Band Structure Of Materials Research Articles

Electronic properties, optical transparency and transport properties of the p-type transparent conductive oxide family Sn2-xPbxNb2O7 (x = 0, 0.5, 1.0, 1.5, and 2.0): a density functional theory study.

Based on density functional theory, we introduce a novel family of p-type transparent conductive oxides, Sn2-xPbxNb2O7 (x = 0, 0.5, 1.0, 1.5, and 2.0), and confirm their thermodynamic and mechanical stabilities through detailed calculations of free energy, mixing enthalpy and elastic constant. We discuss how Pb atom substitution affects the lattice structure, band structure, electronic properties, optical properties, and transport properties of materials in this family and reveal the regulatory mechanisms. The antibonding coupling of Sn-O1 and Pb-O1 contributes to the formation of p-type characteristics. The highly dispersive Sn(Pb)5s(6s) band is formed when the O2-Sn(Pb)-O2 bonding angle is close to 180°, and the large elastic constant and small deformation potential energy all contribute to the high mobility in the system. Based on the evaluation of three empirical criteria, and incorporating the computational analysis of optical and transport properties, we determined that compounds with x = 1.0 and 1.5 are excellent intrinsic p-type transparent conductive materials with high valence band maximum (VBM) positions. The elevated VBM positions in these materials pave the way for significant enhancements in p-type conductivity via acceptor doping techniques.

Modulating the band structure of two‐dimensional black phosphorus via electronic effects of organic functional groups for enhanced hydrogen production activity

Electronic effects of organic functional groups play a fundamental role in determining the rate and/or direction of organic chemical reactions. The implementation of this concept in selective organic catalysis is achieved by tuning the electronic effects of organic functional groups to alter the corresponding reactivity. However, this approach has hardly been applied to modulate the band structure of inorganic materials. Here, we show that modulating the electronic band structure of two‐dimensional black phosphorus (BP) is possible via the electronic effects of organic functional groups covalently modified on its surface. Organic functional group can either donate or withdraw charge density from BP surface, which will alter the bonding/anti‐binding orbitals occupancy and thus shift the band‐edge positions of functionalized BP downward/upward. Therefore, the valence‐band maxima and the conduction‐band minima of functionalized BP can be continuously tuned by changing the binding group with different Hammett parameters. Finally, unexpectedly high hydrogen evolution reaction rates under visible light are achieved using functionalized BP heterojunctions as photocatalysts. This work underscores the significant role of electronic effects in chemically controlling BP’s band structure, offering greater flexibility and affordability beyond physical method limits.

Exploring the Crystal Structure and Electronic Properties of γ-Al2O3: Machine Learning Drives Future Material Innovations.

For decades, researchers have struggled to determine the precise crystal structure of γ-Al2O3 due to its atomic-level disorder and the challenges associated with obtaining high-purity, high-crystallinity γ-Al2O3 in laboratory settings. This study investigates the crystal structure and electronic properties of γ-Al2O3 coatings under the influence of an external electric field, integrating machine learning with density functional theory (DFT). A potential 160-atom supercell structure was identified from over 600,000 γ-Al2O3 configurations and confirmed through high-resolution transmission electron microscopy and selected area electron diffraction. The findings indicate that γ-Al2O3 deviates from the conventional spinel structure, suggesting that octahedral vacancies can reduce the system's energy. Under an external electric field, the material's band structure and density of states (DOS) undergo significant changes: the bandgap narrows from 3.996 to 0 eV, resulting in metallic behavior, while the projected density of states (PDOS) exhibits peak broadening and splitting of oxygen atom PDOS below the Fermi level. These alterations elucidate the variations in the electrical conductivity of alumina coatings under an electric field. These findings clarify the mechanisms of γ-Al2O3's electronic property modulation and offer insights into its covalent and ionic mixed bonding as a wide-bandgap semiconductor. This discovery is essential for understanding dielectric breakdown in insulating materials.

Engineering band structures of two-dimensional materials with remote moiré ferroelectricity.

