Electronic Phenomena Research Articles

Two-channel anomalous Hall effect originating from the intermixing in Mn2CoAl/Pd thin films

The anomalous Hall effect (AHE) is an electronic transport phenomenon with rich physics. In thin magnetic films and multilayers, an unusual peak observed in AHE is often identified as the topological Hall effect (THE), induced by topologically nontrivial spin textures. However, it is a challenge to determine whether this unusual peak truly originates from such spin textures or is an artifact due to inhomogeneities. In this work, we systematically study the Pd thickness and temperature dependence of the Hall effect in ${\mathrm{Mn}}_{2}\mathrm{CoAl}$/Pd thin films. We observe an unusual peak in the Pd thickness dependence and rule out that the origin of the peak is from the topologically nontrivial spin textures by directly imaging the magnetic domain structures. We also build a model for the AHE based on the sum of contributions from ${\mathrm{Mn}}_{2}\mathrm{CoAl}$ and an intermixed CoPd alloy. These materials have opposite signs of the AHE and different coercive fields, which successfully explains the thickness and temperature behaviors of the unusual peak. Our results show that the interface mixing layer can play an important role in the interpretation of the AHE in ferromagnet/heavy metal systems.

Electronic structure and magnetic properties of 3d−4f double perovskite material

Double perovskite-based magnets wherein frustration and competition between emergent degrees of freedom are at play can lead to novel electronic and magnetic phenomena. Herein, we report the electronic structure and magnetic properties of an ordered double perovskite material Ho2CoMnO6. In the double perovskite with general class A2BB'O6, the octahedral B and B'-site has a distinct crystallographic site. The Rietveld refinement of XRD data reveals that Ho2CoMnO6 crystallizes in the monoclinic P21/n space group. The X-ray photoelectron spectroscopy confirms the charge state of cations present in this material. The temperature dependence of magnetization and specific heat exhibit a long-range ferromagnetic ordering at Tc ~ 76 K owing to the presence of super exchange interaction between Co2+ and Mn4+ moments. Furthermore, the magnetization isotherm at 5 K shows a hysteresis curve that confirms ferromagnetic behavior of this double perovskite. We observed a re-entrant glassy state in the intermediate temperature regime, which is attributed to inherent anti-site disorder and competing interactions. A large magnetocaloric effect has been observed much below the ferromagnetic transition temperature. The temperature-dependent Raman spectroscopy studies support the presence of spin-phonon coupling and short-range order above Tc in this double perovskite. The stabilization of magnetic ordering and charge states is further analyzed through electronic structure calculations. The latter also infers the compound to be a narrow band gap insulator with the gap arising between the lower and upper Hubbard Co-d subbands. Our results demonstrate that anti-site disorder and complex 3d-4f exchange interactions in the spin-lattice account for the observed electronic and magnetic properties in this promising double perovskite material.

Identification of a characteristic doping for charge order phenomena in Bi-2212 cuprates via RIXS

Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with charge order (CO) have been inferred from the anomalous enhancement of CO excitations that accompany the reduction of the CO order parameter in the superconducting state. To gain more insight about the interplay between CO and superconductivity, here we investigate the doping dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram using resonant inelastic x-ray scattering (RIXS) at the Cu L3- edge. As doping increases, the CO wavevector decreases, saturating at a commensurate value of 0.25 r.l.u. beyond a characteristic doping pc, where the correlation length becomes shorter than the apparent periodicity (4a0). Such behavior is indicative of the fluctuating nature of the CO; and the proliferation of CO excitations in the superconducting state also appears strongest at pc, consistent with expected behavior at a CO QCP. Intriguingly, pc appears to be near optimal doping, where the superconducting transition temperature Tc is maximal.

Electron-Beam Induced Emergence of Mesoscopic Ordering in Layered MnPS3.

