Session X60: Weyl semimetal, Theory II

Topological semimetals: from classification to material realization

The field of topological semimetals continues to reveal new insights. I will discuss recent developments in the field, starting with the classification of nodal fermions in both magnetic and non-magnetic space groups. I will then introduce new aspects of the bulk-edge correspondence, which elucidate the topological nature of certain non-chiral fermions. Finally, I will discuss routes to material realizations.   

Topological Vortices in Superconducting Time-Reversal Symmetric Weyl Semimetals

Recent years have shown that superconducting vortices in topological insulators and strongly spin-orbit coupled semiconductors are natural platforms for obtaining Majorana zero modes. We ask the question, "under what conditions do superconducting vortices in Weyl semimetals trap protected Majorana zero modes on the surface?" We show that sufficient conditions for a time-reversal symmetric type I Weyl semimetal (TWSM) to host Majorana modes as above when ordinary BCS superconductivity is induced in them, are (i) the TWSM forms by perturbing a Dirac or a nodal line semimetal, so that kz=0,pi planes contain pairs of opposite chirality Weyl nodes with a small k-space separation (where z is the vortex axis), and (ii) the number of quadruplets of Weyl nodes in these planes is odd. We analytically calculate the topological invariant in this limit using Kitaev's Pfaffian criterion and support it with numerics on a cubic lattice model. Using our criteria, we predict TaAs and its isovalent counterparts to form topological trivial vortices, devoid of Majorana modes. Also, we propose Na(3-x)KxBi with broken inversion symmetry, where doping occurs via interstitial substitution, to be an ideal platform for realizing a non-trivial superconducting vortex with Majorana zero modes at its ends.
  

Finite-Size Effects in the Dynamic Conductivity and Faraday Effect of Quantum Anomalous Hall Insulators

We theoretically study the finite-size effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semi-analytic and numerical results are obtained for the wavefunctions and energies of the disk within a continuum Dirac Hamiltonian description subject to a topological infinite mass boundary condition. Using the Kubo formula, we obtain the frequency-dependent longitudinal and Hall conductivities and find that optical transitions between edge states contribute dominantly to the real part of the dynamic Hall conductivity for frequency values both within and beyond the bulk bandgap. We also find that the topological infinite mass boundary condition changes the low-frequency Hall conductivity to e²/h in a finite-size system from the well-known value e²/2h in an extended system. The magneto-optical Faraday rotation is then studied as a function of frequency for the setup of a quantum anomalous Hall insulator mounted on a dielectric substrate, showing both finite-size effects of the disk and Fabry-Perot resonances due to the substrate. Our work demonstrates the important role played by the boundary condition in the topological properties of finite-size systems through its effects on the electronic wavefunctions.   

Interplay of non-Abelian band topology with crystalline symmetry

We discuss the recently discovered non-Abelian topological invariant that characterizes band nodes inside the momentum space of certain non-interacting metals. This non-Abelian topology prominently arises in systems with PT symmetry (space-time inversion) or with C₂T symmetry (composition of π-rotation with time-reversal). Given the prevalence of these symmetries in most space groups, one expects important implications of the non-Abelian invariant for real materials.

In this talk, we first introduce the quaternion formulation of this topological invariant as obtained by Ref. [1]. We subsequently reformulate the topology using frame rotations and Euler class [2] as developed recently by Ref. [3]. We finally present new results concerning the interplay of the non-Abelian band topology with point-group symmetry. We find that this interplay implies non-trivial conversions between Weyl points, nodal lines, and nodal chains as the system parameters (such as strain or tight-binding coefficients) are tuned.

[1] Q.-S. Wu, A. A. Soluyanov, and T. Bzdušek, Science 365, 1273 (2019)
[2] J. Ahn, S. Park, and B-J Yang, Phys. Rev. X 9, 021013 (2019)
[3] A. Bouhon, R.-J. Slager, and T. Bzdušek, arXiv:1907.10611 (2019)   

Strain engineered higher order topological phases for spin-3/2 Luttinger fermions

Recently, the notion of topological phases of matter has been extended to higher order incarnations, supporting gapless modes on even lower dimensional boundaries, such as corners and hinges. We here identify a collection of cubic spin-3/2 fermions with bi-quadratic touching of Kramers degenerate valence and conduction bands as a platform to strain-engineer higher-order topological (HOT) phases: external uniaxial strain gives birth to a HOT Dirac semimetal or an insulator, depending on its sign, featuring topological \emph{hinge} modes in the strain direction. The insulator in fact exhibits \emph{mixed} topology, and in addition supports edge modes on orthogonal planes. These outcomes are germane when the external strain is applied along one of the $C_{4v}$ or coordinate axes, as well as $C_{3v}$ or body-diagonal, directions. Our findings place HgTe, gray-Sn, 227 pyrochlore iridates and half-Heusler compounds at the frontier of strain engineered electronic HOT phases.   

Wiedemann-Franz law and Mott relation for transport coefficients in the non-linear regime

In contrast to their counterparts in the linear regime, the non-linear anomalous Hall, Nernst, and thermal Hall effects can survive in time-reversal symmetric system in the presence of inversion symmetry breaking. Within the framework of semiclassical Boltzmann theory, we calculate the analytical expressions for the non-linear anomalous transport coefficients, namely, the non-linear anomalous Hall, Nernst, and thermal Hall coefficients. With these expressions, we predict the fundamental relations between the non-linear anomalous electric and thermo-electric transport coefficients, which are the analog of the Wiedemann-Franz law and the Mott relation in the non-linear regime. We also make several experimental predictions for non-linear anomalous Nernst Hall effect in bilayer WTe2 and for non-linear anomalous thermal Hall effect for monolayer transition metal dichalcogenide which can be verified in experiments.

