Lattice Symmetry Research Articles

Edge and skin effects in rhombus reciprocal photonic crystals

With the development of non-Hermitian physics, the non-Hermitian skin effect (NHSE) has attracted much attention. Existing research highlights the critical roles of the periodic boundary condition (PBC) spectrum, lattice symmetry, and macroscopic symmetry of the lattice in relation to the geometry-dependent skin effect (GDSE). However, the impact of macroscopic edge geometry is frequently neglected. We find that the GDSE is highly sensitive to the edge and cannot be simply determined by the symmetries. Specifically, the GDSE can emerge at trivial interfaces of rhombus photonic crystals (PhCs) with zigzag edge and bearded edge. Furthermore, we analyze the underlying mechanisms from the perspective of point-gap topology. This work underscores important, yet frequently overlooked, aspects in two-dimensional (2D) reciprocal PhC systems and can be used to enhance design flexibility, allowing the NHSE to have better applications in areas such as lasers and highly sensitive sensors.

Spin-valley locked excited states spectroscoy in a one-particle bilayer graphene quantum dot

Current semiconductor qubits rely either on the spin or on the charge degree of freedom to encode quantum information. By contrast, in bilayer graphene the valley degree of freedom, stemming from the crystal lattice symmetry, is a robust quantum number that can therefore be harnessed for this purpose. The simplest implementation of a valley qubit would rely on two states with opposite valleys as in the case of a single-carrier bilayer graphene quantum dot immersed in a small perpendicular magnetic field (B⊥ ≲ 100 mT). However, the single-carrier quantum dot excited states spectrum has not been resolved to date in the relevant magnetic field range. Here, we fill this gap, by measuring the parallel and perpendicular magnetic field dependence of this spectrum with an unprecedented resolution of 4 μeV. We use a time-resolved charge detection technique that gives us access to individual tunnel events. Our results come as a direct verification of the predicted spectrum and establish a new upper-bound on inter-valley mixing, equal to our energy resolution. Our charge detection technique opens the door to measuring the relaxation time of a valley qubit in a single-carrier bilayer graphene quantum dot.

Visualizing the topological pentagon states of a giant C540 metamaterial

Systems with broken continuous symmetry in ideal lattices cannot be rectified through rearrangement or deformation. Topological metamaterials featuring nontrivial, artificially induced phase transitions have emerged as pivotal constituents for engineering these topological defects, which, until now, have mostly been experimentally realized in linear or planar configurations. Buckminster Fuller lent his name to the C60 ball-shaped carbon allotrope, which is not only the roundest molecule in existence but also embodies 3D topological defects. Here, we construct a C540 metamaterial composed of interspersed pentagons in a hexagonal network of hollow tubes and cavities. By 3D printing this giant closed-cage topology, the nontrivial state-confinements can be fully controlled and visualized, which, in contrast, in synthesized or naturally found fullerenes, is highly challenging. Thanks to our macroscopic metamaterials approach, we are able to map in real-space topological pentagon states probed by sound waves. Our results show how a seemingly unrelated approach can unveil deep physical understanding in carbon allotropes and potentially in a plethora of other complex systems in the near future.

Global Selection Rules and Giant Enhanced Harmonic Generations in LiNbO3 Nonlinear Meta‐Optics

AbstractNonlinear optical metasurfaces provide nanoscale‐level control of harmonic waves, making them highly promising platforms for both fundamental research and applications in nonlinear optics. However, the traditional selection rules theory, which has long served as a guiding principle for nonlinear meta‐optics, is local and neglects the significance of meta‐atomic lattice symmetry. In addition, achieving high‐efficiency harmonic generation along with nonlinear optical Pancharatnam‐Berry (PB) phase control remains challenging. To this end, a novel global selection rule jointly determined by the symmetries of both meta‐atom and lattice is proposed. Nonlinear metasurfaces designed based on this theory enable frequency conversions forbidden by previous local selection rules. A more comprehensive relationship between the nonlinear PB phase and the meta‐atomic rotation angle is revealed. Moreover, an efficient nonlinear PB metasurface platform for second harmonic generations is first demonstrated using LiNbO3 thin films with aligned crystal orientations in a hybrid design. The normalized conversion efficiency reaches approximately two orders of magnitude higher than that of existing nonlinear PB metasurfaces working in the near‐infrared band. These findings not only shed light on the underlying mechanisms of nonlinear light‐matter interactions, but also open up exciting possibilities in terahertz, entangled photon pairs, and high harmonic generations.