Ordered mesoscale structures in 2D materials induced by small misorientations have allowed for a wide variety of electronic, ferroelectric, and quantum phenomena to be explored. Until now, the only mechanism to induce this periodic ordering was via mechanical rotations between the layers, with the periodicity of the resulting moiré pattern being directly related to twist angle. Here we report a fundamentally distinct mechanism for emergence of mesoscopic periodic patterns in multilayer sulfur-containing metal phosphorus trichalcogenide, MnPS3, induced by the electron beam. The formation under the beam of periodic hexagonal patterns with several characteristic length scales, nucleation and transitions between the phases, and local dynamics are demonstrated. The associated mechanisms are attributed to the relative contraction of the layers caused by beam-induced sulfur vacancy formation with subsequent ordering and lattice parameter change. As a result, the plasmonic response of the system is locally altered, suggesting an element of control over plasmon resonances by electron beam patterning. We pose that harnessing this phenomenon provides both insight into fundamental physics of quantum materials and enables device applications by enabling controlled periodic potentials on the atomic scale.

First-principles calculations to investigate the structural, electronic, optical anisotropy, and bonding properties of a newly synthesized ThRhGe equiatomic ternary intermetallic superconductor

Orthorhombic ThRhGe is a newly synthesized TiNiSi-type ternary intermetallic compound that exhibits weak-coupling type-II superconductivity. The optical anisotropy and bonding properties of ThRhGe have not been well investigated, except for some physical, electronic, and superconductivity-related phenomena. These previously unknown characteristics of ThRhGe have been described in this research using first-principles calculations based on density functional theory (DFT). Its superconducting property is revealed by the band structure and density of states plots. Mulliken bond population analysis offers information on the nature of both ionic and covalent bonds, which are also found in the charge density analysis. Six bands of the Fermi surface are also depicted. The anisotropic behavior of ThRhGe can be determined using optical measurements in both visible and high-energy regions. The majority of the findings in this study are novel and should be useful as a reference for future research.

Plasmonic phenomena in molecular junctions: principles and applications.

Molecular junctions are building blocks for constructing future nanoelectronic devices that enable the investigation of a broad range of electronic transport properties within nanoscale regions. Crossing both the nanoscopic and mesoscopic length scales, plasmonics lies at the intersection of the macroscopic photonics and nanoelectronics, owing to their capability of confining light to dimensions far below the diffraction limit. Research activities on plasmonic phenomena in molecular electronics started around 2010, and feedback between plasmons and molecular junctions has increased over the past years. These efforts can provide new insights into the near-field interaction and the corresponding tunability in properties, as well as resultant plasmon-based molecular devices. This Review presents the latest advancements of plasmonic resonances in molecular junctions and details the progress in plasmon excitation and plasmon coupling. We also highlight emerging experimental approaches to unravel the mechanisms behind the various types of light-matter interactions at molecular length scales, where quantum effects come into play. Finally, we discuss the potential of these plasmonic-electronic hybrid systems across various future applications, including sensing, photocatalysis, molecular trapping and active control of molecular switches.

Random strain induced correlations in materials with intertwined nematic and magnetic orders

Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is a composite order arising from a stripe state. Using Monte Carlo to simulate this $\textit{random Baxter-field model}$, we find not only the expected break-up of the system into nematic domains, but also the emergence of nontrivial disorder-promoted magnetic correlations. Such correlations enhance and tie up the fluctuations associated with the two degenerate magnetic stripe states from which nematicity arises, leaving characteristic signatures in the spatial profile of the magnetic domains, in the configurational space of the spin variables, and in the magnetic noise spectrum. We discuss possible experimental manifestations of these effects in iron-pnictide superconductors. Our work establishes the random Baxter-field model as a more complete alternative to the random-field Ising model to describe complex electronic nematic phenomena in the presence of disorder.

Paranormal experiences, sensory-processing sensitivity, and the priming of pareidolia.

