Topological Lifshitz Transition Research Articles

Some thermodynamical peculiarities at the Lifshitz topological transitions in trigonally warped AB-stacked bilayer graphene and graphite near K points

ABSTRACT Similarity has been proven between the Lifshitz topological transitions (LTT) in AB-stacked trigonally warped bilayer graphene (TWBG) and graphite near K points. The density of states (DOS) has been shown to have the van Hove singularities (VHS) of type at LTT in AB-stacked (TWBG) and graphite near K points. The topology evolutions of the iso-energetic lines at LTT have been established, and transitions are realised via four stages. The LTT transition energy in TWBG is ϵc ≈ 1 meV, while in graphite ϵc ≈ 10 meV. Thermodynamical characteristics are investigated of AB-stacked TWBG and graphite near K points at LTT. Thermodynamical parameters possess of the strongest singularities at LTT near the K points: the electron specific heat Ce and compressibility δ diverge as ; and thermal coefficient of pressure δ diverges as (here z = μ–ϵc , and μ is the chemical potential). The similarity between the band structure of graphite near the K point and that of the bilayer graphene logically suggests probing of Lifshitz transitions in the advance study of both systems. The developed methodology can be used for exploration of LTT in other bilayer and multilayer structures, like hBN, silicene, germanene, etc.

Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition

We aim to understand how the spectrum of semi-Dirac fermions is renormalized due to long-range Coulomb electron-electron interactions at a topological Lifshitz transition, where two Dirac cones merge. At the transition, the electronic spectrum is characterized by massive quadratic dispersion in one direction, while it remains linear in the other. We have found that, to lowest order, the unconventional log squared (double logarithmic) correction to the quasiparticle mass in bare perturbation theory leads to resummation into strong mass renormalization in the exact full solution of the perturbative renormalization group equations. This behavior effectively wipes out the curvature of the dispersion and leads to Dirac cone restoration at low energy: the system flows towards Dirac dispersion which is anisotropic but linear in momentum, with interaction-depended logarithmic modulation. The Berry phase associated with the restored critical Dirac spectrum is zero - a property guaranteed by time-reversal symmetry and unchanged by renormalization. Our results are in contrast with the behavior that has been found within the large-$N$ approach.

Colossal variations in the thermopower and n–p conductivity switching in topological tellurides under pressure

Under applied high pressure, the electronic, optical, structural, and other properties of narrow-bandgap telluride semiconductors are subjected to dramatic changes. They can include, for instance, structural and electronic topological transitions. In this work, we investigated the electronic properties of single crystals of three families of tellurides, namely, HgTe, PbTe, and Bi2Te3 by measurements of the thermoelectric power (the Seebeck coefficient) and electrical resistance under high pressure up to 10 GPa. The applied pressure led to spectacular variations in the electronic transport of all three tellurides. We addressed these effects to electronic topological transitions that could be driven by significant narrowing of the bandgaps in the normal-pressure phases of these compounds. In particular, at about 1 GPa, we observed an n-p switching in the conductivity of HgTe, which was well reproducible under multiple pressure cycling. In contrast, in PbTe, we found that an electronic topological transition irreversibly turns the conductivity from p- to n-type. An electronic topological Lifshitz transition in p-type Bi2Te3 crystals with a low carrier concentration enhanced the n-type conductivity in a narrow pressure region about 2–3 GPa and resulted in a double p–n–p conductivity inversion. An irreversible p–n conductivity switching in p-type Bi2Te3 happened already on decompression from a high-pressure phase from about 8 GPa. The stress-controlled p–n inversions of the electrical conductivity in these industrially important telluride materials can potentially find emergent applications in micro- and nanoelectronics.

Floquet engineering and simulating exceptional rings with a quantum spin system

Time-periodic driving in the form of coherent radiation provides powerful tool for the manipulation of topological materials or synthetic quantum matter. In this paper we propose a scheme to realize non-Hermitian semimetals exhibiting exceptional rings in the spectra through Floquet engineering. A transition from a concentric pair of the rings to a dipolar pair is observed. The concentric pair carries only a quantized Berry phase while the dipolar pair possesses opposite Chern numbers in addition, signaling a topological Lifshitz transition of the Fermi surface. The transport properties of the system are addressed, and we find that this transition process is accompanied by the emergency of a nontrivial Hall conductivity. Furthermore, we explore the quantum simulation of non-Hermitian semimetals with a quantum spin system and the characterization of the topology via the long-time dynamics.

