Electron-hole Hybridization Research Articles

Magneto-induced topological phase transition in inverted InAs/GaSb bilayers

We report a magneto-induced topological phase transition in inverted InAs/GaSb bilayers from a quantum spin Hall insulator to a normal insulator. We utilize a dual-gated Corbino device in which the degree of band inversion, or equivalently the electron and hole densities, can be continuously tuned. We observe a topological phase transition around the magnetic field where a band crossing occurs, accompanied by a bulk-gap closure characterized by a bulk conductance peak (BCP). In another set of experiments, we study the transition under a tilted magnetic field (tilt angle ). We observe the characteristic magnetoconductance around BCP as a function of , which dramatically depends on the density of the bilayers. In a relatively deep inversion (hence a higher density) regime, where the electron-hole hybridization dominates the excitonic interaction, the BCP grows with . On the contrary, in a shallowly inverted (a lower density) regime, where the excitonic interaction dominates the hybridization, the BCP is suppressed indicating a smooth crossover without a gap closure. This suggests the existence of a low-density, correlated insulator with spontaneous symmetry breaking near the critical point. Our highly controllable electron-hole system offers an ideal platform to study interacting topological states as proposed by recent theories. Published by the American Physical Society 2024

Magnetoconductance oscillations in electron-hole hybridization gaps and valley splittings in tetralayer graphene

We investigate magnetotransport on Bernal-stacked tetralayer graphene whose band structure consists of two massive subbands with different effective masses. Under a finite displacement field, we observe the valley splitting of Landau levels (LLs) only in the light-mass subband, consistent with a tight-binding model. At low density, we find unexpected magnetoconductance oscillations in bulk gaps which originate from a series of hybridizations between electronlike and holelike LLs due to band inversion in tetralayer graphene. In contrast to a trivial LL quantization gap, these inverted hybridization gaps can lead to a change in the number of edge states which explains the observed oscillations.

Fabry-Pérot interference in 2D low-density Rashba gas

In mesoscopic electronic systems, the Fabry-Pérot (FP) oscillation is observed in various 1D devices. As for higher dimensions, numerous transverse channels usually lead to dephasing that quenches the overall oscillation of the conductance. Up to now, the FP oscillation in 2D electronic systems is only reported in graphene-based devices and very recently, the pn junctions of inverted InAs/GaSb double quantum well (Karalic M. et al., Phys. Rev. X, 10 (2020) 031007). In the latter, the band shape of a sombrero hat plays an essential role, which introduces a novel mechanism of electron-hole hybridization for the 2D FP oscillation. In this work, we propose that such a scenario can be generalized to the 2D planar junction composed of low-density Rashba gas, where the band bottom possesses sombrero hat shape as well. We show that the backscattering between the outer and inner Fermi circles dominates the FP interference and significantly suppresses the dephasing effect between different transverse channels, which leads to a visible oscillation of the tunneling conductance. In particular, the visibility of the oscillating pattern can be enhanced by applying interface barriers, which is in contrast to that in the InAs/GaSb double quantum well. Our results provide a promising way for the implementation of the FP oscillation in the 2D electron gas.

Band structure and end states in InAs/GaSb core-shell-shell nanowires

Quantum wells in InAs/GaSb heterostructures can be tuned to a topological regime associated with the quantum spin Hall effect, which arises due to an inverted band gap and hybridized electron and hole states. Here, we investigate electron-hole hybridization and the fate of the quantum spin Hall effect in a quasi one-dimensional geometry, realized in a core-shell-shell nanowire with an insulator core and InAs and GaSb shells. We calculate the band structure for an infinitely long nanowire using $\mathbf{k \cdot p}$ theory within the Kane model and the envelope function approximation, then map the result onto a BHZ model which is used to investigate finite-length wires. Clearly, quantum spin Hall edge states cannot appear in the core-shell-shell nanowires which lack one-dimensional edges, but in the inverted band-gap regime we find that the finite-length wires instead host localized states at the wire ends. These end states are not topologically protected, they are four-fold degenerate and split into two Kramers pairs in the presence of potential disorder along the axial direction. However, there is some remnant of the topological protection of the quantum spin Hall edge states in the sense that the end states are fully robust to (time-reversal preserving) angular disorder, as long as the bulk band gap is not closed.

