Mirror Reflection Symmetry Research Articles

First‐Principles Investigation of Electronic and Thermodynamic Properties of Honeycomb CuSe

AbstractIn the realm of materials science, a fascinating class of substances known as topological nodal line semimetals have garnered significant attention. These materials possess distinctive quantum states, characterized by topologically nontrivial conduction and valence bands that intricately intersect with the Fermi level. Such unique band structures give these materials a plethora of surprising properties, including the emergence of flat Landau levels and the appearance of long‐range Coulomb interactions. Notably, certain bulk materials, namely PbTaSe2, ZrSiS, PtSn4, and Cu2Si, exhibit these intriguing topological nodal lines. However, the theoretical investigation pertaining to CuSe and its Dirac nodal line properties remains relatively limited. In this work, we have employed simulations on CuSe to elucidate its distinctive physical properties such as a Dirac matter. There exist Dirac bands and band inversion in the vicinity of Fermi levels, and Fermi surface holds a Horn‐like structure. We pointed out the occurrence of mirror reflection symmetry‐protected Dirac nodal line fermions in copper selenide (CuSe) that make CuSe a candidate for Dirac nodal line fermion started by the Se 4p and Cu 3d orbitals. The nontrivial topological edge states further verify our proposal of the mirror reflection symmetry is broken by spin‐orbit coupling. These findings provide a new perspective that advances our comprehension of the remarkable properties exhibited by these materials, thereby paving the way for the development of high‐speed and low‐dissipation devices in the future.

Line-wave waveguide engineering using Hermitian and non-Hermitian metasurfaces

Line waves (LWs) refer to confined edge modes that propagate along the interface of dual electromagnetic metasurfaces while maintaining mirror reflection symmetries. Previous research has both theoretically and experimentally investigated these waves, revealing their presence in the microwave and terahertz frequency ranges. In addition, a comprehensive exploration has been conducted on the implementation of non-Hermitian LWs by establishing the parity-time symmetry. This study introduces a cutting-edge dual-band line-wave waveguide, enabling the realization of LWs within the terahertz and infrared spectrums. Our work is centered around analyzing the functionalities of existing applications of LWs within a specific field. In addition, a novel non-Hermitian platform is proposed. We address feasible practical implementations of non-Hermitian LWs by placing a graphene-based metasurface on an epsilon-near-zero material. This study delves into the advantages of the proposed framework compared to previously examined structures, involving both analytical and numerical examinations of how these waves propagate and the underlying physical mechanisms.

Tunable chiral bound states in a dimer chain of coupled resonators

We study an excitation hopping on a one-dimensional (1D) dimer chain of coupled resonators with the alternate on-site photon energies, which interacts with a two-level emitter (TLE) by a coupling point or two adjacent coupling points. In the single-excitation subspace, this system not only possesses two energy bands with propagating states, but also possesses photonic bound states. The number of bound states depends on the coupling forms between the TLE and the dimer chain. It is found that when the TLE is locally coupled to one resonator of the dimer chain, the bound-state that has mirror reflection symmetry. When the TLE is nonlocally coupled to two adjacent resonators, three bound states with preferred direction arise due to the mirror symmetry breaking. By using chirality to measure the asymmetry, it is found that the chirality of these bound states can be tuned by changing the energy differences of single photon in the adjacent resonators, the coupling strengths and the transition energy of the TLE.

Light-Driven Spontaneous Phonon Chirality and Magnetization in Paramagnets.

Spin-phonon coupling enables the mutual manipulation of phonon and spin degrees of freedom in solids. In this study, we reveal the inherent nonlinearity within this coupling. Using a paramagnet as an illustration, we demonstrate the nonlinearity by unveiling spontaneous symmetry breaking under a periodic drive. The drive originates from linearly polarized light, respecting a mirror reflection symmetry of the system. However, this symmetry is spontaneously broken in the steady state, manifested in the emergence of coherent chiral phonons accompanied by a nonzero magnetization. We establish an analytical self-consistency equation to find the parameter regime where spontaneous symmetry breaking occurs. Furthermore, we estimate realistic parameters and discuss potential materials that could exhibit this behavior. Our findings shed light on the exploration of nonlinear phenomena in magnetic materials and present possibilities for on-demand control of magnetization.