Effects of Eu3+ doping on the structural, magnetocaloric effect and critical behavior of Ruddlesden-Popper compounds La1.4-xEuxSr1.6Mn2O7 (0 ≤ x ≤ 0.1)

The effects of Eu3+ doping on the structural and magnetocaloric effect of Ruddlesden-Popper compounds La1.4-xEuxSr1.6Mn2O7 (0 ≤ x ≤ 0.1) were investigated. The X-ray diffraction and infrared spectroscopy confirmed that La1.4-xEuxSr1.6Mn2O7 compounds exhibited the tetragonal lattice symmetry (I4/mmm) of the Ruddlesden-Popper phase. The crystal structure of La1.4-xEuxSr1.6Mn2O7 compounds distorted and phase separated as the amount of Eu3+ doping varied. The magnetization-temperature curves demonstrated that La1.4-xEuxSr1.6Mn2O7 compounds display a notable transition temperature attributed to its anisotropic exchange coupling. The maximum magnetic entropy changes (−ΔSMmax) of La1.4-xEuxSr1.6Mn2O7(x = 0, 0.075, and 0.1) compounds are 2.82, 3.12 and 3.40 J/(kg·K) at the 5 T applied magnetic field. Meanwhile, its relative cooling power (RCP) was 186.37, 207.42 and 242.54 J/kg, respectively. The critical behavior of La1.4-xEuxSr1.6Mn2O7 (0≤x≤0.1) compounds was analyzed around Tc, and it was found that the critical index (β = 0.413, γ = 1.020, δ = 3.038) is essentially in line with the mean field theory.

Three-Dimensional Moiré Crystal in Ultracold Atomic Gases.

The work intends to extend the moiré physics to three dimensions. Three-dimensional moiré patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moiré pattern features a periodic structure termed a three-dimensional moiré crystal. We emphasize a key distinction of three-dimensional moiré physics: In three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moiré crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.

Entanglement Entropy and Deconfined Criticality: Emergent SO(5) Symmetry and Proper Lattice Bipartition.

We study the Rényi entanglement entropy (EE) of the two-dimensional J-Q model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum MonteCarlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-N conformal field theory with SO(N=5) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for cornerless bipartitions. We here use a 45° tilted cut on the square lattice. Beyond supporting an SO(5) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.

Au25 Cluster-Based Atomically Precise Coordination Frameworks and Emission Engineering through Lattice Symmetry.

The atomically precise metal nanoclusters (NCs) have attracted significant attention due to their superatomic behavior originating from the quantum confinement effect. This behavior makes these materials suitable for various photoluminescence-based applications, including chemical sensing, bioimaging, and phototherapy, owing to their intriguing optical properties. Especially, the manipulation of inter- or intracluster interaction through cluster-assembled materials (CAMs) presents significant pathways for modifying the photophysical properties of NCs. Herein, two distinct CAMs, Au25-Zn-Hex and Au25-Zn-Rod, were synthesized via forming a coordination bond between [Au25(p-HMBA)18]- (p-H2MBA = 4-mercaptobenzoic acid) and Zn2+. Au25-Zn-Rod exhibited a 6-fold higher luminescence intensity in the near-infrared region compared to Au25-Zn-Hex, attributed to synergistic inter- and intracluster interactions that induce exciton delocalization and structure rigidification at the atomic scale. This study highlights the potential of diverse lattice symmetries in cluster-based frameworks for tuning the photophysical properties, contributing to a deeper understanding of the structure-property relationship in Au NCs.

Internal Electric Fields and Structural Instabilities in Insulating Transition Metal Compounds: Influence on Optical Properties

AbstractThis work reviews new ideas developed in the last two decades which play a key role for understanding the optical properties of insulating materials containing transition metal (TM) cations. Initially, this review deals with compounds involving d4 and d9 ions where the local structure of the involved MX6 complexes (M=dn cation, X=ligand) is never cubic but distorted, a fact widely ascribed to the Jahn‐Teller (JT) effect. Nevertheless, that assumption is often wrong as the JT coupling requires an orbitally degenerate ground state in the initial geometry a condition not fulfilled even if the lattice is tetragonal. For this reason, the equilibrium geometry of d4 and d9 complexes in low symmetry lattices, is influenced by two factors: (i) The effects, usually ignored, of the internal electric field, ER, due to the rest of lattice ions on the active electrons localized in the MX6 unit. (ii) The existence of structural instabilities driven by vibronic interactions that lead to negative force constants. As first examples of these ideas, we show that the equilibrium structure, electronic ground state of KZnF3:Cu2+, K2ZnF4:Cu2+ and K2CuF4 obey to different causes and only in KZnF3:Cu2+ the JT effect takes place. These ideas also explain the local structure and optical properties of CuF2, CrF2 or KAlCuF6 compounds where the JT effect is symmetry forbidden and those of layered copper chloroperovskites where the orthorhombic instability explains the red shift of one d−d transition under pressure. In a second step, this review explores stable systems involving d3, d5 or d9 cations, where the internal electric field, ER, is responsible for some puzzling phenomena. This is the case of ruby and emerald that surprisingly exhibit a different color despite the Cr3+‐O2− distance is the same. A similar situation holds when comparing the normal (KMgF3) and the inverted (LiBaF3) perovskites doped with Mn2+ having the same Mn2+‐F distance but clearly different optical spectra. The role of ER is particularly remarkable looking for the origin of the color in the historical Egyptian Blue pigment based on CaCuSi4O10.