1144 Fe based superconductors: natural example of orbital selective self-doping and chemical pressure induced Lifshitz transition

A systematic density functional theory based first principles electronic structure studies on AeAFe4As4 known as, 1144 iron based superconductors (IBSC) for various Ae = Ca, Sr, Eu and different alkali metals A = K, Rb, Cs are presented. Our study reveals multi-orbital derived multi-band nature of the electronic structure as well as Fermi surfaces for all the compounds. In contrast to the electronic structure of most of the Fe-based superconductors, significant contribution from As-4pz and its mixing with Fe-3d is found at the Fermi level. A unique feature of the electronic structure of these compounds reveal orbital selective electron/hole self-doping. This is due to natural chemical pressure of larger/smaller atomic (Ae/A) sizes of various members of 1144 family. The different chemical potential (self-doping) of different orbital derived electron/hole bands causes crossing of the Fermi level for some bands, leading to orbital selective chemical pressure induced topological Lifshitz transition. This natural pressure induced orbital selective Lifshitz transition of hole bands is a unique characteristic of this family of iron based superconductors. Our conclusions remain robust even in presence of moderate electron correlation and spin-orbit coupling. Different combinations of Ae and A in different 1144 materials causes different bandwidths to different orbital selective bands; bandwidths of different bands that crosses Fermi level around Γ-point are evaluated. A large value of bandwidths for most of the compounds including EuAFe4As4 indicates weak correlation effect in these compounds.

Topological phases of quantized light.

Topological photonics is an emerging research area that focuses on the topological states of classical light. Here we reveal the topological phases that are intrinsic to the quantum nature of light, i.e. solely related to the quantized Fock states and the inhomogeneous coupling strengths between them. The Hamiltonian of two cavities coupled with a two-level atom is an intrinsic one-dimensional Su-Schriefer-Heeger model of Fock states. By adding another cavity, the Fock-state lattice is extended to two dimensions with a honeycomb structure, where the strain due to the inhomogeneous coupling strengths of the annihilation operator induces a Lifshitz topological phase transition between a semimetal and three band insulators within the lattice. In the semimetallic phase, the strain is equivalent to a pseudomagnetic field, which results in the quantization of the Landau levels and the valley Hall effect. We further construct an inhomogeneous Fock-state Haldane model where the topological phases can be characterized by the topological markers. With d cavities being coupled to the atom, the lattice is extended to d − 1 dimensions without an upper limit. In this study we demonstrate a fundamental distinction between the topological phases in quantum and classical optics and provide a novel platform for studying topological physics in dimensions higher than three.

Topological Lifshitz transition of the intersurface Fermi-arc loop in NbIrTe4

Surface arcs (SAs) or Fermi arcs connecting pairs of bulk Weyl points with opposite chiralities are the signatures of Weyl semimetals in angle-resolved photoemission spectroscopy (ARPES) studies. The nontrivial topology of the bulk band structure guarantees the existence of these exotic Fermi arcs with connectivity that is strongly dependent on the surface. It has been theoretically proposed and experimentally confirmed that Fermi arcs at opposite surfaces can complete an unusual closed cyclotron orbit called a Weyl orbit, which leads to various intriguing transport properties. In this paper, a systematic ARPES study on opposite terminations (001) of type-II Weyl semimetal ${\mathrm{NbIrTe}}_{4}$ reveals different Fermi arc connections which result in a unique closed intersurface Fermi arc loop configurations (combining both projections of SAs) containing two pairs of Weyl points. In particular, the top surface ARPES data and corresponding ab initio calculation suggests that a topological Lifshitz transition occurs by tuning the chemical potential. SA rewiring on the top surface opens the intersurface arc loop at the Weyl node energy level into an open line, challenging the close-orbit description and leading to an unexplored scenario. Our results demonstrate the intrinsic alteration of Fermi arc connections and propose ${\mathrm{NbIrTe}}_{4}$ as a potential platform to examine Fermi-arc related phenomenon.

Role of the Lifshitz topological transitions in the thermodynamic properties of graphene.

The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established. The peculiarities of the Lifshitz topological transitions in graphene are described at the Brillouin zone centre Γ, the zone corners K in the vicinity of the Dirac points, and at the saddle point M. A general formulation of the thermodynamics at the LTT in graphene is given. The thermodynamic characteristics of graphene are investigated at the Lifshitz topological transitions. Anomalies are found in the electron specific heat Ce, the electron thermal coefficient of pressure, and the coefficients of electron compressibility and thermal expansion in graphene at the LTT. All the thermodynamic parameters possess the strongest singularities in graphene at the LTT near the saddle points. This opens exciting opportunities for inducing and exploring the Lifshitz topological transitions in graphene.

