Catalogue of flat-band stoichiometric materials.

Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems1-3. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website4,5, which provides their structural parameters, space group, band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness with a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices-in either two or three dimensions-that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use the database to extract a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centres that are not strongly localized on the atomic sites. We showcase five representative materials and provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

High-throughput calculations of magnetic topological materials.

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators1-3, have directed fundamental research in solid-state materials. Topological quantum chemistry4 has enabled the understanding of and the search for paramagnetic topological materials5,6. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC)7, here we perform a high-throughput search for magnetic topological materials based on first-principles calculations. We use as our starting point the Magnetic Materials Database on the Bilbao Crystallographic Server, which contains more than 549 magnetic compounds with magnetic structures deduced from neutron-scattering experiments, and identify 130 enforced semimetals (for which the band crossings are implied by symmetry eigenvalues), and topological insulators. For each compound, we perform complete electronic structure calculations, which include complete topological phase diagrams using different values of the Hubbard potential. Using a custom code to find the magnetic co-representations of all bands in all magnetic space groups, we generate data to be fed into the algorithm of MTQC to determine the topology of each magnetic material. Several of these materials display previously unknown topological phases, including symmetry-indicated magnetic semimetals, three-dimensional anomalous Hall insulators and higher-order magnetic semimetals. We analyse topological trends in the materials under varying interactions: 60 per cent of the 130 topological materials have topologies sensitive to interactions, and the others have stable topologies under varying interactions. We provide a materials database for future experimental studies and open-source code for diagnosing topologies of magnetic materials.

KAT8/SIRT7-mediated Fascin-K41 acetylation/deacetylation regulates tumor metastasis in esophageal squamous cell carcinoma.

Fascin actin-bundling protein 1 (Fascin) is highly expressed in a variety of cancers, including esophageal squamous cell carcinoma (ESCC), working as an important oncogenic protein and promoting the migration and invasion of cancer cells by bundling F-actin to facilitate the formation of filopodia and invadopodia. However, it is not clear how exactly the function of Fascin is regulated by acetylation in cancer cells. Here, in ESCC cells, the histone acetyltransferase KAT8 catalyzed Fascin lysine 41 (K41) acetylation, to inhibit Fascin-mediated F-actin bundling and the formation of filopodia and invadopodia. Furthermore, NAD-dependent protein deacetylase sirtuin (SIRT) 7-mediated deacetylation of Fascin-K41 enhances the formation of filopodia and invadopodia, which promotes the migration and invasion of ESCC cells. Clinically, the analysis of cancer and adjacent tissue samples from patients with ESCC showed that Fascin-K41 acetylation was lower in the cancer tissue of patients with lymph node metastasis than in that of patients without lymph node metastasis, and low levels of Fascin-K41 acetylation were associated with a poorer prognosis in patients with ESCC. Importantly, K41 acetylation significantly blocked NP-G2-044, one of the Fascin inhibitors currently being clinically evaluated, suggesting that NP-G2-044 may be more suitable for patients with low levels of Fascin-K41 acetylation, but not suitable for patients with high levels of Fascin-K41 acetylation. © 2024 The Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.

Management of non-contiguous upper and lower cervical spine fractures.

PURPOSE: Upper cervical fracture combined with non-contiguous lower cervical fracture are not uncommon but complicated. In order to outline a management principle for the upper cervical fracture combined with non-contiguous lower cervical fracture and assess its clinical characteristics, we retrospectively analyzed 59 cases of patients who underwent surgical treatment for upper cervical fracture combined with non-contiguous lower cervical fracture. METHODS: 59 patients of upper cervical fracture combined with non-contiguous lower cervical fracture were treated by surgery in our hospital. According to the AO Spine classification for cervical fractures, there were 21 cases of type B atlas fractures, nine cases of type C atlas fractures; 15 cases of type B axis fractures, 14 cases of type C axis fractures; 19 cases of type B lower cervical fractures, 40 cases of type C lower cervical fractures. The operation time, intraoperative blood loss, complications, VAS scores, JOA scores, ASIA grades, and radiological evaluation of cervical lordosis and stability were collected and recorded. RESULTS: Our results showed the segments of upper cervical fracture combined with non-contiguous lower cervical fracture are mainly concentrated in the atlas-axis and C6, C7 levels. There were 43 cases (72.88%) of associated injuries, mainly involving head trauma and thoracic injuries. Four patients underwent anterior approach surgery only, 43 patients underwent posterior approach surgery only, and 12 patients underwent combined anterior and posterior approach surgery in one stage. All patients had regular follow up with an average duration of 67.83 ± 11.25 months (range, 39 to 103 months). The VAS scores and JOA scores at 12 months postoperatively and at final follow-up showed significant improvement compared to preoperative scores (P < 0.05). At the final follow-up, ASIA grades had improved by 0 to 2 levels. The cervical lordosis at the final follow-up (24.71°±7.39°) showed no statistically significant difference compared to preoperative measurements (26.89°±13.32°). Surgical complications occurred in 17 patients. No cases of vertebral artery injury, screw loosening, or other internal fixation failures were found at final follow-up. CONCLUSIONS: Upper cervical fracture combined with non-contiguous lower cervical fracture can result in varying extents of cervical spinal cord injury and combined trauma in other parts. Surgical treatment of these injuries can achieve favourable clinical and radiological outcomes in the medium to long term follow-up. More research is still needed to optimize clinical decision-making regarding surgical approach.

