Inverted Band Structure Research Articles

Quantum oscillations in the magnetization and density of states of insulators

The observation of [Formula: see text]-periodic behavior in Kondo insulators and semiconductor quantum wells challenges the conventional wisdom that quantum oscillations (QOs) necessarily arise from Fermi surfaces in metals. We revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast to metals where all observables exhibit oscillations at the same frequency. The magnetization oscillations arising from occupied Landau levels occur at the same frequency that would exist in the unhybridized case. The LE-DOS oscillations in a disorder-free system are dominated by gap-edge states and exhibit a beat pattern between two distinct frequencies at low temperature. Disorder-induced in-gap states lead to an additional contribution to the DOS at the unhybridized frequency. The temperature dependence of the amplitude and phase of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz-Kosevich form well known in metals. We also compute transport to ensure that we are probing a regime with insulating upturns in the direct current (DC) resistivity.

Photon Drag Currents and Terahertz Generation in α-Sn/Ge Quantum Wells.

We have fabricated α-Sn/Ge quantum well heterostructures by sandwiching nano-films of α-Sn between Ge nanolayers. The samples were grown via e-beam deposition and characterized by Raman spectroscopy, atomic force microscopy, temperature dependence of electrical resistivity and THz time-resolved spectroscopy. We have established the presence of α-Sn phase in the polycrystalline layers together with a high electron mobility μ = 2500 ± 100 cm2 V−1 s−1. Here, the temperature behavior of the resistivity in a magnetic field is distinct from the semiconducting films and three-dimensional Dirac semimetals, which is consistent with the presence of linear two-dimensional electronic dispersion arising from the mutually inverted band structure at the α-Sn/Ge interface. As a result, the α-Sn/Ge interfaces of the quantum wells have topologically non-trivial electronic states. From THz time-resolved spectroscopy, we have discovered unusual photocurrent and THz radiation generation. The mechanisms for this process are significantly different from ambipolar diffusion currents that are responsible for THz generation in semiconducting thin films, e.g., Ge. Moreover, the THz generation in α-Sn/Ge quantum wells is almost an order of magnitude greater than that found in Ge. The substantial strength of the THz radiation emission and its polarization dependence may be explained by the photon drag current. The large amplitude of this current is a clear signature of the formation of conducting channels with high electron mobility, which are topologically protected.

Spin-polarized charge transport through a single barrier in HgTe/CdTe heterostructure interface

We present a theoretically investigation about the electron transport through a single-barrier structures in HgTe/CdTe quantum wells (QWs) with inverted band structure. For HgTe/CdTe QWs structure, the transmission probabilities show great dependence on the Rashba spin–orbit interaction (RSOI), the incident angle, the incident Fermi energy and the electric modulation potential. By tuning the modulation amplitude with gate voltage or the strength of RSOI modulation, the efficient spin-polarized PZ=1 is achieved, which is formed due to the spin-split in band spectrum induced by the RSOI modulation. This electric mechanism provides us a way to manipulate the spin polarization electrically and convenient for experimental verification.

Rashba Spin Splitting in HgCdTe Quantum Wells with Inverted and Normal Band Structures.

In quantum wells (QWs) formed in HgCdTe/CdHgTe heterosystems with a variable composition of Cd(Hg), Shubnikov-de-Haas (SdH) oscillations are investigated to characterize the Rashba-type spin-orbit coupling in QWs with both a normal and inverted band structure. Several methods of extracting the Rashba spin-splitting at zero magnetic field and their magnetic field dependences from the beatings of SdH oscillations are used for greater reliability. The large and similar Rashba splitting (25–27 meV) is found for different kinds of spectrum, explained by a significant fraction of the p-type wave functions, in both the E1 subband of the sample with a normal spectrum and the H1 subband for the sample with an inverted one.