The stacking order and twist angle provide abundant opportunities for engineering band structures of two-dimensional materials, including the formation of moiré bands, flat bands, and topologically nontrivial bands. The inversion symmetry breaking in rhombohedral-stacked transitional metal dichalcogenides endows them with an interfacial ferroelectricity associated with an out-of-plane electric polarization. By utilizing twist angle as a knob to construct rhombohedral-stacked transitional metal dichalcogenides, antiferroelectric domain networks with alternating out-of-plane polarization can be generated. Here, we demonstrate that such spatially periodic ferroelectric polarizations in parallel-stacked twisted WSe2 can imprint their moiré potential onto a remote bilayer graphene. This remote moiré potential gives rise to pronounced satellite resistance peaks besides the charge-neutrality point in graphene, which are tunable by the twist angle of WSe2. Our observations of ferroelectric hysteresis at finite displacement fields suggest the moiré is delivered by a long-range electrostatic potential. The constructed superlattices by moiré ferroelectricity represent a highly flexible approach, as they involve the separation of the moiré construction layer from the electronic transport layer. This remote moiré is identified as a weak potential and can coexist with conventional moiré. Our results offer a comprehensive strategy for engineering band structures and properties of two-dimensional materials by utilizing moiré ferroelectricity.

Band structures based phononic crystals in quasi-Sierpinski fractals with defects

This study presents a detailed analysis of the effects of geometric defects in phononic crystals, focusing on the use of a distribution of Sierpinski fractals for the strategic placement of inclusions. Using theoretical and computational approaches, we investigate the influence of these defects on the material's band structure. Phononic crystals, designed based on fractal geometry inspired by the Sierpinski pattern, are particularly sensitive to the introduction of inclusions, resulting in disorder in the periodic structure. Our study examines in detail how different defect configurations affect the formation of localized modes and the energy distribution in the material's band structure. The results obtained provide valuable insights into how the presence of geometric defects can be exploited or minimized in the design of phononic crystals for practical applications, including acoustic isolation, vibration control, and the development of advanced acoustic devices. These results contribute to the understanding and advancement of fractal phononic crystals, paving the way for future research and promising technological applications, both in terms of frequency and attenuation, depending on the complexity and hierarchy of the fractal structures used.

An Examination of the Electronic, Optical, and Thermodynamic Properties of Β-Gan

The current work involves the systematic examination of the features of Gallium Nitride (GaN) including the electronic, optical, structural, and thermodynamic features, depending on first principles calculation. This is according to approximations, (LDA), (GGA), and (m-GGA). The bandgap energies of Gallium nitride are (1.85 eV, 1.93 eV, and 2.179 eV), respectively. Furthermore, our study also reveals that GaN has a direct bandgap and is highly stable. Finally, our results indicate that the m-GGA method accurately predicts the bandgap energy of GaN. The m-GGA method outperforms both LDA and GGA methods in accuracy to predict the bandgap energy of GaN, as evidenced by its closest approximation to the experimental value. To determine the orbital nature of the Gallium and Nitrogen atoms, the state density and state partial density of Gallium nitride were simulated. The absorption coefficient of Gallium nitride is computed and analyzed in depth for the optical transitions. The absorption coefficient of Gallium nitride is affected by various factors, including the material's band structure, temperature, doping level, and the energy of the incident photons. In addition to that, the thermodynamic properties that can be calculated like enthalpy, entropy, heat capacity, free energy, and Debye temperature enable us to understand the thermal behavior of the compound better. The heat capacity of α-GaN is detected to be (39.9, 25.5, and 32.4) Jmole-1K-1, and a Debye temperature of 807 K, 1134 K, and 866 K for LDA, GGA, and m-GGA, respectively. This research will offer a detailed interpretation of β-GaN, covering all its basic properties and possible applications in electronic devices and optoelectronic devices. The results of this study are very important and the new technologies that will be developed based on the Cubic phase - GaN research will be very beneficial.

The synthesis of Bi2MoO6 with metallic and nonmetallic vacancies for degradation of LVF in visible light

