Topological Lifshitz Transition Research Articles

Tunable hybrid-order Weyl semimetal via staggered magnetic flux

We investigate a hybrid-order Weyl semimetal (HOWS) constructed by stacking the two-dimensional kagome lattice with staggered magnetic flux. By adjusting the magnitude of flux, higher-order topological phases are tunably intertwined with the first-order topological Chern insulators, which is governed by the evolution of Weyl points. Meanwhile the surface Fermi arcs undergo topological Lifshitz transition. Notably, due to the breaking of time-reversal symmetry (TRS), a novel split of a quadratic double Weyl point occurs, giving rise to additional three type-II Weyl points hybridizing with one type-I node. This phenomenon plays a crucial role in realizing high-Chern-number phases with C=±2 and reveals a new mechanism for the emergence of type-II Weyl fermions in topological kagome semimetals. We anticipate that this study will stimulate further investigation into the unique physics of kagome materials and Weyl semimetals.

Nonlocal Acoustic Moiré Hyperbolic Metasurfaces.

The discovery of the topological transition in twisted bilayer (tBL) materials has attracted considerable attention in nano-optics. In the analogue of acoustics, however, no such topological transition has been found due to the inherent nondirectional scalar property of acoustic pressure. In this work, by using a theory-based nonlocal anisotropic design, the in-plane acoustic pressure is transformed into a spatially distributed vector field using twisted multilayer metasurfaces. So-called "acoustic magic angle"-related acoustic phenomena occur, such as nonlocal polariton hybridization and the topological Lifshitz transition. The dispersion becomes flat at the acoustic magic angle, enabling polarized excitations to propagate in a single direction. Moreover, the acoustic topological transition (from hyperbolic to elliptic dispersion) is experimentally observed for the first time as the twist angle continuously changes. This unique characteristic facilitates low-loss tunable polariton hybridization at the subwavelength scale. A twisted trilayer acoustic metasurface is also experimentally demonstrated, and more possibilities for manipulating acoustic waves are found. These discoveries not only enrich the concepts of moiré physics and topological acoustics but also provide a complete framework of theory and methodologies for explaining the phenomena that are observed.

Perekhody Lifshitsa i uglovye diagrammy provodimosti v metallakh so slozhnymi poverkhnostyami Fermi

We consider the Lifshitz topological transitions and the corresponding changes in the galvano-magnetic properties of a metal from the point of view of the general classification of open electron trajectories arising on Fermi surfaces of arbitrary complexity in the presence of magnetic field. The construction of such a classification is the content of the Novikov problem and is based on the division of non-closed electron trajectories into topologically regular and chaotic trajectories. The description of stable topologically regular trajectories gives a basis for a complete classification of non-closed trajectories on arbitrary Fermi surfaces and is connected with special topological structures on these surfaces. Using this description, we describe here the distinctive features of possible changes in the picture of electron trajectories during the Lifshitz transitions, as well as changes in the conductivity behavior in the presence of a strong magnetic field. As it turns out, the use of such an approach makes it possible to describe not only the changes associated with stable electron trajectories, but also the most general changes of the conductivity diagram in strong magnetic fields.

Gate-Tunable Lifshitz Transition of Fermi Arcs and Its Transport Signatures

One hallmark of Weyl semimetals is the emergence of Fermi arcs (FAs) in surface Brillouin zones, where FAs connect the projected Weyl nodes of opposite chiralities. Unclosed FAs can give rise to various exotic effects that have attracted tremendous research interest. Configurations of FAs are usually thought to be determined fully by the band topology of the bulk states, which seems impossible to manipulate. Here, we show that FAs can be simply modified by a surface gate voltage. Because the penetration length of the surface states depends on the in-plane momentum, a surface gate voltage induces an effective energy dispersion. As a result, a continuous deformation of the surface band can be implemented by tuning the surface gate voltage. In particular, as the saddle point of the surface band meets the Fermi energy, the topological Lifshitz transition takes place for the FAs, during which the Weyl nodes switch their partners connected by the FAs. Accordingly, the magnetic Weyl orbits composed of the FAs on opposite surfaces and chiral Landau bands inside the bulk change their configurations. We show that such an effect can be probed by the transport measurements in a magnetic field, in which the switch-on and switch-off conductances by the surface gate voltage signal the Lifshitz transition. Our work opens a new route for manipulating the FAs by surface gates and exploring novel transport phenomena associated with the topological Lifshitz transition.