Transport Spectroscopy of the Field Induced Cascade of Lifshitz Transitions in YbRh2Si2

A series of strong anomalies in the thermoelectric power is observed in the heavy fermion compound YbRh$_2$Si$_2$ under the effect of magnetic field varying in the range from 9.5~T to 13~T. We identify these features with a sequence of topological transformations of the sophisticated Fermi surface of this compound, namely a cascade of Lifshitz topological transitions. In order to undoubtedly attribute these anomalies to the specific topological changes of the Fermi surface, we employ the renormalized band method. Basing on its results we suggest a simplified model consisting of the large peripheral Fermi surface sheet and the number of continuously appearing (disappearing) small "voids" or "necks". We account for the multiple electron scattering processes between various components of the Fermi surface, calculate the corresponding scattering times, and, finally, find the magnetic field dependence of the Seebeck coefficient. The obtained analytical expression reproduces reasonably the observed positions of the maxima and minima as well as the overall line shapes and allows us to identify the character of corresponding topological transformations.

Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

Some peculiarities of thermopower at the Lifshitz topological transitions due to stacking change in bilayer and multilayer graphene

Singularities of thermopower (the Seebeck coefficient) are considered at the Lifshitz topological transitions (LTT) in bilayer graphene (BLG) and multilayer graphene (MLG) due to stacking change from AB to AA . The dependence of singularities on μ , γ 1 and Δ is investigated ( μ is the chemical potential, γ 1 is the interlayer hopping parameter and Δ is the gap value) for the gapped graphene, as well as for the gapless one. The present paper results indicate that effects of the thermopower singularities are appreciable and can be used to observe the LTT, and to explore the degree of stacking change from AB to AA in graphene. Therefore, the thermopower singularities at LTT due to stacking change from AB to AA can be used as a powerful tool to control electronic properties of BLG- and MLG-based structures.

Imbert-Fedorov shift in pseudospin−N/2 semimetals and nodal-line semimetals

The Imbert-Fedorov (IF) shift is the transverse shift of a beam at a surface or an interface. It is a manifestation of the three-component Berry curvature in three dimensions, and has been studied in optical systems and Weyl semimetals. Here we investigate the IF shift in two types of topological systems, topological semimetals with pseudospin-$N/2$ for an arbitrary integer $N$, and nodal-line semimetals (NLSMs). For the former, we find the IF shift depends on the components of the pseudospin, with the sign depending on the chirality. We term this phenomenon the pseudospin Hall effect of topological fermions. The shift can also be interpreted as a consequence of the conservation of the total angular momentum. For the latter, if the NLSM has both time-reversal and inversion symmetries, the IF shift is zero; otherwise it could be finite. We take the NLSM with a vortex ring, which breaks both symmetries, as an example, and show that the IF shift can be used to detect topological Lifshitz transitions. Finally, we propose experimental designs to detect the IF shift.

Magnetic field driven topological transitions in the noncentrosymmetric energy spectrum of the two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction

Spin orbit interaction (SOI) having a complicated energy spectrum with a conical point and four critical points are promising candidates to observe electron topological transitions. In the present paper we have investigated the evolution of the electron spectrum and isoenergetic contours under the influence of parallel magnetic field. General formulas for energies of critical points for arbitrary values of SOI constants and magnetic field are found. The existence of critical magnetic fields at which a number of critical points is changed has been predicted. The magnetic field driving topological Lifshitz transitions in the geometry of isoenergetic contours have been studied. Van Hove's singularities in the electron density of states are calculated. The obtained results can be used for theoretical investigations of different electron characteristics of such 2D systems.

Quantum topological transitions and spinons in metallic ferro- and antiferromagnets

An effective Hamiltonian describing fluctuation effects in the magnetic phases of the Hubbard model in terms of spinon excitations is derived. A comparison of spin-rotational Kotliar–Ruckenstein slave boson and Ribeiro–Wen dopon representations is performed. The quantum transition into the half-metallic ferromagnetic state with vanishing of spin-down Fermi surface is treated as the topological Lifshitz transition in the quasimomentum space. The itinerant-localized magnetism transitions and Mott transition in antiferromagnetic state are considered in the topological context. Related metal-insulator transitions in Heusler alloys are discussed.

Nontrivial topology of bulk HgSe from the study of cyclotron effective mass, electron mobility and phase shift of Shubnikov–de Haas oscillations

In this paper, the authors report the results of an experimental study of effective mass, electron mobility and phase shift of Shubnikov–de Haas oscillations of transverse magnetoresistance in an extended electron concentration region from 8.8 × 1015 cm−3 to 4.3 × 1018 cm−3 in single crystals of mercury selenide. The revealed features indicate that Weyl semimetal phase may exist in HgSe at low electron density. The most significant result is the discovery of an abrupt change of Berry phase at electron concentration 2 × 1018 cm−3, which we explain in terms of a manifestation of topological Lifshitz transition in HgSe that occurs by tuning Fermi energy via doping.