Lattice symmetry relaxation as a cause for anisotropic line broadening and peak shift in powder diffraction.

In powder diffraction, lattice symmetry relaxation causes a peak to split into several components which are not resolved if the degree of desymmetrization is small (pseudosymmetry). Here the equations which rule peak splitting are elaborated for the six minimal symmetry transitions, showing that the resulting split peaks are generally broader and asymmetric, and suffer an hkl-dependent displacement with respect to the high-symmetry parent peak. These results will be of help in Rietveld refinement of pseudosymmetric structures where an exact interpretation of peak deformation is required.

An in-depth study of the synthesis of ReSe2 for anisotropic Raman characteristics

Abstract Two-dimensional transition metal dichalcogenides (TMDs) have received more interest for their potential role in future electronic and optoelectronic applications. Unlike other TMDs, Rhenium diselenide (ReSe2) stands out for its distinctive anisotropic growth characteristics. These unique features arise from its low lattice symmetry and interlayer decoupling, this has sparked significant interest among researchers. Previous research has indicated the presence of various growth patterns, including dendritic formations and structures resembling flowers. In this study, we effectively produced ReSe2 using the ‘Tilting Boat’ method to achieve growth on a 21 μm scale. Through precise manipulation of the growth conditions, we successfully attained flakes of 21 μm scale in comparison to prior findings. Moreover, we successfully produced a variety of shapes, including triangles, diamonds, and hexagons, on 1 × 1 cm2 Si/SiO2 substrates. Furthermore, we achieved the successful production of a continuous ReSe2 film on a 1 × 3 cm2 Al2O3 substrate. We verified the distinct anisotropic properties of ReSe2 via Raman Spectroscopy. Furthermore, we acquired three-dimensional visual representations of ReSe2 flakes and continuous films via SEM measurements. By employing EDS data and analysing x-ray photoelectron spectroscopy spectra, we have established a compositional ratio of 1:2 for Re and Se, which aligns with the MX2 structure. This confirmation indicates the successful synthesis of high-quality ReSe2 flakes.

Topological edge states of acoustic zigzag tubes with triangle scatterers

Tubular geometries in phononic crystals have the advantages of hosting topological edge states without breaking the underlying symmetry of the lattice. The topological relationships between the acoustic zigzag tubes and the dispersion relation of the planar phononic crystal with a zigzag edge boundary are theoretically revealed through 2D k space analysis, circumferential pressure analysis, and lattice symmetry analysis. New cutting lines of the tubes are obtained, which link the winding number of the tubes with the dispersion relation of topological edge states in the planar phononic crystal. The eigenstates analysis shows that the circumferential periodic number of a tubular edge state is regular and corresponds to a specific wavenumber in the circumferential direction. On the basis of the unveiled topological relationships, tubular edge states with tunable properties are obtained by controlling the characteristic length of the boundary scatterers. Moreover, the tubular edge states are confirmed to be highly confined and robust along the designed transmission channel. This study may present a new way to design acoustic tubes with tunability and have potential applications in robust wave propagation and miniaturized phononic devices.