Defect engineering advantages include regulating the band structure of photocatalytic materials, inhibiting the recombination of photoelectron-hole pairs, and promoting the conversion of photogenerated electrons into active radicals. In this paper, bismuth molybdate (Bi2MoO6) photocatalysts with double vacancies (VBi-O-BMO) were prepared by solvothermal and ionic eutectic solvent methods. EPR, TEM, and XPS results confirmed the successful construction of oxygen and bismuth vacancies on Bi2MoO6. The photocatalytic performance of the prepared catalysts was investigated by photodegradation of levofloxacin hydrochloride (LVF) under visible light. The double vacancies markedly enhanced the photocatalytic properties of Bi2MoO6, with the photodegradation rate of VBi-O-BMO reaching 88.36 % for 40 mg/L LVF within 60 min. Kinetic studies have demonstrated that the reaction rate constant of VBi-O-BMO can reach 0.0351 min−1, which is 3.2 times higher than that of bulk-BMO. This can be attributed to the favorable synergistic effect of oxygen and bismuth double vacancies. VO not only captures oxygen and electrons, facilitating the generation of superoxide radicals (O2−), but also elevates the conduction band position and boosts the reduction capability of Bi2MoO6. VBi not only captures photogenerated holes (h+) to directly impact LVF degradation, but also promotes interfacial charge transfer and inhibits the recombination of electron-hole pairs. Furthermore, the intermediates and degradation pathways of LVF photodegradation were surmised based on the LC-MS analysis. The reaction mechanism of LVF photodegradation by VBi-O-BMO was elucidated through the application of the free radical pathway. This study demonstrates a methodology for the creation of double vacancies in catalysts and the significant potential of VBi-O-BMO for the remediation of antibiotic residues in water under visible light.

(Invited) Deformable Electronics Based on Strain-Engineered Van Der Waals Materials

Materials exhibit drastically different physical and chemical properties as their dimensionality varies. Atomically-thin van der Waals (vdW) materials possess unique mechanical, electrical, optical, and thermal characteristics, originated from quantum confined low-dimensionality and a lack of dangling bond. In particular, strong in-plane covalent bonding and weak interlayer vdW interaction of two-dimensional (2D) vdW materials enable exceptional combination of mechanical properties, such as high Young’s modulus, high in-plane strength, and ultralow bending stiffness at a level of cell membrane. Moreover, mechanical strain can induce modulation of electronic and phononic band structures of 2D vdW materials more effectively due to mechanical resilience and high surface-to-volume ratio. For these reasons, deformation engineering has garnered substantial interest in mechanics, materials and electronics communities as a new tuning knob for emerging phenomena and functionalities of 2D vdW materials. In this talk, I will discuss deformation engineering of 2D vdW materials – (1) active and dynamic deformation strategies, including in-plane interfacial slippage and out-of-plane structural deformation, (2) deformation strain induced phenomena, and (3) emerging device concepts based on deformation engineering of 2D vdW materials.

Electroluminescence from pure resonant states in hBN-based vertical tunneling junctions

Defect centers in wide-band-gap crystals have garnered interest for their potential in applications among optoelectronic and sensor technologies. However, defects embedded in highly insulating crystals, like diamond, silicon carbide, or aluminum oxide, have been notoriously difficult to excite electrically due to their large internal resistance. To address this challenge, we realized a new paradigm of exciting defects in vertical tunneling junctions based on carbon centers in hexagonal boron nitride (hBN). The rational design of the devices via van der Waals technology enabled us to raise and control optical processes related to defect-to-band and intradefect electroluminescence. The fundamental understanding of the tunneling events was based on the transfer of the electronic wave function amplitude between resonant defect states in hBN to the metallic state in graphene, which leads to dramatic changes in the characteristics of electrons due to different band structures of constituent materials. In our devices, the decay of electrons via tunneling pathways competed with radiative recombination, resulting in an unprecedented degree of tuneability of carrier dynamics due to the significant sensitivity of the characteristic tunneling times on the thickness and structure of the barrier. This enabled us to achieve a high-efficiency electrical excitation of intradefect transitions, exceeding by several orders of magnitude the efficiency of optical excitation in the sub-band-gap regime. This work represents a significant advancement towards a universal and scalable platform for electrically driven devices utilizing defect centers in wide-band-gap crystals with properties modulated via activation of different tunneling mechanisms at a level of device engineering.

Tailored Cis-Trans Isomeric Metal-Covalent Organic Frameworks for Coordination Configuration-Dependent Electrochemiluminescence.

