiral crystals. However, it remains obscure whether Weyl nodes can be also pinned at points of symmetry in magnetic materials where the time-reversal symmetry is spontaneously broken. In this work, we point out the existence of a new type of Weyl fermions in the inadmissible chiral antiferromagnets that are stabilized and pinned at points of symmetry by the Heesch group, which we call the Heesch Weyl fermions (HWFs). The origin of HWFs is fundamentally different from that of Kramers Weyl fermions, as the emergence of the former does not rely on any anti-unitary symmetry A that satisfies A$^2$ = −1. Through group theory analysis, we classify all the magnetic little co-groups of momenta where Heesch Weyl nodes are enforced and pinned by symmetry. With the guidance of the classification and first-principles calculation, the antiferromagnetic (AFM) perovskite YMnO3 is identified as a candidate host of the AFM-order-induced HWFs. Novel properties of the HWF, such as its axial moving under strain and therefore the potential realization of Weyl braiding, are also explored.   

Interacting Anomaly: Anomalous Massive Propagation and Thermal Transport

The remarkable quantum breaking of the classical chiral symmetry, first discovered in the context of particle physics, has now found new life in condensed matter physics, connecting topological quantum matter and band theory with effective field theoretic models. 

In a previous discussion we investigated how interactions can affect the chiral anomaly and its condensed matter consequences leading to renormalization of excitations and their transport properties in one dimensional systems, and modification of the anomalous response of the system, namely the chiral magnetic and quantum hall effects in three dimensions.

Here we further investigate these properties. First we identify a type of anomalous massive propagation which exists within interacting Weyl semimetals. These massive modes are nonperturbative in nature and are a direct consequence of the chiral anomaly. Then, as a separate phenomena, we investigate the effects of interactions on a type of thermal transport associated with mixed anomalies.   

Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal

Weyl semimetals (WSM), being a topological gapless phase of matter, show various intriguing features, among which are the chiral anomaly and the Hall effect. In this talk, we discuss the chiral anomaly's impact on the infrared properties of a strongly interacting Weyl semimetal.

At the mean-field level, a strongly interacting Weyl semimetal is described as the modified quantum electrodynamics from a time-reversal-breaking Weyl semimetal coupled with a U(1) gauge (electromagnetic) field. A key role is played by the soft dispersion of the photons in a particular direction, say z-direction, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in the z-direction is logarithmically reduced under renormalization group flow, together with the fine structure constant. Meanwhile, fermions acquire a finite lifetime from spontaneous emission of the soft photon, namely the Cherenkov radiation. At low energy E, the inverse of the fermion lifetime scales as τ ⁻¹ ∼ E/PolyLog(E). Therefore, even though fermion quasiparticles are eventually well-defined at very low energy, over a wide intermediate energy window the Weyl semimetal behaves like a marginal Fermi liquid. Phenomenologically, our results are more relevant for emergent Weyl semimetals, where the fermions and photons all emerge from strongly correlated lattice systems. Possible experimental implications are discussed.   

Super-Klein tunneling through a rectangular barrier in multi-Weyl semimetals

Recently, three-dimensional Weyl semimetals with topological charge J=1 have attracted a surge of interest in condensed matter physics. However, multi-Weyl semimetals (MSMs) are allowed to have J>1 and, consequently, the dispersions become linear exclusively in one momentum direction, and exhibit a power law dependence (governed by J) in other two directions. We theoretically study the transport through a rectangular potential barrier, perpendicular to the z-axis, created across a junction between two MSMs. Most strikingly, we find that perfect transmission of omnidirectional particles occurs when the incident energy (E) equals to half of the barrier-height (U), which gives rise to the super-Klein tunneling. On the other hand, the Klein tunneling at normal incidence and the Fabry-Perot-like transmission resonance at oblique incidence emerges for all values of J, when E<U as well as E>U. Remarkably, the super-Klein tunneling disappears as soon as the topological charge differs at two sides of the barrier. Several J-dependent effects emerge in thick as well as thin barrier limits, which could be tested in simple experiments.   

Mixed Charge-Momentum Responses in Higher-Order Topological Semimetals

The theory of topological responses in insulators and semimetals has recently been extended to include mixed translation-electromagnetic responses. These responses encode the charge response to lattice strain and the momentum response to electromagnetic fields. In this work we identify a higher-order topological semimetal that possesses mixed translation-electromagnetic responses in both its bulk and its surface. These responses originate from higher-order Weyl nodes in the 3D bulk and conventional Dirac nodes on 2D surfaces. In addition, when projected to the reduced Brillouin zone on a hinge, the interval between the bulk Weyl and surface Dirac nodes is spanned by flat-band hinge states. These hinge bands realize an equilibrium quadrupole moment of crystal momentum that has not previously been considered.   

Chiral crossings with local and global symmetry constraints

The number of surface states as well as the electric response of Weyl semimetals is determined to a large extent by the Chern number of the Weyl points, a property also known as their chirality. It is known [1,2] that rotation eigenvalues affect the value of the chirality, but so far there is no comprehensive theory that connects rotation eigenvalues and topological charges. Here, we show that the previous works are applications of a local constraint, which holds for arbitrary combinations of symmetries as well as for chiral crossings comprising more than two bands. Using this constraint we explain the chiralities of quadruple Weyl points. Furthermore, with a global constraint, stemming from the periodicity of the Brillouin zone, we can identify enforced topological nodal planes as well as Weyl points at generic positions.

[1] Chen Fang, et al., Phys. Rev. Lett. 108, 266802 (2012)

[2] Stepan S. Tsirkin, et al., Phys. Rev. B 96, 045102 (2017)