Bulk Band Inversion Research Articles

Visualization of spin-polarized surface resonances in Pb-based ternary topological insulators

The formation of the topological surface state originates from bulk band inversion at the top of the valence band and the bottom of the conduction band. The transition between normal and topological insulators is known as a topological phase transition. Here we show spin-polarized electronic states of Pb-based ternary topological insulators Pb(Bi1-xSbx)2Te4 (x = 0.55, 0.70, 0.79) investigated by spin- and angle-resolved photoemission spectroscopy and first-principles calculations. We visualize a pair of spin-polarized surface resonances dispersing along the upper edge of projected bulk bands in occupied states. Interestingly, a branch of the spin-polarized surface resonances continuously connects to the topological surface state. The coexistence of the topological surface state and the spin-polarized surface resonances can be explained by considering the topological phase transition.

Anticipation of Large Intrinsic Spin Hall Conductivity in Mercury Chalcogenides: A First‐Principles Study

AbstractThe report carried out detailed first‐principle calculations of Mercury chalcogenides (HgX; X = Te, Se and S) using density functional theory, verifying the bulk band inversion property with different exchange‐correlation functionals. The Wannier function method is used to study the non‐trivial topology of HgX systems, spin Berry curvature, and intrinsic spin Hall conductivity. Quantized intrinsic spin Hall conductivity is observed in the HgX systems. Large intrinsic spin Hall conductivity is found in the systems due to a strong spin Berry curvature accumulation near the triply degenerate points in the Brillouin zone. Calculation shows that the intrinsic spin Hall conductivity for all three HgX systems has stable plateaus, with Mercury Telluride having a maximum width of up to 1.05 eV. The maximum intrinsic spin Hall conductivity of –931/e () is obtained in mercury sulfide, higher than the reported values for spin Hall conductivity and the plateau width in typical topological insulators such as , , and as well as in transition metal pnictides (TaX, X = As, P and N) and transition metal iridates.

First Principles Studies of Topological Insulating Behavior in Lanthanum‐Monopnictides and their Heterostructures

AbstractThe topological insulating behavior of LaX (X = Bi, Sb, As, and P) and their heterostructure combinations are investigated. The system's bulk‐band‐inversion is analyzed, and the ‐topological indexes are calculated using LDA and mBJLDA exchange functionals. Strong topological insulating behavior in LaBi is confirmed from bulk band inversion. Linearly dispersive Dirac‐cone in the (001)‐surface band structure is observed. The other LaX binaries also exhibit bulk‐band‐inversion under LDA+SOC settings but disappear after including the mBJ potential. The robustness of the surface Dirac cone is tested by estimating the surface band structure under uniaxial strain. The result shows that Dirac‐cone in the (001)‐surface is unaltered only for the LaBi system and destroyed in all other three binaries, concluding the topologically trivial nature of LaP, LaSb, and LaAs. The investigation is further extended to study the multilayer LaX1/LaX2 systems composed of an alternate stacking of two different LaX binaries. The findings suggest that the multilayer structures exhibit topological insulating behavior only when LaBi is present in the system. Bulk‐band‐inversion and surface Dirac‐cone structures in LaBi/LaAs, LaBi/LaSb, and LaBi/LaP multilayers are observed. Furthermore, the surface Dirac cones remain unchanged under the influence of TR‐preserving perturbation, confirming these systems possess strong topological insulating character.

Evolution of Mn1-xGexBi2Te4 Electronic Structure under Variation of Ge Content.

One of the approaches to manipulate MnBi2Te4 properties is the magnetic dilution, which inevitably affects the interplay of magnetism and band topology in the system. In this work, we carried out angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations for analysing changes in the electronic structure of Mn1-xGexBi2Te4 that occur under parameter x variation. We consider two ways of Mn/Ge substitution: (i) bulk doping of the whole system; (ii) surface doping of the first septuple layer. For the case (i), the experimental results reveal a decrease in the value of the bulk band gap, which should be reversed by an increase when the Ge concentration reaches a certain value. Ab-initio calculations show that at Ge concentrations above 50%, there is an absence of the bulk band inversion of the Te pz and Bi pz contributions at the Γ-point with significant spatial redistribution of the states at the band gap edges into the bulk, suggesting topological phase transition in the system. For case (ii) of the vertical heterostructure Mn1-xGexBi2Te4/MnBi2Te4, it was shown that an increase of Ge concentration in the first septuple layer leads to effective modulation of the Dirac gap in the absence of significant topological surface states of spatial redistribution. The results obtained indicate that surface doping compares favorably compared to bulk doping as a method for the Dirac gap value modulation.