Electron-Hole Interference in an Inverted-Band Semiconductor Bilayer

Electron optics in the solid state promises new functionality in electronics through the possibility of realizing micrometer-sized interferometers, lenses, collimators and beam splitters that manipulate electrons instead of light. Until now, however, such functionality has been demonstrated exclusively in one-dimensional devices, such as in nanotubes, and in graphene-based devices operating with p-n junctions. In this work, we describe a novel mechanism for realizing electron optics in two dimensions. By studying a two-dimensional Fabry-P\'{e}rot interferometer based on a resonant cavity formed in an InAs/GaSb double quantum well using p-n junctions, we establish that electron-hole hybridization in band-inverted systems can facilitate coherent interference. With this discovery, we expand the field of electron optics to encompass materials that exhibit band inversion and hybridization, with the promise to surpass the performance of current state-of-the-art devices.

Electron-hole hybridization in bilayer graphene.

Band structure determines the motion of electrons in a solid, giving rise to exotic phenomena when properly engineered. Drawing an analogy between electrons and photons, artificially designed optical lattices indicate the possibility of a similar band modulation effect in graphene systems. Yet due to the fermionic nature of electrons, modulated electronic systems promise far richer categories of behaviors than those found in optical lattices. Here, we uncovered a strong modulation of electronic states in bilayer graphene subject to periodic potentials. We observed for the first time the hybridization of electron and hole sub-bands, resulting in local band gaps at both primary and secondary charge neutrality points. Such hybridization leads to the formation of flat bands, enabling the study of correlated effects in graphene systems. This work may provide a novel way to manipulate electronic states in layered systems, which is important to both fundamental research and application.

Topological Insulator Superlattices

HgTe/CdTe and InAs/GaSb/AlSb superlattices both exhibit a topological insulator transition. In each case, there is an inversion of the s- and p-band ordering for layer thicknesses above a critical value. The resulting topological phase is a 2D bulk insulator at zero temperature, with edges that conduct massless carriers whose direction of motion is locked to their direction of spin. These 1D edge states exhibit essentially dissipationless transport over coherence lengths greater than one micron, with a quantized conductance of e2/h per edge. When a current passes, opposite spins are separated to the two sample edges, giving rise to the so-called quantum spin Hall effect. Effects such as these may be exploited in future low temperature spintronic devices. The edge states in HgTe/CdTe differ from those in InAs/GaSb/AlSb in several ways, due to the type II band alignment and weaker electron–hole hybridization of the III-V superlattice. The former exhibit a simple exponential decay over thousands of Angstroms, while the latter are more strongly confined to the edge, with an oscillating wave function whose period increases with the edge state momentum. In any calculation, the edge state dispersion and the nature of the wave-function depend strongly on the boundary conditions used. A k · p model is presented using standard boundary conditions for the wave function and its derivative, which yields spin polarized edge states with a finite amplitude at the sample edge. The interaction between states at opposite sample edges is also considered.

Optical tuning of the charge carrier type in the topological regime of InAs/GaSb quantum wells

We study the optical tunability of the charge carrier type in InAs/GaSb double quantum wells with its type-II broken band alignment and inverted band structure. Under constant optical excitation, the majority charge carrier type switches from electron to hole. Within the majority charge carrier type transition, the coexisting minority charge carrier contribution indicates electron-hole hybridization with a nontrivial topological insulating phase. The optical tuning is attributed to the negative photoconductivity of antimonide materials in combination with a persistent charge carrier buildup of photogenerated charges at the surface and substrate side of the device, respectively. Our study of the tuning of an InAs/GaSb double quantum well heterostructure reveals that an electro-optical switching is possible and paves the way to an optical control of the phase diagram of InAs/GaSb topological insulators.