Revisiting the physical origin and nature of surface states in inverted-band semiconductors

We revisit the problem of surface states in semiconductors with inverted band structures, such as $\alpha$-Sn and HgTe. We unravel the confusion that arose over the past decade regarding the origin of the surface states, their topological nature, and the role of strain. Within a single minimalistic description, we reconcile different solutions found in the 1980s with the results obtained from modern-day numerical simulations, allowing us to unambiguously identify all branches of surface states around the $\Gamma$-point of the Brillouin zone in different regimes. We also show that strain is a smooth "deformation" to the surface states, following the usual continuity principle of physics, and not leading to any drastic change of the physical properties in these materials, in contrast to what has recently been advanced in the literature. We consider biaxial in-plane strain that is either tensile or compressive, leading to different branches of surface states for topological insulators and Dirac semimetals, respectively. Our model can help in interpreting numerous experiments on topological surface states originating from inverted-band semiconductors.

Evaluating Lead Halide Perovskite Nanocrystals as a Spin Laser Gain Medium.

Spin-polarized charge endows conventional lasers with not only new functionalities but also reduced lasing thresholds thanks to the lifting of spin degeneracy. II-VI and III-V semiconductors have been extensively investigated as spin laser gain mediums; however, the degree of polarization is limited by the light hole and heavy hole degeneracy. Herein, we evaluate the potential of CsPbBr3 nanocrystals─ones that are featured with low band-edge degeneracy and therefore a high degree of polarization as a result of inverted band structure and large spin-orbit coupling─as a gain medium for spin lasers. Our experiment and numerical modeling results reveal that, within the spin relaxation lifetime, the optical gain threshold can be depressed by polarizing the charge using circularly polarized photoexcitation. However, prolonging the spin relaxation lifetime is required to realize a spin laser.

Design strong anomalous Hall effect via spin canting in antiferromagnetic nodal line materials

The interplay between magnetism and topological electronic structure offers a large freedom to design strong anomalous Hall effect (AHE) materials. A nodal line from band inversion is a typical band structure to generate strong AHE. Whereas, in most collinear antiferromagnets (AFMs), the integration of Berry curvatures on Brillouin zone is forced to zero by the joint $TO$ symmetry, where $T$ and $O$ are time reversal and a space group operation, respectively. Even with inverted band structures, such kind of AFM cannot have AHE. Therefore, so far, AFM nodal line band structures constructed by spin degenerated bands didn't get much attentions in AHE materials. In this work, we illustrate that such kind of band structure indeed provides a promising starting point to generated strong local Berry curvature by perturbations and, therefore, strong intrinsic AHE. In specific AFM compounds of $A$MnBi$_2$($A$=Ca and Yb) with inverted band structure, we found a strong AHE induced by a weak spin canting, and due to nodal line in the band structure the anomalous Hall conductivity keeps growing as the canting angle increases. Since such spin-canting can be adjusted via doping experimentally, it provides another effective strategy to generate and manipulate strong AHE

Higher-order topological superconductors based on weak topological insulators

High-order topological phases host robust boundary states at the boundary of the boundary, which can be interpreted from their boundary topology. In this work, considering the interplay between superconductors and magnetic fields to gap the surface states of three-dimensional weak topological insulators, we show that second-order topological superconductors (TSCs) featuring helical or chiral Majorana hinge modes and third-order TSC featuring Majorana corner modes can be realized. Remarkably, the higher-order TSCs in our models can be attributed to their certain boundaries, surfaces, or hinges, which naturally behave as first-order TSC in DIII or D symmetry class. Correspondingly, these higher-order TSCs can be characterized by the boundary first-order topological invariants, such as surface Chern numbers or surface $Z_2$ topological invariants for surface TSCs. Our models can effectively capture the topology of iron-based superconductors with desired inverted band structures and superconducting pairings.