Prevalence and risk factors of training-related abdominal injuries: A multicenter survey study.

PURPOSE: This study aims to identify the prevalence and risk factors of military training-related abdominal injuries and help plan and conduct training properly. METHODS: This questionnaire survey study was conducted from October 2021 to May 2022 among military personnel from 6 military units and 8 military medical centers and participants' medical records were consulted to identify the training-related abdominal injuries. All the military personnel who ever participated in military training were included. Those who refused to participate in this study or provided an incomplete questionnaire were excluded. The questionnaire collected demographic information, type of abdominal injury, frequency, training subjects, triggers, treatment, and training disturbance. Chi-square test and t-test were used to compare baseline information. Univariate and multivariate regression analyses were used to explore the risk factors associated with military training-related abdominal injuries. RESULTS: A total of 3058 participants were involved in this study, among which 1797 (58.8%) had suffered training-related abdominal injuries (the mean age was 24.3 years and the service time was 5.6 years), while 1261 (41.2%) had no training-related abdominal injuries (the mean age was 23.1 years and the service time was 4.3 years). There were 546 injured patients (30.4%) suspended the training and 84 (4.6%) needed to be referred to higher-level hospitals. The most common triggers included inadequate warm-up, fatigue, and intense training. The training subjects with the most abdominal injuries were long-distance running (589, 32.8%). Civil servants had the highest rate of abdominal trauma (17.1%). Age ≥ 25 years, military service ≥ 3 years, poor sleep status, and previous abdominal history were independent risk factors for training-related abdominal injury. CONCLUSION: More than half of the military personnel have suffered military training-related abdominal injuries. Inadequate warm-up, fatigue, and high training intensity are the most common inducing factors. Scientific and proper training should be conducted according to the factors causing abdominal injuries.

BMP5 ameliorates diabetic peripheral neuropathy by augmenting mitochondrial function and inhibiting apoptosis in Schwann cells.

Diabetic peripheral neuropathy is a common and serious complication of diabetes. Bone morphogenetic protein 5 (BMP5) is a multifunctional protein involved in the nervous system. Nevertheless, its effect on diabetic peripheral neuropathy remained uncharacterized. In this study, diabetic neuropathy in mice was induced by a single dose of 150 mg/kg streptozotocin (STZ) via intraperitoneal injection. Lentivirus expressing BMP5 (LV-BMP5) administration improved pain sensitivity, nerve conduction velocities and morphological alterations of the sciatic nerve of diabetic mice. Elevated BMP5 by LV-BMP5 suppressed cell apoptosis in the sciatic nerve, as evidenced by declined TUNEL-positive cells and down-regulated cleaved caspase-3 and cleaved caspase-9 levels. BMP5 enhanced mitochondrial membrane potential and ATP level. BMP5 also increased the phosphorylation of Smad1/5/9. Besides, the role of BMP5 in high glucose (HG)-stimulated Schwann cells was determined. Results of in vitro studies were in line with the in vivo findings. These experimental data seem to imply that BMP5 prevents the development of diabetic neuropathy via the maintenance of Smad1/5/9-mediated mitochondrial function.

Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries.