This investigation tested the effect of priming on pareidolia (the hearing of illusory words in ambiguous stimuli). Participants (41 women, 20 men, mean age 29.95 years) were assigned to primed (n = 30) or unprimed (n = 31) groups: the former were told the study was of ‘purported ghosts voices’, the latter ‘voices in noisy environments.’ Participants were assessed for perception of human voices within recordings of purported electronic voice phenomena (EVP), degraded human speech, normal human speech, and white noise. The primed group had significantly higher perception of voices within EVPs than in degraded speech, this difference was not found for unprimed participants. In contrast to the previous use of this design, the primed group did not have higher perception of voices in EVPs and degraded speech than did the unprimed group. The Aesthetic Sensitivity dimension of the Highly Sensitive Person Scale (HSPS) was associated with detection of degraded stimuli, but not with accuracy of stimulus identification. HSPS score was related to lifetime reporting of anomalous and paranormal experiences. This study partially replicates a paranormal priming effect and shows relationships between HSPS and detection of ambiguous stimuli and anomalous and paranormal experiences.

Two-dimensional Dirac-line semimetals resistant to strong spin–orbit coupling

Several intriguing electronic phenomena and electric properties were discovered in three-dimensional Dirac nodal line semimetals (3D-DNLSM), which are, however, easy to be perturbed under strong spin-orbit coupling (SOC). While two-dimensional (2D) layers are an emerging material category with many advantages, 2D-DNLSM against SOC is yet to be uncovered. Here, we report a 2D-DNLSM in odd-atomic-layer Bi (the brick phase, another Bi allotrope), whose robustness against SOC is protected by the little co-group C_2v \times Z^T_2, the unique protecting symmetry we found in 2D.Specially, (4n+2) valence electrons fill the electronic bands in the brick phase, so that the Dirac nodal line with fourfold degeneracy locates across the Fermi level. There are almost no other low energy states close to the Fermi level; this allows to feasibly observe the neat DNLSM-induced phenomena in transport measurements without being affected by other bands. In contrast, Other VA-group elements also form the brick phases, but their DNL states are mixed with the extra states around the Fermi level. This unprecedented category of layered materials allows for exploring nearly isolated 2DDNL states in 2D.

Detectability of core-level crossing and electronic topological transformations: The case of osmium

Osmium, the least compressible metal, has recently been observed to undergo abrupt changes in the $c/a$ ratio at extreme pressures. These are claimed to provide evidence for two unusual electronic behaviors: a crossing of the semicore $4f$ and $5p$ levels, and an electronic topological transition. We demonstrate that these two electronic phenomena are readily reproduced and understood in density functional theory, but that neither perturbs the trend in $c/a$ ratio against pressure. Hence the observed anomalies in $c/a$ must have another cause. Osmium is also notable for its high yield stress: the $c/a$ anomalies lie well within the differential strains which osmium can support. We propose that observed $c/a$ changes can arise from mechanical yield of crystallites with strong preferred orientation under high deviatoric stress in the experimental data. We discuss what evidence remains for the more general hypothesis that core-level overlap under pressure can have measurable effects on the crystal structure in any material.

Nontrivial band topology coupled thermoelectrics in VSe2/MoSe2 van der Waals magnetic Weyl semimetal

The correlation between topological and thermoelectrics promotes numerous interesting electronic phenomena and sets the stage for efficient thermopower devices. Herein, we report nontrivial band topology of 1T–VSe2/1H–MoSe2 van der Waals system and also probe its thermoelectric (TE) characteristics on the basis of first-principle calculations. The crossover of bands, which creates a close loop near Fermi level along M–K high symmetry points, gets inverted at former crossing points of bands, under spin–orbit coupling effect. The calculated Chern Number C = 1 supports the nontrivial band topology whereas the broken time reversal symmetry asserts its magnetic Weyl semimetallic behavior. The nontrivial band topology falls under the category of Type-I Weyl band crossing. We delve into the TE characteristics of the proposed topological material by employing constant relaxation time approximation. The heterostructure shows high electrical conductivity of order 106 S m−1 at both 300 K and 1200 K, and a low magnitude of Seebeck coefficient (S) value of 79.3 μV K−1 near room temperature. Such interplay between the topological phase and TE characteristics can lay foundation for next-generation topological-TE devices.