References:
[1] C. Zeng, S. Nandy, A. Taraphder, and S. Tewari, “Non-linear Nernst effect in bilayer WTe2,” arXiv e-prints, p. arXiv:1905.09814, May 2019.
[2] C. Zeng, S. Nandy, and S. Tewari, “Wiedemann-Franz law and Mott relation for non-linear anomalous transport phenomena,” arXiv e-prints, p. arXiv: 1909.03047, Sep 2019.   

Phonon induced topological phase transition in ZrTe5

Layered crystalline material ZrTe₅ is a unique material to study topological phase transitions; it is very close to the phase boundary between a weak and strong topological insulator (TI) and one can switch from one phase to another by small perturbations like strain. Recently, photoinduced topological transition from the TI regime to the Dirac semimetallic phase has been reported in this material. Motivated by the aforementioned work, using first-principles calculations and effective model Hamiltonian, we study the transition from the TI regime to the Dirac and Weyl semimetallic phases induced by various phonon
modes. The experimental implications of our results are also discussed.   

Diagnosing and observing topological degeneracies in AI class systems

Topological states have been widely studied in Fermionic systems for many years, wherever, they are sporadically explored in Bosonic systems, even both Fermions and Bosons are fundamental particles in condensed matter physics. Actually, Bosons can offer a better platform to get spinless band structures where nodal lines can be realized with only parity-time reversal (PT) symmetry, such as phonons. By combining first-principles calculations and meV-resolution inelastic x-ray scattering, we demonstrate the first realization of PT symmetry protected helical nodal lines of phonons in a real material. The combination of theoretical analysis and experimental measurements demonstrate the PT-protected helical nodal lines for the first time in phononic materials. This nodal line is robust because of the spinless nature of phonons, which will open a new route to explore exotic topological states in crystalline materials.   

Effects of Van der Waals interaction on the phonon and electron band structures of ZrTe5

Since the theoretical prediction of the existence of the topological insulating phase, ZrTe₅ has attracted a lot of interests in its topological nature, which may lead to the low-energy transport edge channels and the quantum spin Hall (QSH) effect in its two-dimensional form. Possible strain or photon induced topological transition from the topological insulator (TI) to the Dirac semimetal in ZrTe₅ has been recently suggested by experiments. Due to the layered structure of ZrTe₅, the van der Waals (vdW) interaction becomes an essential factor to study atomic vibrational behavior in the topological transition. In this theoretical work, phonon vibration modes and the corresponding electron band structures are explored systematically without and with vdW force correction to reveal the microscopic mechanism of the phase transition in ZrTe₅.   

Bulk and surface polaritons in Weyl semimetals

We report theoretical studies of the optical properties and polariton modes of Type I Weyl semimetals with two Weyl nodes. We present rigorous quantum-mechanical derivation of bulk and surface conductivity tensors including both intraband and interband optical transitions and taking into account all possible combinations of bulk-to-bulk, bulk-to-surface, and surface-to-surface transitions. We show how the information about the electronic structure of Weyl semimetals, such as position and separation of Weyl nodes, Fermi energy, surface states etc. can be unambiguously extracted from their optical response, namely from the reflection, transmission, and polarization change of incident radiation. We predict the optical Hall effect and anomalous dispersion for surface polaritons excited by a nanotip. We show that Weyl semimetals represent a new class of gyrotropic materials with unique electrodynamics due to the combination of strongly anisotropic and gyrotropic bulk conductivity, surface conductivity, and surface dipole layer.   

Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type dispersion. We present symmetry conditions for realizing such hourglass Weyl loops, which involve nonsymmorphic lattice symmetries. Depending on the symmetry, the loops may exhibit different patterns in the Brillouin zone. Based on first-principles calculations, we identify the monolayer GaTeI-family materials as a realistic material platform to realize such loops. These materials host a single hourglass Weyl loop circling around a high-symmetry point. Interestingly, there is also a spin-orbit Dirac point enabled by an additional screw axis. We show that the hourglass Weyl loop and the Dirac point are robust under a variety of applied strains. By breaking the screw axis, the Dirac point can be transformed into a second Weyl loop. Furthermore, by breaking the glide mirror, the hourglass Weyl loop and the spin-orbit Dirac point can both be transformed into a pair of spin-orbit Weyl points. Our work offers guidance and realistic material candidates for exploring fascinating physics of several novel 2D emergent fermions.   

Fermionic analogue of Hawking radiation in bilayer black phosphorous

Topological matters upon the periodic driving of laser can lead to nonequilibrium topological states, which is not accessible in equilibrium topological materials. Here we propose that the periodically driven two-dimensional black phosphorous (BP) thin film with a spatial gradient of Floquet-Dirac states can mimic the “gravity” felt by fermionic quasiparticles as that for a Schwarzschild black hole (SBH). Quantum tunneling of electrons from a type-II Dirac cone (inside BH) to a type-I Dirac cone (outside) emits a SBH-like Hawking radiation spectrum. The obtained T_H of a fermionic analog of BH in BP is approximately 3 K, which is several orders of magnitude higher than previous works. Our work sheds some light on increasing the T_H from the perspective of nonequilibrium topological states under periodic driving of laser. The obtained SBH accessible in nonequilibrium BP provides some clues to access the more Fermionic analogues of astronomy phenomena in solids.