Generalized Dzyaloshinskii–Moriya Interaction and Chirality-Induced Phenomena in Chiral Crystals

This paper is a review of recent advances in studies of the magnetic, electronic, spintronic, and phononic properties of chiral crystals, with a focus on the connection between the Dzyaloshinskii–Moriya interaction (DMI) and chirality in materials. Importantly, a microscopic DMI is elevated to a macroscopic Lifshitz invariant (LI) in chiral crystals, where mirror reflection and inversion symmetry are globally broken. As a consequence, chiral crystals exhibit nontrivial physical responses over a macroscopic scale. Indeed, in chiral magnetism, a chiral spin soliton lattice (CSL) appears in monoaxial chiral magnetic crystals and exhibits various nontrivial physical properties characterized by the coherent and topological nature of the CSL. This CSL isone of the prominent outcomes arising from the DMI and LI, as envisioned by Dzyaloshinskii in the 1960s. Furthermore, a giant spin polarization emerges over a macroscopic scale in a wide range of chiral materials from organic molecules to inorganic crystals. The first-order spatial dispersion, such as the LI, also appears in elastic or phonon degrees of freedom in chiral crystals. These examples show how a time-even pseudoscalar term, which corresponds to a generalized concept of the DMI and LI, is realized in chiral media.

Nodal-line symmetry breaking induced colossal anomalous Hall and Nernst effects in Cu2CoSn Heusler compound

The presence of topological band crossings near the Fermi energy is essential for the realization of large anomalous transport properties in the materials. The topological semimetals host such properties owing to their unique topological band structure, such as Weyl points or nodal lines (NLs), those are protected by certain symmetries of the crystal. When the NLs break out in the system, a large Berry curvature arises in the surrounding area of the gapped NL. In the present work, we studied anomalous transport properties of Cu2CoSn compound, which has a cubic Heusler crystal structure (space group: Fm3¯m). Cu2CoSn full Heusler compound possesses NLs at the Fermi level that is protected by mirror reflection symmetries of the lattice. Upon introducing the spin–orbit coupling in the Hamiltonian and by setting the magnetization axis along the [001] direction, we found that the NLs are gapped out and large Berry curvature arises in the system. The integral of Berry curvature gives the intrinsic anomalous Hall conductivity (AHC) about 1003 S/cm and the anomalous Nernst conductivity (ANC) about 3.98 A/m K at the Fermi level. These values of AHC and ANC are comparable to the largest reported values for the Co2MnGa Heusler compound. Therefore, Cu2CoSn becomes a newborn member of the family of full Heusler compounds, which possesses giant AHC and ANC that can be useful for the spintronics application.

Babinet-complementary structures for implementation of pseudospin-polarized waveguides.

In this work, a theorem is proved stating that in various types of waveguides with mirror reflection symmetries, the electromagnetic duality correspondence between eigenmodes of complementary structures induces counterpropagating spin-polarized states. The mirror reflection symmetries may be preserved around one or more arbitrary planes. Pseudospin-polarized waveguides supporting one-way states manifest robustness. This is similar to topologically non-trivial direction-dependent states guided by photonic topological insulators. Nevertheless, a remarkable aspect of our structures is that they can be implemented in extremely broad bandwidth by simply using complementary structures. Based on our theory, the concept of the pseudospin polarized waveguide can be realized using dual impedance surfaces ranging from microwave to optical regime. Consequently, there is no need to employ bulk electromagnetic materials to suppress backscattering in waveguiding structures. This also includes pseudospin-polarized waveguides with perfect electric conductor-perfect magnetic conductor boundaries where the boundary conditions limit the bandwidth of waveguides. We design and develop various unidirectional systems and the spin-filtered feature in the microwave regime is further investigated.