Exchange Interaction‐Driven Surface State Hybridization in Bi2Se3Topological Insulator

AbstractTopological insulator has gapless surface state, which results from bulk band inversion due to strong spin–orbit coupling. This nontrivial topology robust to nonmagnetic disorders and defects is considered one of the biggest obstacles for modulations of the surface state. In this work, the suppression of surface properties in Bi2Se3of various thicknesses grown on antiferromagnetic NiO, which has a strong exchange interaction is investigated. Under perpendicular magnetic fields, a drastic decrease in mobilityµand in the number of phase coherent channelsαin 5 QL Bi2Se3on NiO are observed. In addition, the THz transmission study shows that an increase in the surface penetration depthξcan accelerate the hybridization of surface states, which is also verified using the optical pump THz probe. This rapid collapse of surface states indicates the unique role of antiferromagnetic materials in band overlap, suggesting that the topological surface nature can be modulated by forming an antiferromagnet‐topological insulator heterostructure.

Axion insulators protected by C2T symmetry, their K -theory invariants, and material realizations

Axion insulators are generally understood as magnetic topological insulators whose Chern-Simons axion coupling term is quantized and equal to $\pi$. Inversion and time reversal, or the composition of either one with a rotation or a translation, are symmetries which protect this invariant. In this work, we focus our attention on the composition of a 2-fold rotation with time reversal, and we show that insulators with this symmetry possess a Z2 invariant arising from Atiyah's real K-theory. We call this invariant the K-theory Kane-Mele invariant due to the similarities it has with the Kane-Mele invariant for systems with time-reversal symmetry. Whenever all Chern numbers vanish, we demonstrate that this invariant is equivalent to the Chern-Simons axion coupling, and in the presence of the inversion symmetry, we show how this invariant could be obtained from the eigenvalues of the inversion operator on its fixed points in momentum space. For the general case of non-trivial Chern numbers, the Chern-Simons axion coupling term incorporates information of the K-theory Kane-Mele invariant as well as information regarding bands with non-trival Chern numbers. An explicit formula in terms of K-theory generators is presented for the Chern-Simons axion coupling term, the relation with the K-theory Kane-Mele invariant is explained, and a formula in terms of eigenvalues of the inversion operator is obtained. Using an effective Hamiltonian model and first-principles calculations, we also show that the occurrence of bulk-band inversion and nontrivial K-theory Kane-Mele invariant index can be observed in axion insulators of the pnictides family. In particular, we demonstrate that NpBi can be classified as an axion insulator due to the detection of additional topological indicators such as the quantum spin Hall effect, gapped surface states, surface quantized anomalous Hall effect, and chiral hinge modes

Non-trivial band topology in Bi doped Lanthanum monopnictides (LaX; X = As and Sb)

In this study, we report first-principles investigation of non-trivial topological characteristics in Bi doped Lanthanum monopnictides, particularly LaAs and LaSb. For this, we varied the concentration of Bi atoms in 1 × 1 × 2 supercell of LaAs and LaSb unit cells along [001] direction, and phonon-dispersion spectra of all these doped arrangements are observed to be dynamically stable.HSE06 band structure calculations with spin–orbit coupling reveal that the non-trivial topological characteristics starts appearing in 50% concentration of Bi atoms in the given supercells of LaAs and LaSb. The non-trivial topological characteristics in the proposed doped arrangements are verified by bulk band inversion, unit Z2 topological invariant, and a surface Dirac cone. Our findings provide promising candidates of non-trivial topological family, which may carry huge potential for extremely large magnetoresistance and spintronics applications.

Inherited weak topological insulator signatures in the topological hourglass semimetal Nb3XTe6 (X=Si, Ge)

Using spin-resolved and angle-resolved photoemission spectroscopy and first-principles calculations, we have identified bulk band inversion and spin polarized surface state evolved from a weak topological insulator (TI) phase in van der Waals materials Nb3XTe6 (X = Si, Ge). The fingerprints of weak TI homologically emerge with hourglass fermions, as multi nodal chains composed by the same pair of valence and conduction bands gapped by spin orbit coupling. The novel topological state, with a pair of valence and conduction bands encoding both weak TI and hourglass semimetal nature, is essential and guaranteed by nonsymmorphic symmetry. It is distinct from TIs studied previously based on band inversions without symmetry protections.

Pressure effect on band inversion in AECd2As2 (AE=Ca, Sr, Ba)

Recent studies have predicted that magnetic EuCd2As2 can host several different topological states depending on its magnetic order, including a single pair of Weyl points. Here we report on the bulk properties and band inversion induced by pressure in the non-magnetic analogs AECd2As2 (AE = Ca, Sr, Ba) as studied with density functional theory calculations. Under ambient pressure we find these compounds are narrow band gap semiconductors, in agreement with experiment. The size of the band gap is dictated by both the increasing ionicity across the AE series which tends to increase the band gap, as well as the larger nearest neighbor Cd-As distance from increasing atomic size which can decrease the band gap because the conduction band edge is an anti-bonding state derived mostly from Cd 5s orbitals. The combination of these two competing effects results in a non-monotonic change of the band gap size across the AE series with SrCd2As2 having the smallest band gap among the three compounds. The application of negative pressure reduces this band gap and causes the band inversion between the Cd 5s and As 4p orbitals along the ${\Gamma}$-A direction to induce a pair of Dirac points. The topological nature of the Dirac points is then confirmed by finding the closed Fermi arcs on the (10-10) surface.