Precise manipulation of the coordination configuration within substances can modulate the band structure and catalytic properties of the target material. Metal-covalent organic frameworks (MCOFs), a crystal material amalgamating the benefits of metal-organic frameworks (MOFs) and covalent organic frameworks (COFs), can integrate a predetermined coordination environment into the frameworks for amplifying the catalytic effect. In this study, we delicately synthesize isomeric MCOFs using bis(glycinato)copper as the aminoligand via kinetically and thermodynamically favorable pathways to yield cis-MCOF and trans-MCOF products, respectively, thereby introducing a cis-trans isomeric coordination field into the framework. Moreover, the twisted skeleton derived from the flexibility of amino acid and β-ketoenamine linkages endows trans-MCOF with surprising water dispersibility. Compared to cis-MCOF, the trans isomerism displays a significant enhancement in cathodic electrochemiluminescence via the catalysis of Cu nodes toward K2S2O8. The density of states analysis shows that the d-band center of trans-MCOF is closer to the Fermi level, leading to more stable adsorption binding to promote the catalysis. This study is the first report on constructing predesign coordination configuration MCOFs via an easy-handling method, which gives the guidelines for the design of amino acid-based MCOF materials.

Adsorption and electron injection studies in N719 sensitized Ag[formula omitted], Au[formula omitted] implanted and O2 annealed titania films

The device performance of novel solar cell configurations with porphyrin, hybrid perovskite-based materials as sensitizers depends on the interfacial processes and engineered interfaces with characteristic material properties can be fabricated employing energetic ion implantations. In this experimental work, the dye adsorption, optical absorption and interfacial electron injection in N719 sensitized Ag−, Au−, sequentially impinged and O2 annealed titania films were studied. Prior to the dye sensitization process, impinged samples were fabricated employing mono-ion type, sequential implantations and a set of the as-implanted films were annealed at 450 °C for 1 h in O2 environment. The N719 molecules are adsorbed onto Ag−, Au− impinged films through SCN ligands, indicated by the appearance of new Raman modes ν(Ag-S), ν(Au-S) respectively. The 1MLCT, 3MLCT bands of the dye molecules are altered upon implantation and annealing processes. A fast interfacial electron injection process with τ2∼3.7 ps has been observed in the sensitized annealed sequentially impinged film at 6 × 1015 ions cm−2 (sensitized pristine TiO2 exhibits τ2∼51 ps) and is attributed to Ag−, Au− implants introducing new states to the conduction band of anatase TiO2. The ability of ion-implantation technique to introduce new states to the band structure of materials has enormous significance in photo-catalytic, water-splitting, solar cell and hot electron injection technologies.

Ultra-flat bands at large twist angles in group-V twisted bilayer materials.

Flat bands in 2D twisted materials are key to the realization of correlation-related exotic phenomena. However, a flat band often was achieved in the large system with a very small twist angle, which enormously increases the computational and experimental complexity. In this work, we proposed group-V twisted bilayer materials, including P, As, and Sb in the β phase with large twist angles. The band structure of twisted bilayer materials up to 2524 atoms has been investigated by a deep learning method DeepH, which significantly reduces the computational time. Our results show that the bandgap and the flat bandwidth of twisted bilayer β-P, β-As, and β-Sb reduce gradually with the decreasing of twist angle, and the ultra-flat band with bandwidth approaching 0eV is achieved. Interestingly, we found that a twist angle of 9.43° is sufficient to achieve the band flatness for β-As comparable to that of twist bilayer graphene at the magic angle of 1.08°. Moreover, we also find that the bandgap reduces with decreasing interlayer distance while the flat band is still preserved, which suggests interlayer distance as an effective routine to tune the bandgap of flat band systems. Our research provides a feasible platform for exploring physical phenomena related to flat bands in twisted layered 2D materials.

Modulating electronic structure by interlayer spacing and twist on bilayer bismuthene.

Modulation of the electronic structure has played a crucial role in advancing the field of two-dimensional materials, but there are still many unexplored directions, such as the twist angle for a novel degree of freedom, for modulating the properties of heterostructures. We observed a distinct pattern in the energy bands of bilayer bismuthene, demonstrating that modulating the twist angle and interlayer spacing significantly influences interlayer interactions. Our study of various interlayer spacings and twist angles revealed a close relationship between bandgap size and interlayer spacing, while the twist angle notably affects the shape of the energy bands. Furthermore, we observed a synergistic effect between these two factors. As the twist angle decreases, the energy bands become flat, and flat bands can be generated without requiring a specific angle on bilayer bismuthene. Our results suggest a promising way to tailor the energy band structure of bilayer 2D materials by varying the interlayer spacing and twist angle.

