Low-energy Model Research Articles

On the engineering of higher-order Van Hove singularities in two dimensions

The properties of correlated electron materials are often intricately linked to Van Hove singularities (VHS) in the vicinity of the Fermi energy. The class of these VHS is of great importance, with higher-order ones—with power-law divergence in the density of states—leaving frequently distinct signatures in physical properties. We use a new theoretical method to detect and analyse higher-order VHS (HOVHS) in two-dimensional materials and apply it to the electronic structure of the surface layer of Sr2RuO4. We then constrain a low energy model of the VHS of the surface layer of Sr2RuO4 against angle-resolved photoemission spectroscopy and quasiparticle interference data to analyse the VHS near the Fermi level. We show how these VHS can be engineered into HOVHS.

Unsupervised learning of effective quantum impurity models

Generalized quantum impurity models—which feature a few localized and strongly correlated degrees of freedom coupled to itinerant conduction electrons—describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean-field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from a bare to an effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can nevertheless be quite inaccurate. Here we develop a nonperturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization-group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and we provide an outlook for more complex models beyond the reach of existing methods. Published by the American Physical Society 2024

Floating particles transport through the free surface vortex technique: A novel numerical study to assess the interaction among different scales of vortex structures

Fat, oil, and grease (FOG) floating particles in the sump of sewage pumping stations will accumulate together to form rigid layers, resulting in failure for pump device. To overcome this, the free surface vortex (FSV) technique has been considered and applied to transport floating particles toward the submerged suction pump inlet. This paper investigates the potential of vortices as a means of downward motion of FOG. The entrainment capacity of FSV is investigated by numerical simulations using a coupled level-set and volume-of-fluid method. Two coherent structures are decomposed by proper orthogonal decomposition: FSV represented by the first two orders with high energy content and spiral vortex bands represented by low energy and high order models. The extracted ridges of the finite-time Lyapunov exponent (FTLE) delineate different regions of the flow field and effectively capture the evolution of Lagrangian coherent structures. The floating particles in the sump are first caught by the dividing line formed by the FTLE ridges, mixed in the entrainment zone, and then merged into the vortex. The enstrophy production term dominates the development of vorticity. Subject to the influence of flow velocity gradients, both radial and tangential vortices undergo a transition into axial vortices. This transformation enhances the vortex's capacity to entrain particles within the vortex core area, leading to their rapid inward spiraling toward the vortex center and eventual expulsion due to the vortex's entrainment effect.

Low-energy modeling of three-dimensional topological insulator nanostructures

Low-energy modeling of three-dimensional topological insulator nanostructures

Hybrid spin-orbit exciton-magnon excitations in FePS3

FePS3 is a layered van der Waals (vdW) Ising antiferromagnet that has recently been studied in the context of true 2D magnetism and emerged as an ideal material platform for investigating strong spin-phonon coupling, and non-linear magneto-optical phenomena. In this work, we demonstrate an important unresolved role of spin-orbit coupling (SOC) in the ground state and excitations of this compound. Combining first-principles calculations with linear flavor wave theory (LFWT), we find strong mixing and spectral overlap of different spin-orbital single-ion states. Low-lying excitations form hybrid spin-orbit exciton/magnon modes. Complete parameterization of the low-energy model requires nearly half a million coupling constants. Despite this complexity, such a model can be inexpensively derived using local many-body-based approaches, which yield quantitative agreement with recent experiments. The results highlight the importance of SOC even in first-row transition metals and provide essential insight into the properties of 2D magnets with unquenched orbital moments.

Flat-band and diverse quasi-fermions in Pb10(PO4)6O4

Employing a combination of first-principles calculations and low-energy effective models, we present a comprehensive investigation on the electronic structure of Pb10(PO4)6O4, which exhibits remarkable quasi-one-dimensional topological flat-band around the Fermi level. These flat bands predominantly originate from the px/py orbitals of the oxygen molecules chain at the fully-occupied 4e Wyckoff positions and thus can be well-captured by a minimal four-band tight-binding model. Furthermore, the abundant crystal symmetry inherent in Pb10(PO4)6O4 provides an ideal platform for the emergence of various quasi-fermions characterized by different dispersion, degeneracy, and dimensionality. These include a 0D four-fold degenerate Dirac fermion exhibiting quadratic dispersion, a 1D quadratic/linear nodal-line fermion along symmetric k-paths, a 1D hourglass nodal-line (HNL) fermion associated with the Dirac fermion, and a 2D symmetry-enforced nodal surface located on the kz = π plane. Moreover, when considering the weak ferromagnetic order, Pb10(PO4)6O4 transforms into a rare semi-half-metal, which is characterized by the presence of Dirac fermion and HNL fermion at the Fermi level for a single spin channel exhibiting 100 % spin polarization. Our findings reveal the rarely coexistence of flat bands, diverse topological semimetal states and ferromagnetism in Pb10(PO4)6O4, which may provide valuable insights for further exploring the intriguing interplay between superconductivity and exotic electronic states.