Transient surface photovoltage spectroscopy of diamond

Contactless and highly sensitive probing of electronic transitions in diamond over a wide spectral range from near infrared to deep ultraviolet is still challenging. Surface photovoltage (SPV) signals depend on electronic transitions and transport phenomena leading to charge separation in space and allow for a contactless study of electronic transitions. Here, transient SPV spectroscopy in an arrangement with a charge amplifier and a laser tunable over a wide range was applied to study an undoped diamond single crystal between 0.8 and 5.9 eV at room temperature in ambient air. SPV transients were measured without and with weak visible bias light, which allowed for suppression of possible parasitic contributions in SPV signals not related to diamond and distinction of processes of charge separation that were independent of band bending. Transitions at 1.0 and 3.1 eV led to preferential separation of photogenerated holes toward the surface. In contrast, a transition at 1.8 eV caused preferential separation of photogenerated electrons toward the surface. Transitions near the indirect bandgap of diamond were observed at 5.27, 5.32, 5.48, and 5.53 eV and could be assigned to absorption assisted (i) by an indirect exciton and absorption of longitudinal optical and acoustic phonons, (ii) by absorption of transverse acoustic phonons, (iii) by emission of transverse acoustic phonons, and (iv) by emission of longitudinal optical and acoustic phonons, respectively. Charge separation under excitation at 5.27 eV was caused by directed charge transfer at/near the diamond surface after exciton diffusion followed by exciton dissociation.

Diagnosis of pairing symmetry by vortex and edge spectra in kagome superconductors

Layered kagome metals AV3Sb5 (A=K, Rb, Cs) exhibit diverse correlated electron phenomena. It includes charge density wave formation and superconductivity the pairing symmetry of which, however, is controversial due to contradictory experimental evidence. Through calculations based on real-space lattice models at the mean-field level, we investigate the vortex and surface spectra of all competitive pairing propensities suggested for AV3Sb5 from a weak coupling analysis of unconventional superconductivity. Chiral p-wave pairing emerges as the only option to host Majorana bound states in the vortex core. We find chiral edge states for both p-wave and d-wave pairing, along with flat Andreev surface bound states for f -wave pairing. Our results expand the fingerprint of superconducting pairing, and thus will contribute to resolving the nature of superconductivity in AV3Sb5.

Electronic properties of twisted multilayer graphene

Twisted bilayer graphene displays many fascinating properties that can be tuned by varying the relative angle (also called twist angle) between its layers. As a notable feature, both the electronic flat bands and the corresponding strong electron localization have been obtained at a specific ‘magic’ angle (), leading to the observation of several strongly correlated electronic phenomena. Such a discovery has hence inspired the creation of a novel research field called twistronics, i.e. aiming to explore novel physical properties in vertically stacked 2D structures when tuning the twist angle between the related layers. In this paper, a comprehensive and systematic study related to the electronic properties of twisted multilayer graphene (TMG) is presented based on atomistic calculations. The dependence of both the global and the local electronic quantities on the twist angle and on the stacking configuration are analyzed, fully taking into account atomic reconstruction effects. Consequently, the correlation between structural and electronic properties are clarified, thereby highlighting the shared characteristics and differences between various TMG systems as well as providing a comprehensive and essential overview. On the basis of these investigations, possibilities to tune the electronic properties are discussed, allowing for further developments in the field of twistronics.

The time-resolved atomic, molecular and optical science instrument at the Linac Coherent Light Source.

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray free-electron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a sub-micrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program.

Emergent ferroelectricity in subnanometer binary oxide films on silicon.

The critical size limit of voltage-switchable electric dipoles has extensive implications for energy-efficient electronics, underlying the importance of ferroelectric order stabilized at reduced dimensionality. We report on the thickness-dependent antiferroelectric-to-ferroelectric phase transition in zirconium dioxide (ZrO2) thin films on silicon. The emergent ferroelectricity and hysteretic polarization switching in ultrathin ZrO2, conventionally a paraelectric material, notably persists down to a film thickness of 5 angstroms, the fluorite-structure unit-cell size. This approach to exploit three-dimensional centrosymmetric materials deposited down to the two-dimensional thickness limit, particularly within this model fluorite-structure system that possesses unconventional ferroelectric size effects, offers substantial promise for electronics, demonstrated by proof-of-principle atomic-scale nonvolatile ferroelectric memory on silicon. Additionally, it is also indicative of hidden electronic phenomena that are achievable across a wide class of simple binary materials.