Modelling of dislocations, twins and crack-tips in HCP and BCC Ti

Ti exhibits complex plastic deformation controlled by active dislocation and twinning systems. Understandings on dislocation cores and twin interfaces are currently not complete or quantitative, despite extensive experimental and simulation studies. Here, we determine the dislocation core, twin, and crack properties in both HCP and BCC Ti using a Deep Potential (DP), DFT and linear elastic fracture mechanics. We compute the core structures, critical resolved shear stresses and mobilities of the 〈a〉 , 〈c+a〉 , 〈c〉 dislocations in HCP and the 〈111〉/2 dislocations in BCC Ti. The 〈a〉 slip consists of slow core migration on pyramidal-I planes and fast migration on prism-planes, and is kinetically limited by cross-slips among them. This behaviour is consistent with “locking–unlocking” phenomena in TEM and is likely an intrinsic property. Large-scale DFT calculations provide a peek at the screw 〈c+a〉 core and glide behaviour, which is further quantified using DP-Ti. The screw 〈c+a〉 is unstable on pyramidal-II planes. The mixed 〈c+a〉 is nearly sessile on pyramidal-I planes, consistent with observations of long dislocations in this orientation. The edge and mixed 〈c+a〉 are unstable against a pyramidal-to-basal (PB) transition and become sessile at high temperatures, corroborate the difficulties in 〈c〉 -axis compression of Ti. Cracks on basal planes are predicted and shown to be intrinsically brittle, consistent with cleavage facets primarily on this plane in experiments. Twin boundary energies vary considerably but all twin boundary structures possess a mirror reflection symmetry. Finally, in BCC Ti, the 〈111〉/2 screw has a degenerate core with average glide on {112} planes; the 〈111〉/2 edge and mixed dislocations have non-dissociated cores on {110} planes. This work paints a self-consistent, complete picture on all dislocations in Ti, rationalises previous experimental observations on Ti plasticity and fracture, and points to future HRTEM examinations of unusual dislocations such as the mixed and PB transformed 〈c+a〉 cores.

Ground states and magnonics in orthogonally coupled symmetric all-antiferromagnetic junctions

In this paper, the rich ground-state structure of orthogonally coupled symmetric all-antiferromagnetic junctions with easy-plane anisotropy is reported. A spin reorientation process rather than the traditional spin flop (SF) occurs, resulting in a phase in which N\'eel vectors preserve the mirror-reflection symmetry (termed MRS phase). The phase transitions in the ground state between SF and MRS phases can be either first or second order. After disturbed by external stimuli, magnons with different parities emerge. For in-plane dc fields, no couplings between magnons occur. When dc fields become oblique, coherent couplings between magnons with opposite parity emerge, leading to anticrossings in resonance frequencies. However, self-hybridization among magnons with the same parity never happens. More interestingly, spin waves based on MRS phases are linearly polarized and their polarization directions can be fine controlled.

Evolution of Weyl-like semi-metallicity in an all-sp2 carbon allotrope

Based on first-principles calculations, we design a stable 3D all-sp2 carbon allotrope by assembling the dehydrogenized helical polyethylenes and dehydrogenized ethylenes. It possesses 32 carbon atoms in its unit cell with orthorhombic symmetry, thus termed oC32. In the absence of spin-orbit-coupling (SOC), oC32 possesses a Weyl-like loop protected by the coexistence of time-reversal, spatial inversion, and mirror reflection symmetries. By displacing the carbon atoms of dehydrogenized ethylenes, the spatial symmetries of oC32 are broken and topological phase transitions occur from the Weyl-like loop state to Weyl-like point states. To probe the origin of the Weyl-like points, we further examine the electronic properties of a 2D sheet composed of the dehydrogenized helical polyethylenes embedded in oC32 since the charge near the Fermi level is regularly distributed around these 2D sheets. We find that the Weyl-like points also appear in these 2D sheets, indicating that the Weyl-like points in the symmetry-broken oC32 come from the 2D sheets embedded in oC32. Our work demonstrates that carbon materials can exhibit rich topological states and topological phase transitions due to the flexible bonding and negligible spin-orbital interaction of carbon atom.

Non-centrosymmetric Weyl semimetal state and strain effect in the twisted-brick phase transition metal monochalcogenides.

Weyl semimetals are a class of gapless electronic excitation topological quantum materials upon breaking time-reversal or inversion symmetry. Here, we demonstrate the existence of the Weyl semimetal state in the non-centrosymmetric twisted-brick phase MoTe theoretically. The topological properties and strain effects of MoTe have been systematically studied based on first-principles calculations and the Wannier-based tight-binding method. In the absence of spin-orbit coupling (SOC), MoTe exhibits gapless nodal loop states related to the mirror reflection symmetry. When the SOC is turned on, the two nodal loops split into 22 pairs of Weyl points (WPs) with opposite chirality. When the effect of uniaxial (εz) strain is taken into account, the Weyl semimetal phase of MoTe shows great robustness and striking tunable topological strength. In particular, the total number of WPs changes significantly under strain. MoTe under +4% and +8% uniaxial strains have only four pairs of WPs with a relatively large separation in momentum space. These results show that MoTe under weak strain is a promising partly ideal type I Weyl semimetal candidate, while the isolog structure WTe both opens a direct gap with and without SOC, showing a compensated semimetal state.