Adding magnetic flux to a band structure breaks Bloch's theorem by realizing a projective representation of the translation group. The resulting Hofstadter spectrum encodes the nonperturbative response of the bands to flux. Depending on their topology, adding flux can enforce a bulk gap closing (a Hofstadter semimetal) or boundary state pumping (a Hofstadter topological insulator). In this Letter, we present a real space classification of these Hofstadter phases. We give topological indices in terms of symmetry-protected real space invariants, which reveal the bulk and boundary responses of fragile topological states to flux. In fact, we find that the flux periodicity in tight-binding models causes the symmetries which are broken by the magnetic field to reenter at strong flux where they form projective point group representations. We completely classify the reentrant projective point groups and find that the Schur multipliers which define them are Arahanov-Bohm phases calculated along the bonds of the crystal. We find that a nontrivial Schur multiplier is enough to predict and protect the Hofstadter response with only zero-flux topology.

Genome analysis-based union of the genera Youhaiella and Paradevosia, and proposal that Methyloterrigena soli Kim et al. 2016 is a later heterotypic synonym of Paradevosia shaoguanensis Geng et al. 2015.

Phylogenetic tree analysis of Youhaiella tibetensis F4T, Paradevosia shaoguanensis J5-3T and Methyloterrigena soli M48T based on 16S rRNA gene sequences revealed that the three genera did not form distinct and independent monophyletic clusters. The 16S rRNA gene sequence similarities were all higher than 99 % between each pair of the three type strains. Average nucleotide identity, digital DNA-DNA hybridization, average amino acid identity and 16S rRNA gene sequence similarity between Paradevosia shaoguanensis J5-3T and Methyloterrigena soli M48T showed that they represented the same species. Physiological and biochemical characteristics of these three strains were similar, such as motility by polar flagella, major respiratory quinone, polar lipids, and fatty acids. Polygenetic trees and other characteristic comparative analysis revealed the need to merge the genera Youhaiella and Paradevosia into one genus.

Assessment of anxiety and depression in patients with Posner-Schlossman syndrome.

BACKGROUND: To assess the anxiety and depression levels in patients with Posner-Schlossman syndrome (PSS) and to determine the potential risk factors. METHODS: In this cross-sectional study, a total of 195 participants, including 93 PSS patients and 102 healthy controls were recruited. Sociodemographic and clinical information were collected for all participants. Hospital Anxiety and Depression scale (HADS) was administered to evaluate the anxiety and depression levels. Visual function (VF) and quality-of-life (QOL) questionnaires were administered to assess variables potentially associated with anxiety and depression. RESULTS: Increased anxiety level was observed in 22 (23.7%) PSS patients as compared to 10 (9.8%) of controls (P = 0.009). While the frequency of depression between the two groups was not significantly different (P = 0.349). The mean anxiety and depression scores were 6.98 ± 4.20 and 6.44 ± 3.66 in PSS patients as compared to 6.67 ± 3.21 (P = 0.564) and 5.96 ± 2.93 (P = 0.311) in controls. Logistic regression analysis showed mental well-being was significantly associated with anxiety (odds ratio [OR] = 0.920, 95% confidence interval [CI] = 0.881-0.962, P < 0.001) and depression (OR = 0.959, CI = 0.926-0.994, P = 0.023) in PSS patients. CONCLUSION: More patients with PSS may experience anxiety as compared to healthy controls. Mental well-being is an independent risk factor for anxiety and depression. It is important for ophthalmologists to be aware of these factors and should pay more attention on mental health when PSS is managed in clinic.

Evaluating brain parcellations using the distance-controlled boundary coefficient.

One important approach to human brain mapping is to define a set of distinct regions that can be linked to unique functions. Numerous brain parcellations have been proposed, using cytoarchitectonic, structural, or functional magnetic resonance imaging (fMRI) data. The intrinsic smoothness of brain data, however, poses a problem for current methods seeking to compare different parcellations. For example, criteria that simply compare within-parcel to between-parcel similarity provide even random parcellations with a high value. Furthermore, the evaluation is biased by the spatial scale of the parcellation. To address this problem, we propose the distance-controlled boundary coefficient (DCBC), an unbiased criterion to evaluate discrete parcellations. We employ this new criterion to evaluate existing parcellations of the human neocortex in their power to predict functional boundaries for an fMRI data set with many different tasks, as well as for resting-state data. We find that common anatomical parcellations do not perform better than chance, suggesting that task-based functional boundaries do not align well with sulcal landmarks. Parcellations based on resting-state fMRI data perform well; in some cases, as well as a parcellation defined on the evaluation data itself. Finally, multi-modal parcellations that combine functional and anatomical criteria perform substantially worse than those based on functional data alone, indicating that functionally homogeneous regions often span major anatomical landmarks. Overall, the DCBC advances the field of functional brain mapping by providing an unbiased metric that compares the predictive ability of different brain parcellations to define brain regions that are functionally maximally distinct.