Electronic Structure and Minimal Models for Flat and Corrugated CuO Monolayers: An Ab Initio Study.

CuO atomic thin monolayer (mlCuO) was synthesized recently. Interest in the mlCuO is based on its close relation to CuO2 layers in typical high temperature cuprate superconductors. Here, we present the calculation of the band structure, the density of states and the Fermi surface of the flat mlCuO as well as the corrugated mlCuO within the density functional theory (DFT) in the generalized gradient approximation (GGA). In the flat mlCuO, the Cu-3dx2-y2 band crosses the Fermi level, while the Cu-3dxz,yz hybridized band is located just below it. The corrugation leads to a significant shift of the Cu-3dxz,yz hybridized band down in energy and a degeneracy lifting for the Cu-3dx2-y2 bands. Corrugated mlCuO is more energetically favorable than the flat one. In addition, we compared the electronic structure of the considered CuO monolayers with bulk CuO systems. We also investigated the influence of a crystal lattice strain (which might occur on some interfaces) on the electronic structure of both mlCuO and determined the critical strains of topological Lifshitz transitions. Finally, we proposed a number of different minimal models for the flat and the corrugated mlCuO using projections onto different Wannier functions basis sets and obtained the corresponding Hamiltonian matrix elements in a real space.

Spectrum, Lifshitz transitions and orbital current in frustrated fermionic ladders with a uniform flux

Ultracold Fermi gases with synthetic gauge field represent an excellent platform to study the combined effect of lattice frustration and an effective magnetic flux close to one flux quantum per particle. The minimal theoretical model to accomplish this task is a system of spinless noninteracting fermions on a triangular two-chain flux ladder. In this paper we consider this model close to half-filling, with interchain hopping amplitudes alternating along the zigzag bonds of the ladder and being small. In such setting qualitative changes in the ground state properties of the model, most notably the flux-induced topological Lifshitz transitions are shifted towards the values of the flux per a diatomic plaquette ($f$) close to the flux quantum ($f\sim 1/2$). Geometrical frustration of the lattice breaks the $k \to \pi - k$ particle-hole spectral symmetry present in non-frustrated ladders, and leads to splitting of the degeneracies at metal-insulator transitions. A remarkable feature of a translationally invariant triangular ladder is the appearance of isolated Dirac node at the Brillouin zone boundary, rendering the ground state at $f=1/2$ semi-metallic. We calculate the flux dependence of the orbital current and identify Lifshitz critical points by the singularities in this dependence at a constant chemical potential $\mu$ and constant particle density $\rho$. The absence of the particle-hole symmetry in the triangular ladder leads to the asymmetry between particle ($\rho>1$) and hole ($\rho<1$) doping and to qualitatively different results for the phase diagram, Lifshitz points and the flux dependence of the orbital current in the settings $\rho={\rm const}$ and $\mu={\rm const}$.

Electronic Structure of InCo2As2 and KInCo4As4: LDA + DMFT

A comparative analysis of the electronic structure obtained in the DFT/LDA and LDA + DMFT approaches of the possible isostructural analogues of iron superconductors InCo2As2 and KInCo4As4 with the electronic structure of the parent high-temperature superconductor system BaFe2As2 is carried out. It is established that in spite of the rather large value of the electron-electron correlations (local Coulomb interaction on the Co-3d shell U = 4.0 eV, the Hund exchange interaction J = 0.85 eV), in the considered systems a relatively small quasiparticle mass renormalization 1.2–1.35 at the Fermi level is observed. The correlation effects lead to the remarkable shift and compression of the spectrum below –0.8 eV. The band structure of InCo2As2 near the Fermi level is qualitatively similar to the previously studied BaCo2As2, and differs significantly from the band structure of BaFe2As2. In the KInCo4As4 system, the bands near the Fermi level resemble the band structure of BaFe2As2, and the Fermi surfaces have a similar topology. This indirectly points to the possibility of superconductivity in KInCo4As4. Also according to the results of LDA + DMFT calculations it is seen that with a rather small hole or electron doping in the KInCo4As4 system will experience topological Lifshitz transitions. We believe that the synthesis of the InCo2As2 and KInCo4As4 compounds considered in this paper is important for the study of superconductivity in this class of materials.