Evolution of the low-temperature Fermi surface of superconducting FeSe1\u2212xSx across a nematic phase transition

The existence of a nematic phase transition in iron-chalcogenide superconductors poses an intriguing question about its impact on superconductivity. To understand the nature of this unique quantum phase transition, it is essential to study how the electronic structure changes across this transition at low temperatures. Here, we investigate the evolution of the Fermi surfaces and electronic interactions across the nematic phase transition of FeSe1−xSx using Shubnikov-de Haas oscillations in high magnetic fields up to 45 T in the low temperature regime down to 0.4 K. Most of the Fermi surfaces of FeSe1−xSx monotonically increase in size except for a prominent low frequency oscillation associated with a small, but highly mobile band, which disappears at the nematic phase boundary near x ~ 0.17, indicative of a topological Lifshitz transition. The quasiparticle masses are larger inside the nematic phase, indicative of a strongly correlated state, but they become suppressed outside it. The experimentally observed changes in the Fermi surface topology, together with the varying degree of electronic correlations, will change the balance of electronic interactions in the multi-band system FeSe1−xSx and promote different kz-dependent superconducting pairing channels inside and outside the nematic phase.

Interplay of Floquet Lifshitz transitions and topological transitions in bilayer Dirac materials

We show how transitions between different Lifshitz phases in bilayer Dirac materials with and without spin-orbit coupling can be studied by driving the system. The periodic driving is induced by a laser and the resultant phase diagram is studied in the high frequency limit using the Brillouin-Wigner perturbation approach to leading order. The examples of such materials include bilayer graphene and spin-orbit coupled materials such as bilayer silicene. The phase diagrams of the effective static models are analyzed to understand the interplay of topological phase transitions, with changes in the Chern number and topological Lifshitz transitions, with the ensuing changes in the Fermi surface. Both the topological transitions and the Lifshitz transitions are tuned by the amplitude of the drive.

Shubnikov–de Haas Oscillations in the Magnetoresistance of Layered Conductors in Proximity to the Topological Lifshitz Transition

The dependence of the resistance of a layered conductor with a quasi-two-dimensional charge carrier energy spectrum on the strength and orientation of a quantizing magnetic field is studied. The case of an organic conductor with a multisheet Fermi surface consisting of a weakly warped cylinder and two adjoining planar sheets is considered. By applying an external pressure to the conductor or doping it with impurity atoms, the gap between the cylinder and the planar sheets of the Fermi surface (FS) may be reduced so that electrons start wandering on the FS, tunneling between its different parts due to magnetic breakdown. If an electron can pass through all the different sheets of the FS several times during the mean free time, its motion in the plane orthogonal to the magnetic field becomes finite. This leads to Shubnikov–de Haas oscillations with a period determined by the area enclosed by the closed breakdown orbit of an electron in momentum space. However, even at a slight tilting of the field from the normal to the layers by an angle ϑ, the equidistance is broken and at certain angles ϑk the probability of the magnetic breakdown to one of the planar FS sheets may become so low that the electron cannot complete the magnetic-breakdown orbit and its motion over the other planar sheet and the cylindrical part of the FS becomes infinite. As a result, magnetic-breakdown quantum oscillations of magnetization and all kinetic properties vanish. This vanishing repeats periodically as a function of tan ϑ with changing the tilt angle. Possibilities for experimental observation and investigation of the influence of magnetic breakdown on quantum oscillation phenomena are discussed.

Realization of a New Topological Crystalline Insulator and Lifshitz Transition in PbTe

AbstractTopological materials boast exotic metallic surface states with linear dispersion and spin‐momentum locking, which makes them potential candidates for dissipationless electronic and spintronic devices. Here, it is theoretically predicted that intrinsic Te antisite defects (TePb) in the narrow‐gap semiconductor PbTe induce a band inversion, turning it into a topological crystalline insulator (TCI). To experimentally verify the exotic properties, TePb antisites are introduced into PbTe crystals via nonstoichiometric growth by molecular beam epitaxy. Semimetallic resistivity and distinct quantum oscillations are observed on the TePb doped PbTe. Most importantly, a π Berry phase is unambiguously revealed by a Landau index analysis, demonstrating the Dirac fermion nature of the topological surface states. The discovered TCI nature in TePb doped PbTe is further explored using magneto‐transport measurements under external pressure, and the theoretical calculations of band structures with applying pressure indicate a pressure‐induced Lifshitz transition. Besides, it is proposed that the contribution of bulk states to transport can be reduced by enlarging the inverted gap with strain.

Correlation-driven Lifshitz transition and orbital order in a two-band Hubbard model

We study by dynamical mean field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localisation while the wider one being still itinerant. At quarter-filling, the physical behaviour is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favour of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.