A k · p treatment of edge states in narrow 2D topological insulators, with standard boundary conditions for the wave function and its derivative

For 2D topological insulators with strong electron–hole hybridization, such as HgTe/CdTe quantum wells, the widely used 4 × 4 k · p Hamiltonian based on the first electron and heavy hole sub-bands yields an equal number of physical and spurious solutions, for both the bulk states and the edge states. For symmetric bands and zero wave vector parallel to the sample edge, the mid-gap bulk solutions are identical to the edge solutions. In all cases, the physical edge solution is exponentially localized to the boundary and has been shown previously to satisfy standard boundary conditions for the wave function and its derivative, even in the limit of an infinite wall potential. The same treatment is now extended to the case of narrow sample widths, where for each spin direction, a gap appears in the edge state dispersions. For widths greater than 200 nm, this gap is less than half of the value reported for open boundary conditions, which are called into question because they include a spurious wave function component. The gap in the edge state dispersions is also calculated for weakly hybridized quantum wells such as InAs/GaSb/AlSb. In contrast to the strongly hybridized case, the edge states at the zone center only have pure exponential character when the bands are symmetric and when the sample has certain characteristic width values.

Tuning the charge states in InAs/GaSb or InAs/GaInSb composite quantum wells by persistent photoconductivity

We have experimentally studied the persistent photoconductivity (PPC) in inverted InAs/GaSb and InAs/GaInSb quantum wells, which can be tuned into a bulk-insulating state by electron-hole hybridization. Specifically we tune the bulk band structure and carriers with light-emitting diode (LED) illuminations. The persistent photoconductivity could be negative or positive, depending on the specific doping structure and the illuminating photon energy. Compared to the widely-used electro-statically gating method, our findings provide a more flexible and non-invasive way to control the band structures and charge states in InAs/GaSb and InAs/GaInSb quantum wells (QWs).

Extracting band structure characteristics of GaSb/InAs core-shell nanowires from thermoelectric properties

Nanowires with a GaSb core and an InAs shell (and the inverted structure) are interesting for studies of electron-hole hybridization and interaction effects due to the bulk broken band-gap alignment at the material interface. We have used eight-band $\mathbf{k\cdot p}$ theory together with the envelope function approximation to calculate the band structure of such nanowires. For a fixed core radius, as a function of shell thickness the band structure changes from metallic (for a thick shell) to semiconducting (for a thin shell) with a gap induced by quantum confinement. For intermediate shell thickness, a different gapped band structure can appear, where the gap is induced by hybridization between the valence band in GaSb and the conduction band in InAs. To establish a relationship between the nanowire band structures and signatures in thermoelectrical measurements, we use the calculated energy dispersions as input to the Boltzmann equation and to ballistic transport equations to study the diffusive limit and the ballistic limit, respectively. Our theoretical results provide a guide for experiments, showing how thermoelectric measurements in a gated setup can be used to distinguish between different types of band gaps, or tune the system into a regime with few electrons and few holes, which can be of interest for studies of exciton physics.

Impact of strain on the electronic properties of InAs/GaSb quantum well systems

Electron-hole hybridization in InAs/GaSb double quantum well structures leads to the formation of a mini band gap. We experimentally and theoretically studied the impact of strain on the transport properties of this material system. Thinned samples were mounted to piezo electric elements to exert strain along the [011] and [001] crystal directions. When the Fermi energy is tuned through the mini gap, a dramatic impact on the resistivity at the charge neutrality point is found which depends on the amount of applied external strain. In the electron and hole regimes, strain influences the Landau level structure. By analyzing the intrinsic strain from the epitaxial growth, the external strain from the piezo elements and combining our experimental results with numerical simulations of strained and unstrained quantum wells, we compellingly illustrate why the InAs/GaSb material system is regularly found to be semimetallic.