Quantized spin Hall conductance in a magnetically doped two dimensional topological insulator

Soon after the discovery of the quantum spin Hall effect, it has been predicted that a magnetic impurity in the presence of strong Coulomb interactions will destroy the quantum spin Hall effect. However, the fate of the quantum spin Hall effect in the presence of magnetic impurities has not yet been experimentally investigated. Here, we report the successful experimental demonstration of a quantized spin Hall resistance in HgTe quantum wells dilutely alloyed with magnetic Mn atoms. These quantum wells exhibit an inverted band structure that is very similar to that of the undoped material. Micron sized devices of (Hg,Mn)Te quantum well (in the topological phase) show a quantized spin Hall resistance of h/2e2 at low temperatures and zero magnetic field. At finite temperatures, we observe signatures of the Kondo effect due to interaction between the helical edge channels and magnetic impurities. Our work lays the foundation for future investigations of magnetically doped quantum spin Hall materials towards the realization of chiral Majorana fermions.

Topological optical and phononic interface mode by simultaneous band inversion

Band inversion in one-dimensional superlattices is a strategy to generate topological interface modes in electronics, optics, acoustics, and nanophononics. Despite their potential for the control of topologically robust interactions, most realizations of these states have so far explored only a single kind of excitation. In this work, we design and fabricate GaAs/AlAs devices with simultaneously inverted band structures for light and phonons. We experimentally observe colocalized interface modes for 1.34 eV photons by optical reflectivity and 18 GHz phonons by coherent phonon generation and detection. Through numerical simulations, we demonstrate the ensuing robustness of the Brillouin interaction between them with respect to a specific type of disorder. Furthermore, we theoretically analyze the efficiency of time-domain Brillouin scattering in different topological designs presenting colocalized states and deduce a set of engineering rules. Potential future applications include the engineering of robust optomechanical resonators in a material system compatible with active media such as quantum wells and quantum dots.

Variety of scenarios for magnetic exchange response in topological insulators

We present an ab initio relativistic k.p theory of the effect of magnetic exchange field on the band structure in the gap region of bulk crystals and thin films of three-dimensional layered topological insulators. For the field perpendicular to the layers (along $z$), we reveal novel unconventional scenarios of the response of the band-gap edges to the magnetization. The modification of the valence and conduction states is considered in terms of their $\Gamma$-point spin $s^z$ and total angular momentum $J^z$ on the atomic sites where the states are localized. The actual scenario depends on whether $s^z$ and $J^z$ have the same or opposite sign. In particular, the opposite sign for the valence state and the same sign for the conduction state give rise to an unconventional response in Bi$_2$Te$_3$ -- both in the bulk crystal and in ultra-thin films, which fundamentally distinguishes this topological insulator from Bi$_2$Se$_3$, where both states have the same sign. To gain a deeper insight into different scenarios in insulators with both inverted and non-inverted zero-field band structure, a minimal four-band third-order k.p model is constructed from first principles. Within this model, we analyze the field-induced band structure of the insulators and identify Weyl nodes that appear in a magnetic phase and behave differently depending on the scenario. We characterize the topology of the modified band structure by the Chern number $\mathcal{C}$ and find the unconventional response to be accompanied by a large Chern number $\mathcal{C}=\pm3$.

Boundary topological superconductors

For strongly anisotropic time-reversal invariant (TRI) insulators in two and three dimensions, the band inversion can occur respectively at all TRI momenta of a high symmetry axis and plane. Although these classes of materials are topologically trivial as the strong and weak $Z_{2}$ indices are all trivial, they can host an even number of unprotected helical gapless edge states or surface Dirac cones on some boundaries. We show in this work that when the gapless boundary states are gapped by $s_{\pm}$-wave superconductivity, a boundary time-reversal invariant topological superconductor (BTRITSC) characterized by a $Z_{2}$ invariant can be realized on the corresponding boundary. Since the dimension of the BTRITSC is lower than the bulk by one, the whole system is a second-order TRI topological superconductor. When the boundary of the BTRITSC is further cut open, Majorana Kramers pairs and helical gapless Majorana modes will respectively appear at the corners and hinges of the considered sample in two and three dimensions. Furthermore, a magnetic field can gap the helical Majorana hinge modes of the three-dimensional second-order TRI topological superconductor and lead to the realization of a third-order topological superconductor with Majorana corner modes. Our proposal can potentially be realized in insulator-superconductor heterostructures and iron-based superconductors whose normal states take the desired inverted band structures.