Fano resonances in tilted Weyl semimetals in an oscillating quantum well

Considering the low-energy model of tilted Weyl semimetal, we study the electronic transmission through a periodically driven quantum well, oriented in the transverse direction with respect to the tilt. We adopt the formalism of Floquet scattering theory and investigate the emergence of Fano resonances as an outcome of matching between the Floquet sidebands and quasi-bound states. The Fano resonance energy changes linearly with the tilt strength suggesting the fact that tilt-mediated part of quasi-bound states energies depends on the above factor. Given a value of momentum parallel (perpendicular) to the tilt, we find that the energy gap between two Fano resonances, appearing for two adjacent values of transverse (collinear) momentum with respect to the tilt direction, is insensitive (sensitive) to the change in the tilt strength. Such a coupled (decoupled) behavior of tilt strength and the collinear (transverse) momentum can be understood from the tilt-mediated and normal parts of the quasi-bound state energies inside the potential well. We vary the other tilt parameters and chirality of the Weyl points to conclusively verify the exact form of the tilt-mediated part of the quasi-bound state energy that is the same as the tilt term in the static dispersion. The tilt orientation can significantly alter the transport in terms of evolution of Fano resoance energy with tilt momentum. We analytically find the explicit form of the bound state energy that further supports all our numerical findings. Our work paves the way to probe the tilt-mediated part of quasi-bound state energy to understand the complex interplay between the tilt and Fano resonance.

Impact of a local CP -odd domain in hot QCD on the axionic domain-wall interpretation of NANOGrav 15-year data

We argue that the axionic domain-wall with a QCD bias may be incompatible with the NANOGrav 15-year data on a stochastic gravitational wave (GW) background, when the domain wall network collapses in the hot-quantum chromodynamics (QCD) induced local CP-odd domain. This is due to the drastic suppression of the QCD bias set by the QCD topological susceptibility in the presence of the CP-odd domain with nonzero θ parameter of order one which the QCD sphaleron could generate. We quantify the effect on the GW signals by working on a low-energy effective model of Nambu-Jona-Lasinio type in the mean field approximation. We find that only at θ=π, the QCD bias tends to get significantly large enough due to the criticality of the thermal CP restoration, which would, however, give too big signal strengths to be consistent with the NANOGrav 15-year data and would also be subject to the strength of the phase transition at the criticality. Published by the American Physical Society 2024

A Bridge between Trace Anomalies and Deconfinement Phase Transitions

Inspired by the fact that both the dilaton potential encoding the trace anomalies of QCD and the Polyakov loop potential measuring the deconfinement phase transition can be expressed in the logarithmic forms, as well as the fact that the scale symmetry is expected to be restoring and colors are deconfined in extreme conditions such as high temperatures and/or densities, we conjecture a relation between the dilaton potential and the Polyakov loop potential. Explicitly, we start from the Coleman–Weinberg type potential of a real scalar field—a dilaton or conformal compensator—and make an ansatz of the relation between this scalar field and the Polyakov loop to obtain the Polyakov loop potential, which can be parameterized in Lattice QCD (LQCD) in the pure glue sector. We find that the coefficients of Polyakov potential fitted from Lattice data are automatically satisfied in this ansatz, the locations of deconfinement and scale restoration are locked to each other, and the first-order phase transition can be realized. Extensions to the low-energy effective quark models are also discussed. The conjectured relation may deepen our understanding of the evolution of the universe, the mechanism of electroweak symmetry breaking, the phase diagram of QCD matter, and the properties of neutron stars.

Twisto-Electrochemical Activity Volcanoes in Trilayer Graphene.