Unusual Quadrupole NMR of Topological Insulator Bi2Te3

Very recently, nuclear magnetic resonance (NMR) of 209Bi has been shown to provide quantitative access to the bulk band inversion in the topological insulator Bi2Se3 and detected a highly unusual f...

Field-induced charge symmetry revealed by nuclear magnetic resonance in the topological insulator Bi2Te3

Nuclear magnetic resonance (NMR) was recently shown to measure the bulk band inversion of Bi$_2$Se$_3$ through changes in the $^{209}$Bi nuclear quadrupole interaction, and the corresponding tensor of the local electric field gradient was found to follow, surprisingly, the direction of the external magnetic field if the sample is rotated. This manifests a hidden property of the charge carriers in the bulk of this topological insulator, which is explored here with another material, Bi$_2$Te$_3$. It is found that two electric field gradients appear to be present at $^{209}$Bi, one rests with the lattice, as usual, while a second follows the external field if it is rotated with respect to the crystal axes. These electronic degrees of freedom correspond to an effective rotation of $j$-electrons, and their level life time is believed to be responsible for a new quadrupolar relaxation that should lead to other special properties including the electronic specific heat.

Deterministic interface modes in two-dimensional acoustic systems

The interface state in two-dimensional (2D) sonic crystals (SCs) was obtained based on trying or cutting approach, which greatly limits its practical applications. In this paper, we theoretically demonstrate that one category of interface states can deterministically exist at the boundary of two square-lattice SCs due to the geometric phase transitions of bulk bands. First, we derive a tight-binding formalism for acoustic waves and introduce it into the 2D case. Furthermore, the extended 2D Zak phase is employed to characterize the topological phase transitions of bulk bands. Moreover, the topological interface states can be deterministically found in the nontrivial bandgap. Finally, two kinds of SCs with the [Formula: see text] symmetry closely resembling the 2D Su–Schrieffer–Heeger (SSH) model are proposed to realize the deterministic interface states. We find that tuning the strength of intermolecular coupling by contacting or expanding the scatterers can effectively induce the bulk band inversion between the trivial and nontrivial crystals. The presence of acoustic interface states for both cases is further demonstrated. These deterministic interface states in 2D acoustic systems will be a great candidate for future waveguide applications.

Signature of band inversion in the antiferromagnetic phase of axion insulator candidate EuIn2As2

We have performed angle-resolved photoemission spectroscopy on EuIn2As2 which is predicted to be an axion insulator in the antiferromagnetic state. By utilizing soft-x-ray and vacuum-ultraviolet photons, we revealed a three-dimensional hole pocket centered at the Gamma point of bulk Brillouin zone together with a heavily hole-doped surface state in the paramagnetic phase. Upon entering the antiferromagnetic phase, the band structure exhibits a marked reconstruction characterized by the emergence of a "M"-shaped bulk band near the Fermi level. The qualitative agreement with first-principles band-structure calculations suggests the occurrence of bulk-band inversion at the Gamma point in the antiferromagnetic phase. We suggest that EuIn2As2 provides a good opportunity to study the exotic quantum phases associated with possible axion-insulator phase.

Observation of inverted band structure in the topological Dirac semimetal candidate CaAuAs

We have performed high-resolution angle-resolved photoemission spectroscopy of ternary pnictide CaAuAs which is predicted to be a three-dimensional topological Dirac semimetal (TDS). By accurately determining the bulk-band structure, we have revealed the coexistence of three-dimensional and quasi-two-dimensional Fermi surfaces with dominant hole carriers. The band structure around the Brillouin-zone center is characterized by an energy overlap between hole and electron pockets, in excellent agreement with first-principles band-structure calculations. This indicates the occurrence of bulk-band inversion, supporting the TDS state in CaAuAs. Because of the high tunability in the chemical composition besides the TDS nature, CaAuAs provides a precious opportunity for investigating the quantum phase transition from TDS to other exotic topological phases.

Signatures of non-trivial band topology in LaAs/LaBi heterostructure

In this article, we investigate non-trivial topological features in a heterostructure of extreme magnetoresistance (XMR) materials LaAs and LaBi using density functional theory. The proposed heterostructure is found to be dynamically stable and shows bulk band inversion with non-trivial Z2 topological invariant and a Dirac cone at the surface. In addition, its electron and hole carrier densities ratio is also calculated to investigate the possibility to possess XMR effect. Electrons and holes in the heterostructure are found to be nearly compensated, thereby facilitating it to be a suitable candidate for XMR studies.

