Quantum-well States Research Articles

Bringing ultimate depth to scanning tunnelling microscopy: deep subsurface vision of buried nano-objects in metals.

A method for subsurface visualization and characterization of hidden subsurface nano-structures based on scanning tunelling microscopy/spectroscopy (STM/STS) has been developed. Nano-objects buried under a metal surface up to several tens of nanometers can be visualized through the metal surface and characterized with STM without destroying the sample. This non-destructive method exploits quantum well (QW) states formed by partial electron confinement between the surface and buried nano-objects. The specificity of STM allows for nano-objects to be singled out and easily accessed. Their burial depth can be determined by analysing the oscillatory behaviour of the electron density at the surface of the sample, while the spatial distribution of electron density can give additional information about their size and shape. The proof of concept was demonstrated with different materials such as Cu, Fe, and W in which the nanoclusters of Ar, H, Fe and Co were buried. For each material, the maximal depth of subsurface visualisation is determined by the material parameters and ranges from several nanometers to several tens of nanometers. To demonstrate the ultimate depth of subsurface STM-vision as the principal limit of our approach, the system of Ar nanoclusters embedded into a single-crystalline Cu(110) matrix has been chosen since it represents the best combination of the mean free path, smooth interface and inner electron focusing. With this system we experimentally demonstrated that Ar nanoclusters of several nanometers large buried as deep as 80 nm can still be detected, characterized and imaged. The ultimate depth of this ability is estimated to be 110 nm. This approach using QW states paves the way for enhanced 3D characterization of nanostructures hidden well below a metallic surface.

Polarization-dependent electronic structure of Ag quantum well states on the MoS2 (0001) surface using ARPES and DFT studies

The electronic band structure of clean and Ag-induced quantum well states on the ${\mathrm{MoS}}_{2}$(0001) surface has been investigated using polarization-dependent angle-resolved photoemission spectroscopy (ARPES) along with first-principle-based density functional theory (DFT) calculations. Using selective linearly polarized light, the orbital symmetry and $k$ dispersion of the surface localized electronic states have been unambiguously determined. The quantum well states (QWS) originating from the Ag ${p}_{z}$ orbitals are confined within the Ag overlayer, while the quantum well resonance states (QWRS) are hybridized with substrate Mo $4{d}_{{z}^{2}}$ and S $3{p}_{z}$ orbitals. The photon energy dependence of the dispersion characteristics confirms the two-dimensional (2D) nature of these quantum states while their momentum dependence is a consequence of the finite lateral coherence length of the electrons. Our ARPES experiments using incident circularly polarized light on ${\mathrm{MoS}}_{2}$(0001) surface show circular dichroism effects (CD-ARPES), similar to recent studies where it is used to probe the initial state orbital angular momentum or the Berry curvature. While the QWS on the Ag overlayer does not exhibit any intensity asymmetry with the helicity of the incident light, the Ag QWRS show circular dichroism characteristics. The observed circular dichroism from the QWRS is attributed to the hybridization of these quantum states to the substrate states. We compare our ARPES results with the calculated orbital projected band structure to obtain a microscopic insight into the electronic behavior, which is critically important for manipulating wave functions for potential device applications.

Appearance of Ferromagnetism in Pt(100) Ultrathin Films Originated from Quantum-well States

Ferromagnetism was observed in a Pt(100) ultrathin film deposited on a SrTiO3(100) substrate. The ferromagnetism, which appears in films with thicknesses of 2.2-4.4 nm, periodically changes with a period of approximately 1 nm (5-6 monolayers) depending on the film thickness. This is consistent with the period derived from the quantum-well states formed in the thin film. X-ray magnetic circular dichroism measurements show the evidence of appearance of intrinsic ferromagnetism in Pt(100) ultra-thin film. In addition, present results suggest a possibility that the orbital magnetic moment of pure Pt is much smaller than that of the Pt/ferromagnetic multilayer system. These results will provide a potential new mechanism for origin of the large magnetic anisotropy in Pt components.

Epitaxial growth, magnetoresistance, and electronic band structure of GdSb magnetic semimetal films

Motivated by observations of extreme magnetoresistance (XMR) in bulk crystals of rare-earth monopnictide (RE-V) compounds and emerging applications in novel spintronic and plasmonic devices based on thin-film semimetals, we have investigated the electronic band structure and transport behavior of epitaxial GdSb thin films grown on III-V semiconductor surfaces. The ${\mathrm{Gd}}^{3+}$ ion in GdSb has a high spin $S=7/2$ and no orbital angular momentum, serving as a model system for studying the effects of antiferromagnetic order and strong exchange coupling on the resulting Fermi surface and magnetotransport properties of RE-Vs. We present a surface and structural characterization study mapping the optimal synthesis window of thin epitaxial GdSb films grown on III-V lattice-matched buffer layers via molecular-beam epitaxy. To determine the factors limiting XMR in RE-V thin films and provide a benchmark for band-structure predictions of topological phases of RE-Vs, the electronic band structure of GdSb thin films is studied, comparing carrier densities extracted from magnetotransport, angle-resolved photoemission spectroscopy (ARPES), and density-functional theory (DFT) calculations. ARPES shows a hole-carrier rich, topologically trivial, semimetallic band structure close to complete electron-hole compensation, with quantum confinement effects in the thin films observed through the presence of quantum-well states. DFT-predicted Fermi wave vectors are in excellent agreement with values obtained from quantum oscillations observed in magnetic field-dependent resistivity measurements. An electron-rich Hall coefficient is measured despite the higher hole-carrier density, attributed to the higher electron Hall mobility. The carrier mobilities are limited by surface and interface scattering, resulting in lower magnetoresistance than that measured for bulk crystals.