Investigation of spectro-temporal high-order sideband generation from transition metal dichalcogenides [Invited

High-order sideband generation (HSG) in semiconductors under intense terahertz fields has been extensively studied, because it provides essential information for studying ultrafast dynamics in strong-field-dressed quantum materials. In particular, transition metal dichalcogenides (TMDCs), characterized by their unique band structures, provide an exemplary semiconductor system to explore the influence of material band structure on strong-field-induced modulation of HSG. In this work, we investigate the spectro-temporally resolved HSG from different bulk TMDC materials. Our results reveal distinct temporal HSG spectra, which can be attributed to the different absorption behaviors of these materials. Simulations based on the strong-field approximation and Floquet theory can well reproduce the experimental observations. Our work also delves into the spectro-temporal interference that emerges when neighboring harmonic orders overlap in the HSG spectrum. This work enhances our understanding of high-order sideband dynamics in strong-field-dressed semiconductors, offering insights for applications in spectrum- and phase-resolved ultrafast measurements.

Ab-initio investigation of the structural, electronic and optical properties of CsPbBr3 perovskite under pressure using the DFT-1/2 method

Pressure-induced phase transitions in metal halide perovskites lead to significantly different material properties and offer great potential for diverse applications. The electronic, structural, and optical properties of Cesium lead bromide (CsPbBr3) crystals are investigated using density functional theory (DFT) to draw an integrated picture of orbital morphology, absorption spectra, and band gap values. Spin-orbit coupling and DFT-1/2 correction are used to gain a better insight into electronic properties and band splitting in the cubic phase. Calculations of pressure-induced phase transitions, electronic band gap engineering, and manipulation of optical absorption edges of CsPbBr3 are conducted. In the cubic and tetragonal crystal lattices, a band gap closure and opening occurs demonstrating a Dirac cone upon application and increase of pressure. Indeed, in the tetragonal lattice of CsPbBr3, a topological band occurs. Orthorhombic perovskite crystal lattice undergoes successive direct-indirect and indirect-direct band gap transitions, followed by a space group change at extreme pressures. However, under pressure, orthorhombic non-perovskite lattice experiences a sudden band gap breakdown. Phase and band gap transitions are explained by orbital hybridizations and structural symmetry evolution (e.g., bond length contraction/dilation and octahedral cage rotation/distortion). These results provide comprehensive guidelines for further experimental studies on pressure engineering, advanced photovoltaic and optoelectronic applications, discovering and understanding new topological band structures of perovskite materials.

Vanadium Metal Doping of Monolayer MoS2 for p-Type Transistors and Fast-Speed Phototransistors.

Modulating the electrical properties of two-dimensional (2D) materials is a fundamental prerequisite for their development to advanced electronic and optoelectronic devices. Substitutional doping has been demonstrated as an effective method for tuning the band structure in monolayer 2D materials. Here, we demonstrate a facile selective-area growth of vanadium-doped molybdenum disulfide (V-doped MoS2) flakes via pre-patterned vanadium-metal-assisted chemical vapor deposition (CVD). Optical microscopy characterization revealed the presence of flake arrays. Transmission electron microscopy, Raman spectroscopy, and X-ray photoelectron spectroscopy were employed to identify the chemical composition and crystalline structure of as-grown flakes. Electrical measurements indicated a light p-type conduction behavior in monolayer V-doped MoS2. Furthermore, the response time of phototransistors based on V-doped MoS2 monolayers exhibited a remarkable capability of 3 ms, representing approximately 3 orders of magnitude faster response than that observed in pure MoS2 phototransistors. This work hereby provides a feasible approach to doping of 2D materials, promising a scalable pathway for the integration of these materials into emerging electronic and optoelectronic devices.

Filling-enforced obstructed atomic insulators

Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial insulators at the Fermi level. In this paper, we show that, remarkably, for a subset of the topologically trivial insulators, knowing only their electron number and the Wyckoff positions of the atoms we can separate them into two groups: the obstructed atomic insulator (OAI) and the atomic insulator (AI). The interesting group, the OAI, have a center of charge not localized on the atoms. Using the theory of topological quantum chemistry, in this work we first derive the necessary and sufficient conditions for a topologically trivial insulator to be a filling enforced obstructed atomic insulator (feOAI) in the 1651 Shubnikov space groups. Remarkably, the filling enforced criteria enable the identification of obstructed atomic bands without knowing the representations of the band structures. Hence, no calculations are needed for the filling enforced criteria, although they are needed to obtain the band gaps. With the help of the Topological Quantum Chemistry website, we have performed a high-throughput search for feOAIs and have found that 957 ICSD entries (638 unique materials) are paramagnetic feOAIs, among which 738 (475) materials have an indirect gap. The metallic obstructed surface states of feOAIs are also showcased by several material examples. Published by the American Physical Society 2024