Band inversion and topology of the bulk electronic structure in FeSe0.45Te0.55

FeSe${}_{0.45}$Te${}_{0.55}$ (FeSeTe) has recently emerged as a promising candidate to host topological superconductivity, with a Dirac surface state and signatures of Majorana bound states in vortex cores. However, correlations strongly renormalize the bands compared to electronic structure calculations, and there is no evidence for the expected bulk band inversion. We present here a comprehensive angle resolved photoemission (ARPES) study of FeSeTe as function of photon energies ranging from 15 - 100 eV. We find that although the top of bulk valence band shows essentially no $k_z$ dispersion, its normalized intensity exhibits a periodic variation with $k_z$. We show, using ARPES selection rules, that the intensity oscillation is a signature of band inversion indicating a change in the parity going from $\Gamma$ to Z. Thus we provide the first direct evidence for a topologically non-trivial bulk band structure that supports protected surface states.

Switching of band inversion and topological surface states by charge density wave

Topologically nontrivial materials host protected edge states associated with the bulk band inversion through the bulk-edge correspondence. Manipulating such edge states is highly desired for developing new functions and devices practically using their dissipation-less nature and spin-momentum locking. Here we introduce a transition-metal dichalcogenide VTe2, that hosts a charge density wave (CDW) coupled with the band inversion involving V3d and Te5p orbitals. Spin- and angle-resolved photoemission spectroscopy with first-principles calculations reveal the huge anisotropic modification of the bulk electronic structure by the CDW formation, accompanying the selective disappearance of Dirac-type spin-polarized topological surface states that exist in the normal state. Thorough three dimensional investigation of bulk states indicates that the corresponding band inversion at the Brillouin zone boundary dissolves upon the CDW formation, by transforming into anomalous flat bands. Our finding provides a new insight to the topological manipulation of matters by utilizing CDWs’ flexible characters to external stimuli.

Unusual change in the Dirac-cone energy band upon a two-step magnetic transition in CeBi

We performed angle-resolved photoemission spectroscopy (ARPES) on CeBi which undergoes a two-step antiferromagnetic (AF) transition with temperature. Soft-x-ray ARPES revealed the inverted band structure at the $X$ point of bulk Brillouin zone for CeBi (and also for LaBi) as opposed to LaSb with noninverted band structure. Low-energy ARPES on CeBi revealed the Dirac-cone band at the $\overline{\mathrm{\ensuremath{\Gamma}}}$ point in the paramagnetic phase associated with the bulk band inversion. On the other hand, a double Dirac-cone band appears on entering the first AF phase at $T$ = 25 K, whereas a single Dirac-cone band recovers below the second AF transition at $T$ = 14 K. The present result suggests an intricate interplay between antiferromagnetism and topological surface states in CeBi.

Magnetic quantum ring in two-dimensional topological insulators

The quantum properties of topological insulator magnetic quantum rings formed by inhomogeneous magnetic fields are investigated using a series expansion method for the modified Dirac equation. Cycloid-like and snake-like magnetic edge states are respectively found in the bulk gap for the normal and inverted magnetic field profiles. The energy spectra, current densities and classical trajectories of the magnetic edge states are discussed in detail. The bulk band inversion is found to manifest itself through the angular momentum transition in the ground state for the cycloid-like states and the resonance tunneling effect for the snake-like states.

Probing the origin of extreme magnetoresistance in Pr/Sm mono-antimonides/bismuthides

Combining angle-resolved photoemission spectroscopy and magneto-transport measurements, we systematically investigated the possible origin of the extreme magnetoresistance in Pr/Sm mono-antimonides/bismuthides (PrSb, SmSb, PrBi, SmBi). Our photoemission measurements reveal that the bulk band inversion and surface states are absent (present) in Pr/Sm antimonides (bismuthides), implying that topological surface states are unlikely to play an important role for the observed extreme magnetoresistance. We found that the electron-hole compensation is well satisfied in all these compounds and the bulk band structure exhibits no obvious temperature dependence from 10 K up to 150 K. Simultaneous fittings of the magnetoresistance and Hall coefficient reveal that the carrier mobility is dramatically enhanced at low temperature, which naturally explains the suppression of extreme magnetoresistance at high temperatures. Our results therefore show that the extreme magnetoresistance in these compounds can be well accounted for by the two-band model with good electron-hole compensation. Finally, we found that both PrSb and SmSb exhibit highly linear bulk bands near the X point and lie close to the transition point between a topologically trivial and nontrivial phase, which might be relevant for the observed anomalous quantum oscillations.