Квантовые осцилляции магнетосопротивления в гетероструктурах HgCdTe/HgTe/HgCdTe с инвертированным зонным спектром

The effects observed in the Shubnikov - de Haas oscillation regime in the HgCdTe/HgTe/HgCdTe heterostructure with a wide (20.3 nm) HgTe quantum well with an inverted band structure are discussed. In a topologically trivial 2D system, Pi(Greek letter) - shift of magnetooscillation phase is found. A thorough experimental study and theoretical analysis of the data is presented to understand the physical causes of this anomalous phase shift. The value of the effective electron mass m_c/m_0 = (0.022+-0.002), obtained from the region of doubly degenerate peaks of magnetoresistance, is approximately half the theoretical estimates. In the region of stronger magnetic fields for nondegenerate peaks of magnetoresistance, we have m_c/m_0 = (0.034+-0.003), which is in good agreement with both theoretical predictions and experimental results obtained from the analysis of activation conductivity in the quantum Hall effect regime. The reasons for this discrepancy are discussed.

Quasiclassical calculations of Landau level spectrum for 20.5-nm-wide H gTe quantum well: “extremum loop” model and effects of cubic symmetry

Quasiclassical calculations of the effective cyclotron mass and the spectrum of Landau levels have been carried out for carriers of the size-quantized H2 subband with a nonmonotonic dispersion law, which forms a valence band of 20.5-nm-wide HgTe quantum well with an inverted band structure. The model of the so-called “extremum loop”, previously developed by Rashba and Sheka for semiconductors with a wurtzite lattice, has been used for calculations. The results obtained are compared both with the empirical picture and with quantum-mechanical calculations of the Landau level spectrum for the HgTe quantum well in the semimetallic phase.

Landau levels in spin-orbit coupling proximitized graphene: Bulk states

We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included, to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning probe spectroscopy experiments. We compare different parameter regimes to identify fingerprints of relative and absolute magnitudes of intrinsic spin-orbit coupling in the spectra. The inverted band structure of graphene proximitized by WSe$_2$ leads to an interesting crossing of Landau states across the bulk gap at a crossover field, providing insights into the size of Rashba spin-orbit coupling. Landau level spectroscopy can help to resolve the type and signs of the intrinsic spin-orbit coupling by analyzing the symmetry in energy and number of crossings in the Landau fan chart. Finally, our results suggest that the strong response to the magnetic field of Dirac electrons in proximitized graphene can be associated with extremely large self-rotating magnetic moments.

Effects of the Electron—Electron Interaction in the Magneto-Absorption Spectra of HgTe/CdHgTe Quantum Wells with an Inverted Band Structure

Magneto-absorption in HgTe/CdHgTe quantum wells with an inverted band structure in magnetic fields up to 30 T has been studied. It has been shown that the positions of magneto-absorption lines for transitions from the zero-mode Landau levels in a wide range of magnetic field cannot in principle be described in the “single-electron” approximation using the eight-band Kane model even taking into account effects associated with the absence of spatial inversion symmetry. The revealed dependence of the energies of optical transitions on the magnetic field can be qualitatively explained within a “many-body” picture, where transitions between Landau levels are considered as collective modes hybridized by the electron-electron interaction.

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.