Six-Year Incidence and Risk Factors for Primary Angle-Closure Disease: The Singapore Epidemiology of Eye Diseases Study.

PURPOSE: To determine the incidence and risk factors of primary angle-closure disease (PACD) over 6 years in a multi-ethnic Asian population. DESIGN: Population-based, longitudinal study. PARTICIPANTS: The Singapore Epidemiology of Eye Diseases study is a population-based cohort study conducted among adults aged 40 years or more. The baseline examination was conducted between 2004 and 2010, and the 6-year follow-up visit was conducted between 2011 and 2017. Of 6762 participants who attended the follow-up examination, 5298 at risk for primary angle-closure glaucoma (PACG) and 5060 at risk for PACD were included for analyses. METHODS: Standardized examinations including slit-lamp biomicroscopy, indentation gonioscopy, intraocular pressure (IOP) measurement, and static automated perimetry were performed. In this study, PACD includes primary angle-closure suspect (PACS), primary angle-closure (PAC), and PACG. MAIN OUTCOME MEASURES: The 6-year PACD incidence was evaluated among an at-risk population excluding adults with baseline glaucoma, PACS, PAC, pseudophakia at baseline or follow-up, or laser peripheral iridotomy or iridectomy at baseline visit. Logistic regression analysis adjusting for age, gender, and ethnicity was performed to evaluate associations between PACD development and demographic or ocular characteristics. Forward selection based on the Quasi-likelihood Information Criterion was used in multivariable analysis to reduce potential multicollinearity. RESULTS: The 6-year age-adjusted PACD incidence was 3.50% (95% confidence interval [CI], 2.94-4.16). In multivariable analysis, increasing age per decade (odds ratio [OR], 1.35; 95% CI, 1.15-1.59), higher IOP (OR, 1.04; 95% CI, 1.00-1.08), and shallower anterior chamber depth (OR, 1.11; 95% CI, 1.08-1.14) at baseline were associated with higher odds of PACD, whereas late posterior subcapsular cataract (PSC) (OR, 0.60; 95% CI, 0.48-0.76) was associated with lower odds of PACD. The 6-year age-adjusted incidences of PACG, PAC, and PACS were 0.29% (95% CI, 0.14-0.55), 0.46% (95% CI, 0.29-0.75), and 2.54% (95% CI, 2.07-3.12), respectively. CONCLUSIONS: Our study showed that the 6-year incidence of PACD was 3.50%. Increasing age, higher IOP, and shallower anterior chamber were associated with a higher risk of incident PACD, whereas late PSC was associated with a lower odds of PACD. These findings can aid in future projections and formulation of health care policies for screening of at-risk individuals for timely intervention.

Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem.

Magic-angle (θ=1.05°) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological semimetallic conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f and c electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f electrons coupled to nearly free c electrons-we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries of Refs. [1-5] as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations [2,6,7], and the minima of the charge gap at the Γ_{M} point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG.

Precision Spectroscopy of the Pionic Helium-4.

The transition frequency of (n,ℓ)=(17,16)→(16,15) in pionic helium-4 is calculated to an accuracy of 4 ppb (parts per billion), including relativistic and quantum electrodynamic corrections up to O(R_{∞}α^{5}). Our calculations significantly improve the recent theoretical values [Hori et al., Phys. Rev. A 89, 042515 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042515]. In addition, collisional effects between pionic helium and target helium on transition frequencies are estimated. Once measurements reach the ppb level, our Letter will improve the value of the π^{-} mass by 2-3 orders of magnitude.

The post-translational modification of Fascin: impact on cell biology and its associations with inhibiting tumor metastasis.

The post-translational modifications (PTMs), which are crucial in the regulation of protein functions, have great potential as biomarkers of cancer status. Fascin (Fascin actin-bundling protein 1, FSCN1), a key protein in the formation of filopodia that is structurally based on actin filaments (F-actin), is significantly associated with tumor invasion and metastasis. Studies have revealed various regulatory mechanisms of human Fascin, including PTMs. Although a number of Fascin PTM sites have been identified, their exact functions and clinical significance are much less explored. This review explores studies on the functions of Fascin and briefly discusses the regulatory mechanisms of Fascin. Next, to review the role of Fascin PTMs in cell biology and their associations with metastatic disease, we discuss the advances in the characterization of Fascin PTMs, including phosphorylation, ubiquitination, sumoylation, and acetylation, and the main regulatory mechanisms are discussed. Fascin PTMs may be potential targets for therapy for metastatic disease.