Observation of Topological Flat Bands in the Kagome Semiconductor Nb3Cl8.

The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including Fe3Sn2, FeSn, CoSn, and YMn6Sn6. Nonetheless, kagome materials that are both exfoliable and semiconducting are lacking, which seriously hinders their device applications. Herein, we show that Nb3Cl8, which hosts a breathing kagome lattice, is gapped out because of the absence of inversion symmetry, while the TFBs survive because of the protection of the mirror reflection symmetry. By angle-resolved photoemission spectroscopy measurements and first-principles calculations, we directly observe the TFBs and a moderate band gap in Nb3Cl8. By mechanical exfoliation, we successfully obtain monolayer Nb3Cl8, which is stable under ambient conditions. In addition, our calculations show that monolayer Nb3Cl8 has a magnetic ground state, thus providing opportunities to study the interplay among geometry, topology, and magnetism.

Symmetry Transformations in Metazoan Evolution and Development

In this review, we consider transformations of axial symmetry in metazoan evolution and development, the genetic basis, and phenotypic expressions of different axial body plans. In addition to the main symmetry types in metazoan body plans, such as rotation (radial symmetry), reflection (mirror and glide reflection symmetry), and translation (metamerism), many biological objects show scale (fractal) symmetry as well as some symmetry-type combinations. Some genetic mechanisms of axial pattern establishment, creating a coordinate system of a metazoan body plan, bilaterian segmentation, and left–right symmetry/asymmetry, are analysed. Data on the crucial contribution of coupled functions of the Wnt, BMP, Notch, and Hedgehog signaling pathways (all pathways are designated according to the abbreviated or full names of genes or their protein products; for details, see below) and the axial Hox-code in the formation and maintenance of metazoan body plans are necessary for an understanding of the evolutionary diversification and phenotypic expression of various types of axial symmetry. The lost body plans of some extinct Ediacaran and early Cambrian metazoans are also considered in comparison with axial body plans and posterior growth in living animals.

Unidirectional emission and nanoparticle detection in a deformed circular square resonator.

We propose a novel deformed square resonator which has four asymmetric circular sides. Photons leak out from specific points, depending on the interplay between stable islands and unstable manifolds in phase space. By carefully breaking the mirror reflection symmetry, optical modes with strong chirality approaching 1 and unidirectional emission can be achieved simultaneously. Upon binding of a nanoparticle, the far-field emission pattern of the deformed microcavity changes drastically. Due to the EP point of the degenerate mode pairs in the deformed cavity, chirality-based far-field detection of nanoparticles with ultra-small size can be realized.

The low-energy electron band structure of a two-dimensional Dirac nodal-line semimetal grown on a silicon surface

The low-energy electron band structure of Cu $$_2$$ Si on Si(111) has been investigated using angle-resolved photoemission spectroscopy. Cu $$_2$$ Si exhibits two Dirac nodal-lines, stemming from the crossing of one electron-pocket with two hole-pockets, that are protected by mirror reflection symmetry. When Cu $$_2$$ Si is placed on Si(111), the hole-pockets and their satellite bands due to the quasi- $$5\times 5$$ periodicity are clearly observed whereas the electron-pocket is observed with very weak spectral intensity. Interestingly, close to the Fermi energy, the hole-pockets exhibit almost linear energy-momentum dispersion when their spectral width is also linearly proportional to energy. These findings indicate that Cu $$_2$$ Si on Si(111) can host Dirac nodal-line fermions, of which low-energy excitations might depart from those of the conventional Fermi liquid.

Intrinsic topological superconductivity with exactly flat surface bands in the quasi-one-dimensional A2Cr3As3 (A=Na, K, Rb, Cs) superconductors

A spin-U(1)-symmetry protected momentum-dependent integer-$Z$-valued topological invariant is proposed to time-reversal-invariant (TRI) superconductivity (SC) whose nonzero value will lead to exactly flat surface band(s). The theory is applied to the weakly spin-orbit coupled quasi-1D A$_2$Cr$_3$As$_3$ (A=Na, K, Rb, Cs) superconductors family with highest $T_c$ up to 8.6 K with $p_z$-wave pairing in the $S_z=0$ channel. It's found that up to the leading atomic spin-orbit-coupling (SOC), the whole (001) surface Brillouin zone is covered with exactly-flat surface bands, with some regime hosting three flat bands and the remaining part hosting two. Such exactly-flat surface bands will lead to very sharp zero-bias conductance peak in the scanning tunneling microscopic spectrum. When a tiny subleading spin-flipping SOC is considered, the surface bands will only be slightly split. The application of this theory can be generalized to other unconventional superconductors with weak SOC, particularly to those with mirror-reflection symmetry.