Spin–orbit coupling controlling the superconducting dome of artificial superlattices of quantum wells

While it is known that a resonant amplification of Tc in two-gap superconductors can be driven by using the Fano–Feshbach resonance tuning the chemical potential near a Lifshitz transition, little is known on tuning the Tc resonance by cooperative interplay of the Rashba spin–orbit coupling (RSOC) joint with phonon mediated (e-ph) pairing at selected k-space spots. Here, we present first-principles quantum calculation of superconductivity in an artificial heterostructure of metallic quantum wells with 3 nm period where quantum size effects give two-gap superconductivity with RSOC controlled by the internal electric field at the interface between the nanoscale metallic layers intercalated by insulating spacer layers. The key results of this work show that fundamental quantum mechanics effects including RSCO at the nanoscale [Mazziotti et al., Phys. Rev. B, 103, 024523 (2021)] provide key tools in applied physics for quantitative material design of unconventional high temperature superconductors at ambient pressure. We discuss the superconducting domes where Tc is a function of either the Lifshitz parameter (η) measuring the distance from the topological Lifshitz transition for the appearing of a new small Fermi surface due to quantum size effects with finite spin–orbit coupling and the variable e-ph coupling g in the appearing second Fermi surface linked with the energy softening of the cut off ω0.

Topological Lifshitz transition and one-dimensional Weyl mode in HfTe5.

Landau band crossings typically stem from the intra-band evolution of electronic states in magnetic fields and enhance the interaction effect in their vicinity. Here in the extreme quantum limit of topological insulator HfTe5, we report the observation of a topological Lifshitz transition from inter-band Landau level crossings using magneto-infrared spectroscopy. By tracking the Landau level transitions, we demonstrate that band inversion drives the zeroth Landau bands to cross with each other after 4.5 T and forms a one-dimensional Weyl mode with the fundamental gap persistently closed. The unusual reduction of the zeroth Landau level transition activity suggests a topological Lifshitz transition at 21 T, which shifts the Weyl mode close to the Fermi level. As a result, a broad and asymmetric absorption feature emerges due to the Pauli blocking effect in one dimension, along with a distinctive negative magneto-resistivity. Our results provide a strategy for realizing one-dimensional Weyl quasiparticles in bulk crystals.

Detection of Weyl fermions and the metal to Weyl-semimetal phase transition in WTe2 via broadband high resolution NMR

Weyl fermions (WFs) in the type-II Weyl semimetal (WSM) ${\mathrm{WTe}}_{2}$ are difficult to resolve experimentally because the Weyl bands disperse in an extremely narrow region of the ($E\text{\ensuremath{-}}k$) space. Here, by using DFT-assisted high-resolution $^{125}\mathrm{Te}$ solid-state nuclear magnetic resonance (ssNMR) in the temperature range 50--700 K, we succeeded in detecting low energy WF excitations and monitoring their evolution with temperature. Remarkably, WFs are observed to emerge at $T\ensuremath{\sim}120$ K, while at lower temperatures ${\mathrm{WTe}}_{2}$ behaves as a trivial metal. This intriguing phenomenon is induced by the rapid raise of the Fermi level upon heating, which crosses the Weyl bands only for $T&gt;120$ K. The abrupt change of the NMR parameters at this temperature is signature of a topological Lifshitz transition instead of a cursive energy-bands crossing.