Luminescence performance, temperature sensing characteristics and Judd-Ofelt theory analysis of Y2MoO6:Er3+/Yb3+/Li+ upconversion phosphors

A series of Y2MoO6:0.01Er3+/0.09Yb3+ upconversion phosphors doped with different concentrations of Li+ ions (0.05, 0.10, 0.15, 0.20, 0.25, and 0.30 mol) were prepared by the high temperature solid phase reaction method, and their physical phase structures and upconversion luminescence were analyzed. At the excitation wavelength of 980 nm, the addition of Li+ sharply increased the upconversion luminescence intensity. With the increase of Li+ ion content, the luminescence intensity first increases and then decreases. When the doping amount reaches 0.25 mol, the luminescence intensity reaches the maximum, and the sample emits green light in the two-photon process. Y2MoO6:0.01Er3+/0.09Yb3+/0.25Li+ exhibits excellent temperature sensing properties. Its absolute sensitivity Sa reaches up to 0.012 K-1, the relative sensitivity Sr is 0.017 K-1 and the measurement error δT is less than 0.3 K at room temperature. Its temperature sensing performance is far superior to similar materials. In addition, Judd-Ofelt theory calculations revealed that in comparison with Y2MoO6:0.01Er3+/0.09Yb3+, its Ω2 increased from 0.56×10-20 cm2 to 3.68×10-20 cm2 , and the spectroscopic quality factor Ω4/Ω6 ratio reached 4.09, which is much higher than that of the other fluorescent materials. The main reason is that Li+ replaces the Y3+ ion lattice site, causing lattice distortion and reducing the lattice symmetry around the active ion. The increase in asymmetry increases the possibility of spontaneous radiative transitions. It is shown that the prepared upconversion luminescent materials have potential applications in the field of solid-state lasers and optical sensing.

Nematic Superconductivity and Its Critical Vestigial Phases in the Quasicrystal.

We propose a general mechanism to realize nematic superconductivity (SC) and reveal its exotic vestigial phases in the quasicrystal (QC). Starting from a Penrose-Hubbard model, our microscopic studies suggest that the Kohn-Luttinger mechanism driven SC in the QC is usually gapless due to violation of Anderson's theorem, rendering that both chiral and nematic SCs are common. The nematic SC in the QC can support novel vestigial phases driven by pairing phase fluctuations above its T_{c}. Our combined renormalization group and MonteCarlo studies provide a phase diagram in which, besides the conventional charge-4e SC, two critical vestigial phases emerge, i.e., the quasinematic (QN) SC and QN metal. In the two QN phases, discrete lattice rotation symmetry is counterintuitively "quasibroken" with power-law decaying orientation correlation. They separate the phase diagram into various phases connected via Berezinskii-Kosterlitz-Thouless (BKT) transitions. These remarkable critical vestigial phases, which resemble the intermediate BKT phase in the q state (q≥5) clock model, are a consequence of the fivefold (or higher) anisotropy field brought about by the unique QC symmetry, which are absent in conventional crystalline materials.

Superconductivity and Mott Physics in Organic Charge Transfer Materials.

The phase diagrams of quasi two-dimensional organic superconductors display a plethora of fundamental phenomena associated with strong electron correlations, such as unconventional superconductivity, metal-insulator transitions, frustrated magnetism and spin liquid behavior. We analyze a minimal model for these compounds, the Hubbard model on an anisotropic triangular lattice, using cutting-edge quantum embedding methods respecting the lattice symmetry. We demonstrate the existence of unconventional superconductivity by directly entering the symmetry-broken phase. We show that the crossover from the Fermi liquid metal to the Mott insulator is associated with the formation of a pseudogap. The predicted momentum-selective destruction of the Fermi surface into hot and cold regions provides motivation for further spectroscopic studies. Our theoretical results agree with experimental phase diagrams of κ-BEDT organics.

Lieb-Schultz-Mattis theorems for symmetry-protected topological phases

The Lieb-Schultz-Mattis (LSM) theorem and its generalizations are a class of powerful no-go theorems that rule out any short-range-entangled (SRE) symmetric ground state irrespective of the specific Hamiltonian, based only on certain microscopic inputs, such as symmetries and particle filling numbers. In this work, we introduce and provide physical arguments for a new class of LSM-type theorems, where any symmetry-allowed SRE ground state must be a symmetry-protected topological (SPT) phase with robust gapless edge states, such as topological insulators and superconductors. The key ingredient is to replace the lattice translation symmetry in usual LSM theorems by the magnetic translation symmetry. These theorems provide new insights into realistic models and experimental realizations of SPT phases in interacting bosons and fermions.

