Dynamical symmetry indicators for Floquet crystals

Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes.

Different types of spin currents in the comprehensive materials database of nonmagnetic spin Hall effect

Spin Hall effect (SHE) has its special position in spintronics. To gain new insight into SHE and to identify materials with substantial spin Hall conductivity (SHC), we performed high-precision high-throughput ab initio calculations of the intrinsic SHC for over 20,000 nonmagnetic crystals. The calculations revealed a strong relationship between the magnitude of the SHC and the crystalline symmetry, where a large SHC is typically associated with mirror symmetry-protected nodal line band structures. This database includes 11 materials with an SHC comparable to or even larger than that of Pt. Materials with different types of spin currents were additionally identified. Furthermore, we found that different types of spin current can be obtained by rotating applied electrical fields. This improves our understanding and is expected to facilitate the design of new types of spin-orbitronic devices.

Hidden quasi-symmetries stabilize non-trivial quantum oscillations in CoSi

Unlocking the exotic properties promised to occur in topologically non-trivial semi-metals currently requires significant fine-tuning. Crystalline symmetry restricts the location of topological defects to isolated points (0D) or lines (1D), as formalized by the Wigner-Von Neumann theorem. The scarcity of materials in which these anomalies occur at the chemical potential is a major obstacle towards their applications. Here we show how non-crystalline quasi-symmetries stabilize near-degeneracies of bands over extended regions in energy and in the Brillouin zone. Specifically, a quasi-symmetry is an exact symmetry of a k∙p Hamiltonian to lower-order that is broken by higher-order terms. Hence quasi-symmetric points are gapped, yet the gap is parametrically small and therefore does not influence the physical properties of the system. We demonstrate that in the eV-bandwidth semi-metal CoSi an internal quasi-symmetry stabilizes gaps in the 1-2 meV range over a large near-degenerate plane (2D). This quasi-symmetry is key to explaining the surprising simplicity of the experimentally observed quantum oscillations of four interpenetrating Fermi surfaces around the R-point. Untethered from the limitations of crystalline symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce sources of large Berry curvature to occur at the chemical potential, and thereby lead to new Wigner-Von Neumann classifications of solids. Quasi-symmetries arise from a comparable splitting of degenerate states by spin-orbit coupling and by orbital dispersion - suggesting a hidden classification framework for symmetry groups and materials in which quasi-symmetries are critical to understand the low-energy physics.

Tunable dynamical magnetoelectric effect in antiferromagnetic topological insulator MnBi2Te4 films

Axion was postulated as an elementary particle to solve the strong charge conjugation and parity puzzle, and later axion was also considered to be a possible component of dark matter in the universe. However, the existence of axions in nature has not been confirmed. Interestingly, axions arise out of pseudoscalar fields derived from the Chern–Simons theory in condensed matter physics. In antiferromagnetic insulators, the axion field can become dynamical due to spin-wave excitations and exhibits rich exotic phenomena, such as axion polariton. However, antiferromagnetic dynamical axion insulator has yet been experimentally identified in realistic materials. Very recently, MnBi2Te4 was discovered to be an antiferromagnetic topological insulator with a quantized static axion field protected by inversion symmetry $${\mathcal{P}}$$ P and magnetic-crystalline symmetry $${\mathcal{S}}$$ S . Here, we studied MnBi2Te4 films in which both the $${\mathcal{P}}$$ P and $${\mathcal{S}}$$ S symmetries are spontaneously broken and found that substantially enhanced dynamical magnetoelectric effects could be realized through tuning the thickness of MnBi2Te4 films, temperature, or element substitutions. Our results show that thin films of MnBi2Te4 and related compounds could provide a promising material platform to experimentally study axion electrodynamics.

Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn2As2

Knowledge of magnetic symmetry is vital for exploiting nontrivial surface states of magnetic topological materials. EuIn2As2 is an excellent example, as it is predicted to have collinear antiferromagnetic order where the magnetic moment direction determines either a topological-crystalline-insulator phase supporting axion electrodynamics or a higher-order-topological-insulator phase with chiral hinge states. Here, we use neutron diffraction, symmetry analysis, and density functional theory results to demonstrate that EuIn2As2 actually exhibits low-symmetry helical antiferromagnetic order which makes it a stoichiometric magnetic topological-crystalline axion insulator protected by the combination of a 180∘ rotation and time-reversal symmetries: $${C}_{2}\times {\mathcal{T}}={2}^{\prime}$$ C 2 × T = 2 ′ . Surfaces protected by $${2}^{\prime}$$ 2 ′ are expected to have an exotic gapless Dirac cone which is unpinned to specific crystal momenta. All other surfaces have gapped Dirac cones and exhibit half-integer quantum anomalous Hall conductivity. We predict that the direction of a modest applied magnetic field of μ0H ≈ 1 to 2 T can tune between gapless and gapped surface states.

Valley polarization caused by crystalline symmetry breaking

The crystallographic symmetry rather than the time-reversal asymmetry plays in introducing valley polarization.

Phase diagrams of superconducting topological surface states

In this paper, we present a detailed study on the phase diagrams of superconducting topological surface states, especially, focusing on the interplay between crystalline symmetry and topology of the effective BdG Hamiltonian. We show that for the 4 x 4 kinematic Hamiltonian of the normal state, a mirror symmetry M can be defined, and for the M-odd pairings, the classification of the 8 x 8 BdG Hamiltonian is ℤ⊕ℤ, and the time-reversal symmetry is broken intrinsically. The topological non-trivial phase can support chiral Majorana edge modes, and can be realized in the thin films of iron-based superconductor such as FeSeTe.

Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurface in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

Controlling spin current polarization through non-collinear antiferromagnetism

The interconversion of charge and spin currents via spin-Hall effect is essential for spintronics. Energy-efficient and deterministic switching of magnetization can be achieved when spin polarizations of these spin currents are collinear with the magnetization. However, symmetry conditions generally restrict spin polarizations to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced. Here, we show control of the spin polarization direction by using a non-collinear antiferromagnet Mn3GaN, in which the triangular spin structure creates a low magnetic symmetry while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn3GaN/permalloy heterostructures can generate unconventional spin-orbit torques at room temperature corresponding to out-of-plane and Dresselhaus-like spin polarizations which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spin-orbit torque, enabling high-efficient antiferromagnetic spintronics.