Nodal-line driven anomalous susceptibility in ZrSiS

We demonstrate a unique approach to test the signature of the nodal-line physics by thermodynamic methods. By measuring magnetic susceptibility in ZrSiS we found an intriguing temperature-driven crossover from dia- to paramagnetic behavior. We show that the anomalous behavior represents a real thermodynamic signature of the underlying nodal-line physics through the means of chemical pressure (isovalent substitution of Zr for Hf), quantum oscillations, and theoretical modeling. The anomalous part of the susceptibility is orbital by nature, and it arises due to the vicinity of the Fermi level to a degeneracy point created by the crossing of two nodal lines. Furthermore, an unexpected Lifshitz topological transition at the degeneracy point is revealed by tuning the Fermi level. The present findings in ZrSiS give an attractive starting point for various nodal-line physics-related phenomena to be tested by thermodynamic methods in other related materials.

Topological Lifshitz transition in Weyl semimetal NbP decorated with heavy elements

Studies of the Fermi surface modification after $\mathit{in}\phantom{\rule{0.16em}{0ex}}\mathit{situ}$ covering NbP semimetal with heavy elements Pb and Nb ultrathin layers were performed by means of angle-resolved photoemission spectroscopy (ARPES). First, the electronic structure was investigated for pristine single crystals with two possible terminations (P and Nb) of the (0 0 1) surface. The nature of the electronic states of these two cleaving planes is different: the P-terminated surface shows spoon and bow tie-shaped surface states, whereas these shapes are not present in the Nb-terminated surface. ARPES studies show that even one monolayer (ML) of Pb causes topological Lifshitz transition (TLT) in P-terminated NbP where the surface Fermi arcs (SFAs) teleport to another pair of Weyl points connecting two adjacent Brillouin zones. Depositing one ML of Pb modifies the Fermi surface along with a shift in the Fermi energy. On the other hand, the deposition of approximately 0.8 ML of Nb modifies the electronic structure of P-terminated NbP, pushing the system on the verge of TLT but not yet fully transformed. Regardless of the dramatic surface evolution, SFAs remain connected to topologically protected Weyl points. Additionally, we studied the Nb-terminated NbP covered with 1.9 ML of Pb with only altered trivial surface states caused by an ordinary Lifshitz transition.

Topological Lifshitz transitions, orbital currents, and interactions in low-dimensional Fermi gases in synthetic gauge fields

Low-dimensional systems of interacting fermions in a synthetic gauge field have been experimentally realized using two-component ultra-cold Fermi gases in optical lattices. Using a two-leg ladder model that is relevant to these experiments, we have studied the signatures of topological Lifshitz transitions and the effects of the inter-species interaction U on the gauge-invariant orbital current in the regime of large intra-leg hopping Ω. Focusing on non-insulating regimes, we have carried out numerically exact density-matrix renormalization-group (DMRG) calculations to compute the orbital current at fixed particle number as a function of the interaction strength and the synthetic gauge flux per plaquette. Signatures of topological Lifshitz transitions where the number Fermi points changes are found to persist even in the presence of very strong repulsive interactions. This numerical observation suggests that the orbital current can be computed from an appropriately renormalized mean-field band structure, which is also described here. Quantitative agreement between the mean-field and the DMRG results in the intermediate interaction regime where U ≲ Ω is demonstrated. We also have observed that interactions can change the sign of the current susceptibility at zero field and induce Lifshitz transitions between two metallic phases, which is also captured by the mean-field theory. Correlation effects beyond mean-field theory in the oscillations of the local inter-leg current are also reported. We argue that the observed robustness against interactions makes the orbital current a good indicator of the topological Lifshitz transitions.

Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene

We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moiré reciprocal lattice. Theanisotropy of the Dirac cones and a concomitant cascade of saddle points induce a series of topological Lifshitz transitions that can be tuned by the twist angle and perpendicular electric field. We discuss the possibility of direct observation of Dirac magic as well as its consequences for the correlated states of electrons in this moiré system.