Insights into the aftereffects phenomenon in solids based on DFT and time-differential perturbed γ−γ angular correlation studies in 111In (→ 111Cd) -doped tin oxides

Recently, a model based on a combined ab initio/time-differential perturbed $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlation (TDPAC) study in the $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped ${\mathrm{SnO}}_{2}$ semiconductor was proposed to enlighten the origin of the dynamic hyperfine interactions (HFIs) observed in oxides after the electron-capture (EC) decay of the probe nucleus of the $^{111}\mathrm{In}$ parent. It was demonstrated that both the EC as well as the acceptor level introduced by the Cd impurity can contribute to the variation of the electric-field gradient (EFG) at the Cd site (responsible for this phenomenon) due to charge fluctuations of the electronic holes created [Darriba et al., J. Phys. Chem. C 122, 17423 (2018)]. To disentangle both effects, we performed here TDPAC reversible experiments in $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped SnO in the temperature range 20--900 K and a complete electronic structure density functional theory study of the Cd-doped SnO system as a function of the charge state $(q)$ of the impurity. The isovalent $^{111}\mathrm{Cd}$ probe impurity in this isocationic oxide was selected to demonstrate that the acceptor character of the probe is not a necessary condition to observe this electronic phenomenon when the EC is already present. A majority fraction of probes sensed a time-dependent HFI (HFI1) for all temperatures, and the unexpected minority always sensed a static interaction (HFI2). Comparing results from these experiments, the ab initio calculations of the EFG tensor and defect formation energies, HFI1 and HFI2, were assigned to $^{111}\mathrm{Cd}$ probes localized at substitutional Sn sites free of defects [with the valence band (VB) completely filled, $q=0$] and with an electronic hole trapped $(q=1+)$, respectively. In addition, we show that the systems with charge state between these values have very similar formation energies at the top of the VB and different predicted EFGs, giving support from first principles to the existence of random fluctuations between different EFGs, necessary in the construction of the on-off perturbation factor used. We demonstrate that all the probes fill their electronic holes before the TDPAC time window except the outermost one, giving a quantification of the number of electronic holes involved in the production of the dynamic effect, only one in SnO. The probes related to HFI2 reach their stable electronic configuration $(q=1+)$ before the emission of the first \ensuremath{\gamma} ray $({\ensuremath{\gamma}}_{1})$ of the \ensuremath{\gamma}-\ensuremath{\gamma} cascade, while those related to HFI1 fill the last hole after the emission of ${\ensuremath{\gamma}}_{1}$, producing the dynamic interaction. Enlighted by these results and reviewing TDPAC experiments from the literature using probes with different nuclear decay characteristics, we concluded that, in the absence of EC decay of the probe nucleus of the parent, any probe impurity introducing acceptor or donor states (in semiconductors and insulators) whose ionization changes the EFG should observe a time-dependent HFI provided the lifetime of the nuclear levels that feed the ${\ensuremath{\gamma}}_{1}$ level and this level itself is shorter than the lifetime of the recovery process (i.e., the lifetime of the electronic holes or the ionized donor electrons).