Weyl fermions in ferromagnetic high-temperature phase of K2Cr8O16

By combining first-principles calculations and symmetry arguments, we propose that the half-metallic phase of K2Cr8O16 presents ferromagnetic Weyl fermions. In particular, K2Cr8O16 possesses two pairs of Weyl nodes, which originate from two groups of nodal lines connected by the mirror reflection symmetry. We show that the non-trivial topological properties of K2Cr8O16 come from the partially occupied t2g states of Cr, and we also demonstrate that such exotic topological feature is robust. The topological surface states and corresponding Fermi arcs are revealed. As K2Cr8O16 is a realistic and widely studied material, our results suggest that K2Cr8O16 is an ideal candidate for studying ferromagnetic Weyl fermions. In addition, K2Cr8O16 possesses several interesting phenomena, such as the co-existence of charge density wave and Weyl fermions, even pairs of FM Weyl points, and tunable distribution of Weyl points, which will attract intensive attentions in this field.

First-principles design of a Dirac semimetal: An NP monolayer

We report a two-dimensional (2D) Dirac semimetal in an orthorhombic $\mathit{Pmma}$ structure, an NP monolayer, based on first-principles calculations. The NP monolayer is found to be stable according to phonon dispersion and molecular dynamical simulations. It exhibits a pair of anisotropic Dirac cones exactly at the Fermi level, located along high symmetry lines in the Brillouin zone, and shows highly anisotropic in-plane stiffness. First-principles calculations show that Dirac cones are locally stable under strains along the $x$ or $y$ direction and electric fields perpendicular to the monolayer. The Dirac nodes are protected from gap opening by the mirror-reflection symmetry in the $x$ direction. We construct an effective two-band tight-binding model to characterize the Dirac states. Our result provides a promising 2D material for special electronics applications.

Photovoltaic effect generated by spin-orbit interactions

An AC electric field applied to a junction comprising two spin-orbit coupled weak links connecting a quantum dot to two electronic terminals is proposed to induce a DC current and to generate a voltage drop over the junction if it is a part of an open circuit. This photovoltaic effect requires a junction in which mirror reflection-symmetry is broken. Its origin lies in the different fashion inelastic processes modify the reflection of electrons from the junction back into the two terminals, which leads to uncompensated DC transport. The effect can be detected by measuring the voltage drop that is built up due to that DC current. This voltage is an even function of the frequency of the AC electric field and is {\em not} related to quantum pumping.

Fully spin-polarized open and closed nodal lines in β -borophene by magnetic proximity effect

Recently, the experimental realization of Dirac fermions in ${\ensuremath{\beta}}_{12}$- and ${\ensuremath{\chi}}_{3}$-boron sheets has attracted tremendous attention and simulated a broad exploration for the novel topologically nontrivial states in two-dimensional materials. Herein, by combining first-principles and tight-binding calculations, we discover a coexistence of open nodal arc and closed nodal loop produced by three-band touching in the recently synthesized $\ensuremath{\beta}$-boron sheet [Q. Zhong et al., Phys. Rev. Mater. 1, 021001 (2017)]. The symmetry analysis reveals that the nodal lines are protected by both time-reversal symmetry (TRS) and mirror-reflection symmetry (MRS). Intriguingly, when TRS is broken, e.g., via introducing magnetic proximity effect, a topological phase transition occurs, namely, the original spin-degenerate nodal line (loop) decays into fully spin-polarized nodal line (loop). Furthermore, when Rashba spin-orbit coupling (SOC) is turned on to break the MRS, spin-up and -down states are shifted toward opposite momentum directions, leading to the emergence of two new nodal loops around the $\mathrm{\ensuremath{\Gamma}}$ point. In addition, inclusion of both Rashba SOC and exchange field leads to band-gap opening of the Dirac points and nodal lines. Our findings not only reveal a form of nodal line in the $\ensuremath{\beta}$-boron sheet, but also offer an alternative approach to realize spin-polarized nodal line semimetals with promising applications in spintronic devices.