Band-inverted gaps in InAs/GaSb and GaSb/InAs core-shell nanowires.

The [111]-oriented InAs/GaSb and GaSb/InAs core-shell nanowires have been studied by the 8 × 8 Luttinger-Kohn Hamiltonian to search for non-vanishing fundamental gaps between inverted electron and hole bands. We focus on the variations of the band-inverted fundamental gap, the hybridization gap, and the effective gap with the core radius and shell thickness of the nanowires. The evolutions of all the energy gaps with the structural parameters are shown to be dominantly governed by the effect of quantum confinement. With a fixed core radius, a band-inverted fundamental gap exists only at intermediate shell thicknesses. The maximum band-inverted gap found is ~4.4 meV for GaSb/InAs and ~3.5 meV for InAs/GaSb core-shell nanowires, and for the GaSb/InAs core-shell nanowires the gap persists over a wider range of geometrical parameters. The intrinsic reason for these differences between the two types of nanowires is that in the shell the electron-like states of InAs is more delocalized than the hole-like state of GaSb, while in the core the hole-like state of GaSb is more delocalized than the electron-like state of InAs, and both favor a stronger electron-hole hybridization.

Landau level transitions in InAs/AlSb/GaSb quantum wells**Project supported by the National Natural Science Foundation of China (Grant Nos. 61076092 and 61290303).

The electronic structure of InAs/AlSb/GaSb quantum wells embedded in AlSb barriers and in the presence of a perpendicular magnetic field is studied theoretically within the 14-band k·p approach without making the axial approximation. At zero magnetic field, for a quantum well with a wide InAs layer and a wide GaSb layer, the energy of an electron-like subband can be lower than the energy of hole-like subbands. As the strength of the magnetic field increases, the Landau levels of this electron-like subband grow in energy and intersect the Landau levels of the hole-like subbands. The electron–hole hybridization leads to a series of anti-crossing splittings of the Landau levels. The magnetic field dependence of some dominant transitions is shown with their corresponding initial-states and final-states indicated. The dominant transitions at high fields can be roughly viewed as two spin-split Landau level transitions with many electron–hole hybridization-induced splittings. When the magnetic field is tilted, the electron-like Landau level transitions show additional anti-crossing splittings due to the subband-Landau level coupling.

Strong terahertz absorption in long-period InAs/GaSb type-II superlattices with inverted band structures

We present a theoretical investigation on the terahertz (THz) absorption by long-period InAs/GaSb type-II superlattices (SLs) with inverted band structures. It is found that in such SLs the band inversion causes a significant electron–hole hybridization and a strong THz absorption can be induced by this hybridization. The THz absorption coefficient is even larger than mid-infrared absorption coefficient for short-period InAs/GaSb SLs. Moreover, we find that the strong THz absorption can be further improved and optimized by the proper choice of InAs/GaSb layer widths. The interesting absorption features are well manifested in hybridization gaps and optical transition matrix elements. This study is pertinent to the potential application of long-period inverted InAs/GaSb type-II SLs as high-efficiency THz photodetectors.

Finite conductivity in mesoscopic Hall bars of inverted InAs/GaSb quantum wells

We have studied experimentally the low-temperature conductivity of mesoscopic size InAs/GaSb quantum well Hall bar devices in the inverted regime. Using a pair of electrostatic gates we move the Fermi level into the electron-hole hybridization state, observing a mini gap and Van Hove singularity at its edge. Temperature dependence of the conductivity in the gap shows a residual conductivity, which can be consistently explained by the contributions from the free as well as the hybridized carriers in the presence of impurity scattering, as proposed by Naveh and Laikhtman, [Europhys. Lett. 55, 545 (2001)]. Experimental implications for the stability of proposed quantum spin Hall helical edge states will be discussed.