Microvirga puerhi sp. nov., isolated from Puerh tea garden soil.

Strain WGZ8T was isolated from a soil sample of Puerh tea garden in Pu'er city, Southwest China. The isolate was rod-shaped, Gram-stain negative, facultative anaerobic, non-motile. Growth occurred within 0-3.0% (w/v) NaCl (optimal concentration, 0-1.0%), pH 5.0-11.0 (optimal pH, 7.0) and 10-40 °C (optimal temperature, 28 °C). 16S rRNA gene sequence-based phylogenetic and phylogenomic analysis revealed that WGZ8T belonged to the genus Microvirga. Its major cellular fatty acids were C19:0 cyclo ω8c, C16:0, C18:1ω7c and/or C18:1ω6c. The profile of polar lipids included phosphatidyldimethylethanolamine, phosphatidylmonomethylethanolamine, phosphatidylethanolamine, phosphatidylcholine, diphosphatidylglycerol and phosphatidylglycerol. The only respiratory quinone was detected as ubiquinone 10 (Q-10). The genome size of strain WGZ8T was 5.17 MB, and the content of DNA G + C was 61 mol%. Based on the results of digital DNA-DNA hybridization and phenotypic results, strain WGZ8T could be concluded as a novel species of the genus Microvirga, for which the name Microvirga puerhi sp. nov. is proposed. The type strain is WGZ8T (= CGMCC 1.19171 T = JCM 35317 T).

Brevibacillus dissolubilis sp. nov., Isolated from Fresh Water.

A Gram-positive-staining, strictly aerobic, motile, ellipsoidal endospore-forming bacterial strain, designated CHY01T, was isolated from the Chishui river in a section of Maotai Town, Guizhou Province, Southwest China. Strain CHY01T was found to grow optimally at pH 8.0 and 28 °C. The 16S rRNA gene sequence analysis indicated that strain CHY01T belonged to the genus Brevibacillus and clustered with the type strain of Brevibacillus panacihumi, with which it exhibited 16S rRNA gene sequence similarity values of 97.8%. The predominant respiratory quinone was MK-7, and the major polar lipids were phosphatidylethanolamine and phosphatidylglycerol. The major fatty acids were C14:0, iso-C15:0, anteiso-C15:0, C16:0, C15:1iso-H and/or C13:0 3-OH, and C16:1ω7c and/or C16:1ω6c. Genome sequencing revealed a genome size of 6.1 Mbp and a G + C content of 50.6%. The results of physiological and biochemical tests allowed strain CHY01T to be distinguished genotypically and phenotypically from Brevibacillus species with validly published names. Pairwise determined whole-genome average nucleotide identity (ANI) and digital DNA-DNA hybridization (dDDH) values suggested that strain CHY01T represents a new species, for which we propose the name Brevibacillus dissolubilis sp. nov. with the type strain CHY01T (= CGMCC 1.15916 T = KCTC 33863 T).

Military training-related abdominal injuries and diseases: Common types, prevention and treatment.

Military training is intense, difficult and often dangerous, so all kinds of injuries or diseases frequently occur during training. Most of the previous studies and reviews on military training-related injuries focused on musculoskeletal system, whereas there are no reviews of abdominal injuries and diseases. Although the incidence of military training-related abdominal injuries and diseases is relatively low, the patients' condition is often critical especially in the presence of abdominal organ injury, leading to multi-organ dysfunction syndrome and even death. This paper elaborates on common types of military training-related abdominal injuries and diseases as well as the prevention and treatment measures, which provides some basis for scientific and reasonable training and improvement of medical security.

Fragile Topology and Flat-Band Superconductivity in the Strong-Coupling Regime.

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight D_{s}, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a nonzero Chern number or fragile topology sets a lower bound for D_{s}, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we numerically use exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. Then, we investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.

Delocalization Transition of a Disordered Axion Insulator.

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that, under quenched disorder respecting inversion symmetry on average, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be ν=1.42±0.12. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low-energy k·p expansion.