In this work, we develop a twist-dependent electrochemical activity map, combining a low-energy continuum electronic structure model with modified Marcus-Hush-Chidsey kinetics in trilayer graphene. We identify a counterintuitive rate enhancement region spanning the magic angle curve and incommensurate twists in the system geometry. We find a broad activity peak with a ruthenium hexamine redox couple in regions corresponding to both magic angles and incommensurate angles, a result qualitatively distinct from the twisted bilayer case. Flat bands and incommensurability offer new avenues for reaction rate enhancements in electrochemical transformations.

Peri-lesion regions in differentiating suspicious breast calcification-only lesions specifically on contrast enhanced mammography.

The explore the added value of peri-calcification regions on contrast-enhanced mammography (CEM) in the differential diagnosis of breast lesions presenting as only calcification on routine mammogram. Patients who underwent CEM because of suspicious calcification-only lesions were included. The test set included patients between March 2017 and March 2019, while the validation set was collected between April 2019 and October 2019. The calcifications were automatically detected and grouped by a machine learning-based computer-aided system. In addition to extracting radiomic features on both low-energy (LE) and recombined (RC) images from the calcification areas, the peri-calcification regions, which is generated by extending the annotation margin radially with gradients from 1 mm to 9 mm, were attempted. Machine learning (ML) models were built to classify calcifications into malignant and benign groups. The diagnostic matrices were also evaluated by combing ML models with subjective reading. Models for LE (significant features: wavelet-LLL_glcm_Imc2_MLO; wavelet-HLL_firstorder_Entropy_MLO; wavelet-LHH_glcm_DifferenceVariance_CC; wavelet-HLL_glcm_SumEntropy_MLO;wavelet-HLH_glrlm_ShortRunLowGray LevelEmphasis_MLO; original_firstorder_Entropy_MLO; original_shape_Elongation_MLO) and RC (significant features: wavelet-HLH_glszm_GrayLevelNonUniformityNormalized_MLO; wavelet-LLH_firstorder_10Percentile_CC; original_firstorder_Maximum_MLO; wavelet-HHH_glcm_Autocorrelation_MLO; original_shape_Elongation_MLO; wavelet-LHL_glszm_GrayLevelNonUniformityNormalized_MLO; wavelet-LLH_firstorder_RootMeanSquared_MLO) images were set up with 7 features. Areas under the curve (AUCs) of RC models are significantly better than those of LE models with compact and expanded boundary (RC v.s. LE, compact: 0.81 v.s. 0.73, p < 0.05; expanded: 0.89 v.s. 0.81, p < 0.05) and RC models with 3 mm boundary extension yielded the best performance compared to those with other sizes (AUC = 0.89). Combining with radiologists' reading, the 3mm-boundary RC model achieved a sensitivity of 0.871 and negative predictive value of 0.937 with similar accuracy of 0.843 in predicting malignancy. The machine learning model integrating intra- and peri-calcification regions on CEM has the potential to aid radiologists' performance in predicting malignancy of suspicious breast calcifications.

Emergent macroscopic electromagnetism in the 3-dimensional non-Hermitian double-cover Lieb model

In this paper, we investigate the behaviors of the 3-dimensional non-Hermitian double-cover Lieb model near the band-touching points. The double-cover Lieb model is composed of two copies of Lieb configurations. Our analysis demonstrates that, near the band-touching points, the double-cover Lieb model emerges macroscopic electromagnetism, which incorporates permittivity and permeability that serve as primary causes for numerous electromagnetic phenomena. By analyzing the polarized phases of flavor and spin spaces in the double-cover Lieb model, we classify different topological phases of the model corresponding to different material phases induced by permittivity and permeability. We also discuss possible experimental schemes for realizing the 3-dimensional non-Hermitian double-cover Lieb model. The double-cover Lieb models model bears similarity to low-energy quantum chromodynamics models, extension of the non-Hermitian double-cover Lieb model could enable the exploration of even richer phase phenomena.

Characterization of the Edge States in Colloidal Bi2Se3 Platelets.

The remarkable development of colloidal nanocrystals with controlled dimensions and surface chemistry has resulted in vast optoelectronic applications. But can they also form a platform for quantum materials, in which electronic coherence is key? Here, we use colloidal, two-dimensional Bi2Se3 crystals, with precise and uniform thickness and finite lateral dimensions in the 100 nm range, to study the evolution of a topological insulator from three to two dimensions. For a thickness of 4-6 quintuple layers, scanning tunneling spectroscopy shows an 8 nm wide, nonscattering state encircling the platelet. We discuss the nature of this edge state with a low-energy continuum model and ab initio GW-Tight Binding theory. Our results also provide an indication of the maximum density of such states on a device.