Intersubband optical transitions in InAs/GaSb quantum wells

The effects of electron-hole hybridization, structural asymmetry with respect to spatial inversion, bulk asymmetry, and the interface Hamiltonian upon the optical absorption of linearly polarized light in broken-gap heterostructures are treated with the use of the eight-band Burt-Foreman envelope function theory and the self-consistent solution of the Schrodinger equation and the Poisson equation. The broken-gap heterostructures, specifically, the AlSb/InAs/GaSb/AlSb quantum wells, grown along the [001] direction offer promise for the fabrication of various devices. The anisotropy induced by the above-listed effects in the dispersion relations of size-quantization subbands and in optical matrix elements is established. The bulk asymmetry and the interface Hamiltonian modify the selection rules for intersubband transitions on the exposure of the structures to linearly polarized light. As a result, the initially forbidden spin-flip transitions are allowed. This brings about a large number of peaks in the dependence of the absorption coefficient on the photon energy, if the light polarization vector is directed along the axis of growth of the structure. If the light polarization vector is in the plane of the structure, the bulk asymmetry and the interface Hamiltonian induce strong longitudinal anisotropy of the absorption due to the hybridization of states with oppositely oriented spins. These effects are comprehensively studied for optical transitions involving hybridized electron-hole states in quantum wells grown on InAs.

Spin states in InAs/AlSb/GaSb semiconductor quantum wells

We investigate theoretically the spin states in InAs/AlSb/GaSb broken-gap quantum wells by solving the Kane model and the Poisson equation self-consistently. The spin states in InAs/AlSb/GaSb quantum wells are quite different from those obtained by the single-band Rashba model due to the electron-hole hybridization. The Rashba spin splitting of the lowest conduction subband shows an oscillating behavior. The D'yakonov-Perel' spin-relaxation time shows several peaks with increasing the Fermi wave vector. By inserting an AlSb barrier between the InAs and GaSb layers, the hybridization can be greatly reduced. Consequently, the spin orientation, the spin splitting, and the D'yakonov-Perel' spin-relaxation time can be tuned significantly by changing the thickness of the AlSb barrier.

Optical absorption of polarized light in InAs/GaSb quantum wells

Using an eight-band k ⋅ p model Hamiltonian with the Burt–Foreman envelope function theory, we have investigated the optical absorption of both linearly and circularly polarized light, as well as related phenomena in InAs/GaSb broken-gap quantum wells grown along the [0 0 1] direction, with emphasis on the effects of electron–hole hybridization and the various symmetry-breaking mechanisms such as structural inversion asymmetry, bulk inversion asymmetry and interface Hamiltonian. The optical matrix elements exhibit unusual angular dependence in close connection with the spin-flip transitions which are originally forbidden. The spin split of the 2e subband results in two profound absorption peaks for the 1hh–2e transition for both linearly polarized and circularly polarized light. A large lateral optical anisotropy appears in the absorption coefficient of linearly polarized light, which can reach almost 100% with a reducing thickness of the quantum well. For the absorption of circularly polarized light, we found a large enhancement of electron spin polarization in the upper 2e subband, which was generally considered as forbidden if the polarization is along the direction perpendicular to the plane-of-light incidence.

Temperature-dependent cyclotron resonance in a hybridized electron–hole system in InAs/GaSb heterostructures

Cyclotron resonance measurements are performed as a function of temperature on InAs/GaSb quantum well structures. The effects of electron–hole hybridization on cyclotron resonance are found to be strongly temperature dependent. As the temperature increases, the cyclotron resonance spectra narrow dramatically and multiple splittings due to electron–hole hybridizations disappear. This phenomenon is believed to be due to the classical Coulomb interaction between electrons with different cyclotron effective masses. The influence of the minigap formed due to electron–hole coupling is shown to be particularly important in narrower gap structures where strong thermal excitation of carriers is observed across the minigap. The influence of the minigap on the system is confirmed by the application of large parallel magnetic fields which decouple the electron and hole bands.