Boosting tetracycline degradation of BaTiO3-based piezo-catalysts via modulating phase boundary and band structure

Piezoelectric catalysis, which converts mechanical energy into chemical activity, has important applications in environmental remediation. However, the piezo-catalytic activity of various piezoelectric materials is limited by the weak piezoelectricity as well as the mismatched band-gap, leading to inefficient electron-hole pair generation and difficult carrier migration. Here, a simple strategy combining phase boundary and energy band structure modulation was innovatively proposed to enhance the piezo-catalytic activity of BaTiO3 ferroelectric by Ce ions selecting different doping sites. Thanks to the coexistence of tetragonal (P4mm) and orthorhombic (Amm2) phases effectively flattened the Gibbs free-energy and thus enhanced the piezoelectric activity, as well as suitable energy bandwidth facilitating the carrier migration were realized in the B-sites doped Ba(Ti0.95Ce0.05)O3. The degradation rate constant k of tetracycline (TC) was high to 30.56 × 10-3 min−1, which was 2.03 times higher than that of pure BaTiO3 and superior to most representative lead-free perovskite piezoelectric materials. Theoretical calculations validated that the charge density and high O2 and OH– adsorption energy on the Ba(Ti0.95Ce0.05)O3 surface promoted more efficient •O2– and •OH radicals conversion and bettered response to piezo-catalytic reaction. This work is important to design high-performance piezo-catalysts by synergistic regulation of phase boundary and energy band structure in perovskite materials for long-term antibiotic tetracycline removal.

Boosting Thermoelectric Performance in Nanocrystalline Ternary Skutterudite Thin Films through Metallic CoTe2 Integration.

Metal-semiconductor nanocomposites have emerged as a viable strategy for concurrently tailoring both thermal and electronic transport properties of established thermoelectric materials, ultimately achieving synergistic performance. In this investigation, a series of nanocomposite thin films were synthesized, embedding metallic cobalt telluride (CoTe2) nanophase within the nanocrystalline ternary skutterudite (Co(Ge1.22Sb0.22)Te1.58 or CGST) matrix. Our approach harnessed composition fluctuation-induced phase separation and in situ growth during thermal annealing to seamlessly integrate the metallic phase. The distinctive band structures of both materials have developed an ohmic-type contact characteristic at the interface, which raised carrier density considerably yet negligibly affected the mobility counterpart, leading to a substantial improvement in electrical conductivity. The intricate balance in transport properties is further influenced by the metallic CoTe2 phase's role in diminishing lattice thermal conductivity. The presence of the metallic phase instigates enhanced phonon scattering at the interface boundaries. Consequently, a 2-fold enhancement in the thermoelectric figure of merit (zT ∼ 1.30) is attained with CGST-7 wt. % CoTe2 nanocomposite film at 655 K compared to that of pristine CGST.

Bound-in-continuum-like corner states in the type-II Dirac photonic lattice

Dirac points are special points in the energy band structure of various materials, around which the dispersion is linear. If the corresponding Fermi surface is projected as a pair of crossing lines—or touching cones in two dimensions, the Dirac point is known as the type-II; such points violate the Lorentz invariance. Until now, thanks to its unique characteristics, the Klein tunneling is successfully mimicked and the topological edge solitons are obtained in the type-II Dirac photonic lattices that naturally possess type-II Dirac points. However, the interplay between these points and corner states is still not investigated. Here, we report both linear and nonlinear corner states in the type-II Dirac photonic lattice with elaborate boundaries. The states, classified as in-phase and out-of-phase, hide in the extended bands that are similar to the bound states in the continuum (BIC). We find that the nonlinear BIC-like corner states are remarkably stable. In addition, by removing certain sites, we establish the fractal Sierpiński gasket structure in the type-II Dirac photonic lattice, in which the BIC-like corner states are also demonstrated. The differences between results in the fractal and nonfractal lattices are rather small. Last but not least, the corner breather states are proposed. Our results provide a novel view on the corner states and may inspire fresh ideas on how to manipulate/control the localized states in different photonic lattices.