SH waves in a stressed piezoelectric semiconductor plates: Electron and hole drift phenomenon

• Simplified version of ODE method for a stressed piezoelectric semiconductor plate • The influence of biaxial stresses on the drift of electrons and holes phenomenon • For σ 11 0 =2.7 GPa, phase velocity in piezoelectric plate is exactly similar to that found in stressed PSC plate Can the residual stresses affect significantly the drift of electrons and holes? The main goal of this research is to provide answers to this question. Although the behavior of acoustic wave in stressed purely piezoelectric plates is a thoroughly studied subject, very few works account for piezoelectric semiconductor (so-called piezotronics) structures because of the complexity related to the large size of the square matrix to be solved. To study the characteristics of stressed piezotronics material, this paper presents a numerical matrix solution to predict the dispersion curves of shear horizontal (SH) modes. Detailed formulations of waves are given to highlight the differences from the piezoelectric and piezotronics materials. Some interesting observations are observed from the numerical and physical points of views. Numerically, existing efforts mainly focused on finding a balance between the large sizes of the square matrix, accuracy solution and the time spend for obtained the solution. Accordingly, a simplified version of ordinary differential equation (ODE) method is proposed. This version presents one of the significant improvement of the present work. Physically, drift of electrons and holes phenomenon is present for the pre-stressed piezotronics medium that undoubtedly can disruption the ideal vibration of acoustic wave (decrease the kinetic of waves). Thereby, a comparison of the dispersion curves of SH modes in pre-stressed piezoelectric and piezotronics plates answers this need and sets forth to explore the effects of semi-conductive properties. Overall, frequency spectrum of fundamental mode can reach about 2.8 × 10 9 rad/s and 2.7 × 10 9 rad/s for piezoelectric and piezotronics, respectively. In addition, this article highlights the challenges faced in the acoustoelastic effect on drift of electrons and holes and provides a discussion of the influence of biaxial stresses. Therefore, this critical point could provide the deep understanding of the stressed semiconductor structures. Besides answering a basic question about the numerical and physical problems of piezotronics thin structures, our results find applications especially in areas of smart devices with small sizes.

Impact of Work Function Tunability on Thermal and RF Performance of P-type Window based Junctionless Transistor

The choice of gate metal technology for junctionless transistors needs to have diverse characteristics as metals have distinct work functions and hence, they show incompatibility while tailoring threshold of the device. In such a scenario, bimetallic stacked gate can be a promising candidate to present wide range of tunable work functions required for nano-regime junctionless transistors. This paper explores the electronic phenomena occurring at metal-metal interface and the impact of Platinum (Pt)/Titanium (Ti) bimetallic stacked gate-based work function tunability on the RF and thermal performances of p-type window-based Silicon on Insulator Junctionless Transistor (SOI JLT) using numerical simulator SILVACO ATLAS. The parameters considered for performance evaluation are ON-state current (I_{ON}), OFF-state current (I_{OFF}), I_{ON}/I_{OFF} ratio, transconductance (g_m),\linebreak cutoff frequency (f_T), Transconductance Frequency Product (TFP), Intrinsic Gate Delay (IGD), intrinsic gain (A_V), and Global Device Temperature (GDT). The g_m, f_T, TFP, A_V and GDT improve for modified over conventional in the ON state at higher work function, while IGD improves at lower work function. The improvements of 11.7% and 2.21% are obtained in maximum g_m and f_T, respectively, for modified transistor over conventional. The findings suggest that bimetallic stacked gate modified SOIJLT is a better option than conventional for low-power RF application.

Nonsymmorphic symmetry-protected band crossings in a square-net metal PtPb4

Topological semimetals with symmetry-protected band crossings have emerged as a rich landscape to explore intriguing electronic phenomena. Nonsymmorphic symmetries in particular have been shown to play an important role in protecting the crossings along a line (rather than a point) in momentum space. Here we report experimental and theoretical evidence for Dirac nodal line crossings along the Brillouin zone boundaries in PtPb4, arising from the nonsymmorphic symmetry of its crystal structure. Interestingly, while the nodal lines would remain gapless in the absence of spin–orbit coupling (SOC), the SOC, in this case, plays a detrimental role to topology by lifting the band degeneracy everywhere except at a set of isolated points. Nevertheless, the nodal line is observed to have a bandwidth much smaller than that found in density functional theory (DFT). Our findings reveal PtPb4 to be a material system with narrow crossings approximately protected by nonsymmorphic crystalline symmetries.