Topological Lifshitz transition and novel edge states induced by non-Abelian SU(2) gauge field on bilayer honeycomb lattice

We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

Resonant multi-gap superconductivity at room temperature near a Lifshitz topological transition in sulfur hydrides

The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in Tc vs pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The high-order anisotropic Van Hove singularity near the Fermi level observed in band-structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wire modules forming a nanoscale heterostructure at an atomic limit called the superstripe phase. Here, we propose that pressurized sulfur hydrides behave as a heterostructure made of a nanoscale superlattice of interacting quantum wires with a multicomponent electronic structure. We present first-principles quantum calculation of a universal superconducting dome where Tc amplification in multi-gap superconductivity is driven by the Fano–Feshbach resonance due to a configuration interaction between open and closed pairing channels, i.e., between multiple gaps in the BCS regime, resonating with a single gap in the BCS–Bose–Einstein condensation crossover regime. In the proposed three dimensional phase diagram, the critical temperature shows a superconducting dome where Tc is a function of two variables: (i) the Lifshitz parameter (η) measuring the separation of the chemical potential from the Lifshitz transition normalized by the inter-wire coupling and (ii) the effective electron–phonon coupling (g) in the appearing new Fermi surface including phonon softening. The results will be of help for material design of room-temperature superconductors at ambient pressure.

Sign reversal of magnetoresistivity in massive nodal-line semimetals due to the Lifshitz transition of the Fermi surface

Topological nodal-line semimetals offer an interesting research platform to explore novel phenomena associated with its torus-shaped Fermi surface. Here, we study magnetotransport in the massive nodal-line semimetal with spin-orbit coupling and finite Berry curvature distribution which exists in many candidates. The magnetic field leads to a deformation of the Fermi torus through its coupling to the orbital magnetic moment, which turns out to be the main scenario of the magnetoresistivity (MR) induced by the Berry curvature effect. We show that a small deformation of the Fermi surface yields a positive MR $\propto B^2$, different from the negative MR by pure Berry curvature effect in other topological systems. As the magnetic field increases to a critical value, a topological Lifshitz transition of the Fermi surface can be induced, and the MR inverts its sign at the same time. The temperature dependence of the MR is investigated, which shows a totally different behavior before and after the Lifshitz transition. Our work uncovers a novel scenario of the MR induced solely by the deformation of the Fermi surface and establishes a relation between the Fermi surface topology and the sign of the MR.

Superconductivity in the twisted bilayer graphene: emergent mystery in the magic angle, the topological bosons and the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover

ABSTRACT Theory of superconductivity in twisted bilayer graphene (tBLG) is presented, based on the fact that Dirac fermions are pairing creating the topological bosons as consequence of topologically protected Lifshitz topological transition (TPLTT). We have shown that multiple TPLTTs are realised at low twisting angles in tBLG. At TPLTT the Berry phase changes from 2π in bilayer graphene to π in tBLG. It is favourable to form the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover (BCS-BEUC) when the attractive interaction for pairing dominates the repulsive screened Coulomb interaction. The theory yields a second-order phase transition for BCS-BEUC, and values of specific heat and the Ginzburg−Landau coherence length are calculated. The problem has been solved of emergent mystery in the magic angles at which there exists possibility for observation of BCS-BEUC. The solution is connected with the Umklapp processes when the quasiwave vector of the superconducting carriers is shifted from the Brillouin zone to other cell of the reciprocal space. The table is given of the allowed magic angles which include the corresponding effective masses of the pairing Dirac fermions.

Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals

Non-Hermitian topological systems are the newest additions to the growing field of topological matter. In this work, we report the light-driven exceptional physics in a multi-Weyl semimetal. The driving is not only a key ingredient to control the position of the exceptional contours (ECs); light also has the ability to generate new ECs. Interestingly, we also demonstrate topological charge distribution and Lifshitz transition, which are controllable by the driving field in such generated ECs. Our findings present a promising platform for the manipulation and control over exceptional physics in non-Hermitian topological matter.

Two-band superconductivity in a Mo–Re alloy with an equal concentration of the components

An observed correlation between the critical temperature of a superconducting transition in high-temperature superconductors and a proximity of their electronic structure to the topological Lifshitz transition needs to be verified on simple model materials. Here we show that such an object could be a Mo–Re alloy with an equal concentration of constituent elements. We present new evidence of the presence of two energy gaps in this material, obtained using point-contact spectroscopy, and argue that the studied Mo–Re alloy can be used for implementing new quantum effects associated with the phase difference of electron wave functions from the different bands.