Unique magnetic structure of the vdW antiferromagnet VBr3

VBr3 is a van der Waals antiferromagnet below the Néel temperature of 26.5 K with a saturation moment of 1.2 µB/f.u. above the metamagnetic transitions detected in the in-plane and out-of-plane directions. To reveal the AFM structure of VBr3 experimentally, we performed a single-crystal neutron diffraction study on a large high-quality crystal. The collected data confirmed a slight monoclinic distortion of the high-temperature rhombohedral structure below 90 K. The magnetic structure was, nevertheless, investigated within the R-3 model. The antiferromagnetic structure propagation vector k = (1, 0, ½) was revealed. In an attempt to determine the magnetic structure, 72 non-equivalent magnetic reflections were recorded. The experimental data were confronted with the magnetic space groups dictated by the R-3 lattice symmetry and propagation vector. The best agreement between the experimental data and the magnetic structure model was obtained for the space group P-1.1′_c. The magnetic unit cell of the proposed unique antiferromagnetic structure with periodicity 6c is built from two identical triple layers antiferromagnetically coupled along the c axis. Each triple layer comprises a Néel antiferromagnetic monolayer sandwiched between two antiferromagnetically coupled ferromagnetic monolayers.

Observation of flat bands and Dirac cones in a pyrochlore lattice superconductor

Emergent phases often appear when the electronic kinetic energy is comparable to the Coulomb interactions. One approach to seek material systems as hosts of such emergent phases is to realize localization of electronic wavefunctions due to the geometric frustration inherent in the crystal structure, resulting in flat electronic bands. Recently, such efforts have found a wide range of exotic phases in the two-dimensional kagome lattice, including magnetic order, time-reversal symmetry breaking charge order, nematicity, and superconductivity. However, the interlayer coupling of the kagome layers disrupts the destructive interference needed to completely quench the kinetic energy. Here we demonstrate that an interwoven kagome network—a pyrochlore lattice—can host a three dimensional (3D) localization of electron wavefunctions. Meanwhile, the nonsymmorphic symmetry of the pyrochlore lattice guarantees all band crossings at the Brillouin zone X point to be 3D gapless Dirac points, which was predicted theoretically but never yet observed experimentally. Through a combination of angle-resolved photoemission spectroscopy, fundamental lattice model and density functional theory calculations, we investigate the novel electronic structure of a Laves phase superconductor with a pyrochlore sublattice, CeRu2. We observe evidence of flat bands originating from the Ce 4f orbitals as well as flat bands from the 3D destructive interference of the Ru 4d orbitals. We further observe the nonsymmorphic symmetry-protected 3D gapless Dirac cone at the X point. Our work establishes the pyrochlore structure as a promising lattice platform to realize and tune novel emergent phases intertwining topology and many-body interactions.

Brightening dark excitons in inorganic halide perovskites by local symmetry breaking

Thermally activated delayed fluorescence (TADF) phenomenon, defined as thermal activation of triplet dark-state excitons into singlet state excitons through reverse intersystem crossing (RISC), has become a prevalent principle for designing organic-based electro-/photo-luminescent molecules. However, activating dark excitons in inorganic metal halide perovskites (MHPs) still remains challenging. Herein, we report an efficient strategy of doping-induced local symmetry breaking to brighten dark excitons in inorganic halide perovskite Cs2ZrCl6, which result in a 500 % enhancement of low-temperature luminescence emission. Lattice symmetry breaking confirmed by the X-ray absorption spectroscopy measurements could disturb the local coordination environment at the Zr site. The singlet-triplet energy gap (ΔEST) fitted from temperature-dependent photoluminescence decay curves decreases from 0.087 to 0.071 eV, thus reducing up-conversion barrier of dark excitons. Theoretical calculation indicates large spatial separation of charge density favorable for enhanced TADF emission. Furthermore, a flexible X-ray scintillator screen with poly (dimethylsiloxane) as the matrix could obtain high-quality X-ray imaging with a 14 lp mm−1 resolution. This work gives insights into improving photoemission of inorganic MHPs via brightening dark excitons.

Altermagnetism Induced by Sliding Ferroelectricity via Lattice Symmetry-Mediated Magnetoelectric Coupling.

Altermagnets, distinct from conventional ferromagnets or antiferromagnets, have recently attracted attention as the third category of collinear magnets, which exhibit the coexistence of zero net magnetization and spin polarization due to their unique lattice symmetries. Meanwhile, the additional layer degrees of freedom in multilayer sliding ferroelectrics offer opportunities for coupling with lattice symmetries, paving the way for an innovative approach to constructing multiferroic lattices. In this study, altermagnetic tuning in SnS2/MnPSe3/SnS2 heterostructures is achieved by breaking and restoration of lattice inversion symmetry through sliding ferroelectric switching. First-principles calculations reveal that the spin density and corresponding time-reversal symmetry of MnPSe3 can be manipulated by lattice symmetry, triggering phase transitions between antiferromagnetism and altermagnetism. This research establishes a novel form of magnetoelectric coupling mediated by lattice symmetry and provides a theoretical basis for the design of miniature information processing and memory devices based on altermagnetism.