Spin-reorientation driven emergent phases and unconventional magnetotransport in quasi-2D vdW ferromagnet Fe4GeTe2

Non-trivial spin textures driven by strong exchange interaction, magneto-crystalline anisotropy, and electron correlation in a low-dimensional magnetic material often lead to unusual electronic transitions. Through a combination of transport experiments in exfoliated nanoflakes down to 16 layers and first principle calculations, we unravel emergent electronic phases in quasi-2D van der Waals ferromagnet, Fe4GeTe2, possessing ferromagnetic TC ~ 270 K, along with a spin-reorientation transition (TSR ~ 120 K) with the change of magnetic easy axis. Two electronic transitions are identified. The first transition near TSR exhibits a sharp fall in resistivity, followed by a sign change in the ordinary Hall coefficient (R0), together with, maximum negative magnetoresistance (MR) and anomalous Hall conductivity. Another unusual electronic transition, hitherto unknown, is observed near ~ 40–50 K (TQ), where R0 again changes sign and below which, the resistivity shows a quadratic temperature dependence, and MR becomes positive. An analysis of the experimental data further uncovers the role of competing inelastic scattering processes in anomalous magnetotransport behavior. The density-functional theory based first-principle calculations unveil two possible magnetic phases, followed by a low-energy model Hamiltonian which captures the essence of these phases as well as explains the observed magnetotransport behavior. Thus, we demonstrate an interplay between magnetism and band topology and its consequence on electron transport in Fe4GeTe2, important for spintronic applications.

Stabilizing nodal integration in dynamic smoothed particle finite element method: A simple and efficient algorithm

The Smoothed Particle Finite Element Method (SPFEM) is a powerful numerical tool for the modelling of large deformation problems in the field of geomechanics. However, the standard SPFEM with nodal integration suffers from the rank deficiency problem due to under-integration. In this study, an hourglass-control based stabilization scheme is presented to overcome the rank deficiency in standard SPFEM with nodal integration. By introducing the hourglass-control based correction forces, the spurious low-energy models in standard SPFEM with nodal integration can be effectively suppressed. The presented stabilization scheme is simple and computationally efficient compared to the existing strain gradient-based stabilization approaches in SPFEM. The proposed hourglass-control based stabilized SPFEM is firstly validated by means of three benchmark examples and the results show that the stabilization scheme based on the hourglass-control can eliminate the rank deficiency instability in standard SPFEM and free of volumetric locking. Finally, two numerical examples related to the cohesive soil flow and the progressive failure of sensitive clay slopes are studied to highlight the robustness of the proposed stabilized SPFEM in solving large deformation geotechnical problems.

Flipped SU(6) unification of the sequential SU(3)c×SU(3)L×U(1)X model

We propose to partially unify the sequential SU(3)c×SU(3)L×U(1)X model (with β=1/3) into the flipped SU(6) model with the gauge group SU(6)×U(1)K. Gauge anomaly cancellation can easily be satisfied. We discuss the relevant Higgs sector, the low energy model spectrum, and the unification of SU(3)c and SU(3)L gauge couplings. Neutrino mass generation and successful gauge coupling unification can set lower/upper bounds on the breaking scale. The partial proton decay lifetime of various channels, for example, the p→e+π0 channel, in flipped SU(6) GUT are discussed. We find that certain parameter region with M331∼1015 GeV of case II (for case with M331 scale H˜3,8 Higgs field) can predict a partial proton lifetime of order 1034 years for p→e+π0 mode, which can be tested soon by future DUNE and Hyper-Kamiokande experiments. Published by the American Physical Society 2024

Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals

We examine the response of the Fermi arc in the context of quasiparticle interference (QPI) with regard to a localized surface impurity on various three-dimensional Weyl semimetals (WSMs). Our study also reveals the variation of the local density of states (LDOS), obtained by Fourier transforming the QPI profile, on the two-dimensional surface. We use the T-matrix formalism to numerically (analytically and numerically) capture the details of the momentum space scattering in QPI (real-space decay in LDOS), considering relevant tight-binding lattice and/or low-energy continuum models modeling a range of different WSMs. In particular, we consider multi-WSM (mWSM), hosting multiple Fermi arcs between two opposite chirality Weyl nodes (WNs), where we find a universal 1/r decay (r measuring the radial distance from the impurity core) of the impurity-induced LDOS, irrespective of the topological charge. Interestingly, the inter-Fermi arc scattering is only present for triple WSMs, where we find an additional 1/r3 decay as compared to double and single WSMs. The untilted single (double) [triple] WSM shows a straight line (leaf-like) [oval-shaped] QPI profile. The above QPI profiles are canted for hybrid WSMs where type-I and type-II Weyl nodes coexist; however, hybrid single WSM demonstrates strong nonuniformity, unlike the hybrid double and triple WSMs. We also show that the chirality and the positions of the Weyl nodes imprint marked signatures in the QPI profile. This allows us to distinguish between different WSMs, including the time-reversal-broken WSMs from the time-reversal-invariant WSM, even though both of the WSMs can host two pairs of Weyl nodes. Our study can thus shed light on experimentally obtainable complex QPI profiles and help differentiate different WSMs and their surface band structures. Published by the American Physical Society 2024

Photogalvanic response in multi-Weyl semimetals

We investigate the dependence of the photogalvanic response of a twofold degenerate multi-Weyl semimetal on its topological charge, tilt, and chemical potential. We derive analytical expressions for the shift and injection conductivities for tilted charge-n Weyl points using a low-energy two-band effective Hamiltonian. We compute the response for more realistic tight-binding models of a double-Weyl semimetal with broken time-reversal symmetry to find significant deviations from the effective low-energy continuum model predictions. We analyze several different limits of these models, describe the nature of these deviations, and provide estimates of their dependence on the frequency and other model parameters. Our analysis provides a simple explanation for the first-principle calculation based frequency dependence of the injection current in SrSi2. We also obtain analytical results for the charge-4 Weyl semimetal using a new approach, providing all relevant information about the nature of its second-order dc response and the precise condition for observing quantized circular photogalvanic effect. This approach can easily be extended to a systematic study of second harmonic generation and first-order optical conductivity in charge-4 Weyl semimetals. Published by the American Physical Society 2024

Hosohedral nodal-line superconductivity in hexagonal ABC Dirac semimetals

The recently identified hexagonal non-polar phase of KZnBi, an archetypal topological semimetal, has been found to cohost superconductivity on the surface. We propose that KZnBi can realize an unconventional topological superconductor featuring the hosohedral formation of nodal lines and Bogoliubov Fermi surface emerging under a magnetic field. Our density functional theory (DFT)-based low-energy model shows that the nonsymmorphic band degeneracy of the Dirac bands generically triggers topological nodal line superconductivity fostered by inter-band Coulomb interaction. In particular, the nodal lines of the gap resemble a hexagonal hosohedron with the Schläfli symbol of {2, 6}. Remarkably, the holohedral nodal line superconductor defines the topological phase boundary of the Bogoliubov Fermi surface in the limit where time-reversal symmetry is restored. Our results demonstrate that line nodes readily inflate to the Bogoliubov Fermi surface under an external magnetic field. We provide an experimentally verifiable explanation for the observed superconductivity and suggest a feasible platform for observing topological superconductivity in the hexagonal ABC ternary systems class.

Two-dimensional quadratic Weyl points, nodal loops, and spin-orbit Dirac points in PtS, PtSe, and PtTe monolayers.

Topological quasiparticles have garnered significant research attention in condensed matter physics. However, they are exceedingly rare in two-dimensional systems, particularly those hosting unconventional topological quasiparticles. In this work, employing first-principles calculations and symmetry analysis, we demonstrate that PtS, PtSe, and PtTe monolayers serve as high-quality two-dimensional topological semimetal materials. These materials exhibit multiple types of topological quasiparticles around the Fermi level in the absence of spin-orbit coupling, such as conventional linear Weyl points and unconventional quadratic Weyl points in the PtS monolayer, as well as nodal loops in PtSe and PtTe monolayers. When spin-orbit coupling (SOC) is introduced, a tiny gap opens, transforming the systems into quantum spin hall insulators. Simultaneously, three spin-orbit Dirac points, robust against SOC, appear at the X, Y, and M points. We illustrate the symmetry protection, low-energy effective model, and edge states of these topological states. Our work provides an excellent material platform for studying novel two-dimensional topological quasiparticles and topological insulators.