Signature of band inversion in the perovskite thin-film alloys BaSn1–xPbxO3

Perovskite oxides ABO$_3$ containing heavy B-site elements are a class of candidate materials to host topological metals with a large spin-orbit interaction. In contrast to the band insulator BaSnO$_3$, the semimetal BaPbO$_3$ is proposed to be a typical example with an inverted band structure, the conduction band of which is composed of mainly the O-2p orbital. In this study, we exemplify a band-gap modification by systematic structural, optical, and transport measurements in BaSn$_{1-x}$Pb$_x$O$_3$ films. A sudden suppression of the conductivity and an enhancement of the weak antilocalization effect at $x$ = 0.9 indicate the presence of a singular point in the electronic structure as a signature of the band inversion. Our findings provide an intriguing platform for combining topological aspects and electron correlation in perovskite oxides based on band-gap engineering.

Magnetotransport properties and stress control of HgCdTe thin film

In recent years, the research on topological materials, including topological insulator and topological semimetal, has received a lot of attention in condensed matter physics. HgCdTe, widely used in infrared detection, also holds huge potential in this field. It has been reported that the strained thin Hg<sub>0.865</sub>Cd<sub>0.135</sub>Te can realize topological insulator phase by using a CdZnTe substrate. However, the stress caused by changing substrate has great limitations. For example, the stress cannot be changed once the sample has been grown. Hence, we try to use a piezoceramics (PZT) instead to implement the stress and control the properties of HgCdTe. The main purpose of our experiment is to verify its validity. As is well known, the band structure of Hg<sub>1–<i>x</i></sub>Cd<i><sub>x</sub></i>Te can be precisely controlled by changing the content of Cd. When <i>x</i> lies between 0 and 0.165, HgCdTe features an inverted band structure, which is the premise of realizing topological phase. In this work, an inversion layer is induced on a single crystal grown HgCdTe bulk material by anodic oxidation, whose content of Cd is confirmed to be 0.149 by using XRD. Then the sample is thinned and attached to a PZT, which the tuning of stress is realized by applying a voltage to. Ohmic contacts are realized by indium in van der Pauw configuration. All measurements are carried out by using an Oxford Instruments <sup>4</sup>He cryostat with magnetic field applied perpendicularly to the sample plane. At 1.5 K and zero voltage, an evident SdH oscillation is observed. By fitting the linear relationship between filling factor and the reciprocal of magnetic field, the concentration is obtained to be <inline-formula><tex-math id="M2">\begin{document}${n_{\rm{s}}} = 1.25 \times {10^{16}}\;{{\rm{m}}^{ - 2}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20191330_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20191330_M2.png"/></alternatives></inline-formula>. Subsequently, we scan the voltage from 200 V to –200 V continuously in different magnetic fields. Two phenomena with different characteristics are observed. It is found that the resistance changes linearly with stress at zero field while an SdH oscillation-like behavior occurs at high field. We attribute such a difference to the existence of two conductive channels: one is the bulk material and the other is the two-dimensional electron gas. It is also noteworthy that the topological phase in our sample cannot be determined because the quantum Hall conductance is polluted by the conductance of bulk material. In conclusion, our results show that it is an effective way to use the PZT to tune the stress and this method can also be applied to the research of other materials.

Electrical tuning of helical edge states in topological multilayers

Mainstream among topological insulators, GaSb/InAs quantum wells present a broken gap alignment for the energy bands which supports the quantum spin Hall insulator phase and forms an important building block in the search of exotic states of matter. Such structures allow the band-gap inversion with electrons and holes confined in adjacent layers, providing a fertile ground to tune the corresponding topological properties. Using a full 3D eight-band method we investigate the inverted band structure of GaSb/InAs/GaSb and InAs/GaSb/InAs multilayers and the behavior of the helical edge states, under the influence of an electric field applied along the growth direction. By tuning the electric field modulus, we induce the change of the energy levels of both conduction and valence bands, resulting in a quantum spin Hall insulator phase where the helical edge states are predominantly confined in the GaSb layer. In particular, we found that InAs/GaSb/InAs has a large hybridization gap of about and, therefore, are promising to observe massless Dirac fermions with a large Fermi velocity. Our comprehensive characterization of GaSb/InAs multilayers creates a basis platform upon which further optimization of III–V heterostructures can be contrasted.