Characterization of helical states in semiconductor quantum wells using quantum information quantities

The information content of one-electron bulk and edge states in semiconductor quantum wells is calculated in the inverted regime, where edge states, topologically protected, are responsible for the conduction in Spin Quantum Hall effect experiments. To study the information content of these states we first calculate realistic two dimensional one-electron states, solving first the eight-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian to obtain the bulk states and then a four band effective Hamiltonian to obtain the edge states. The behavior of information-like quantities, as a function of the different parameters that define the quantum well, is analyzed. The results presented show that the helical edge states can be singled out using different quantities that characterize the rich phenomenology of these states.

Nearly Ideal Two-Dimensional Electron Gas Hosted by Multiple Quantized Kronig-Penney States Observed in Few-Layer InSe.

A theoretical ideal two-dimensional electron gas (2DEG) was characterized by a flat density of states independent of energy. Compared with conventional two-dimensional free-electron systems in semiconductor heterojunctions and noble metal surfaces, we report here the achievement of ideal 2DEG with multiple quantized states in few-layer InSe films. The multiple quantum well states (QWSs) in few-layer InSe films are found, and the number of QWSs is strictly equal to the number of atomic layers. The multiple stair-like DOS as well as multiple bands with parabolic dispersion both characterize ideal 2DEG features in these QWSs. Density functional theory calculations and numerical simulations based on quasi-bounded square potential wells described as the Kronig-Penney model provide a consistent explanation of 2DEG in the QWSs. Our work demonstrates that 2D van der Waals materials are ideal systems for realizing 2DEG hosted by multiple quantized Kronig-Penney states, and the semiconducting nature of the material provides a better chance for construction of high-performance electronic devices utilizing these states, for example, superlattice devices with negative differential resistance.

High quality Mg(0001) films grown on Si(111)[formula omitted]-B surface at room temperature

Rotational epitaxy of Mg(0001) film on the Si(111) surface has been demonstrated at room temperature using a Si(111)3×3-B surface reconstruction as a template. The 3×3-B reconstruction, which spontaneously forms on the surface of a heavily-doped Si(111) substrate upon annealing, prevents the formation of magnesium silicide and provides the proper orientation of the film at which the lattice mismatch is lowered down. The film has excellent crystal quality as revealed by diffraction, scanning tunneling microscopy at low temperature (60 K) and photoelectron spectroscopy methods. Density functional theory calculations prove the hexagonal close-packed structure typical for the bulk Mg. The film demonstrates a pronounced quantum-well states effect. The energy position of the surface state is close to the relaxed bulk-like position at early stages of growth, which indicates the smaller interaction of the film with the substrate compared to growth on the bare Si(111).

Linewidths and energy shifts of electron-impurity resonant states in quantum wells with infinite barriers

The linewidths and the energy shifts of the resonant states of the impurity electron in GaAs-based quantum wells (QWs) with infinite barriers are calculated. The two-dimensional Schr\"{o}dinger equation for the charge impurity in the QW is solved by the developed finite-difference method combined with the complex-scaling technique. A dependence of the linewidths and energy shifts on the QW width for the impurity localized in the center of QW is studied. The calculated results extend and improve theoretical estimations of these quantities in the GaAs-based QW by Monozon and Schmelcher [Phys. Rev. B 71, 085302 (2005)]. In particular, in agreement with their studies we obtain that resonant states originating from the second quantum-confinement subband have negligibly small linewidths. In contrast to previous estimations, we show that for the QW widths of the order of the impurity's Bohr radius the linewidths of resonant states associated to the third quantum-confinement subband linearly depend on the thickness of the QW. We show how the previous theoretical predictions can be improved for such QW widths. We also calculate linewidths for the case when the electron impurity is localized away from the center of the QW.

Dimensionality of mobile electrons at x-ray-irradiated LaAlO3/SrTiO3 interfaces

Electronic structure of LaAlO3/SrTiO3 (LAO/STO) samples, grown at low oxygen pressure and post-annealed ex situ, was investigated by soft-x-ray ARPES focussing on the Fermi momentum (k F) of the mobile electron system (MES). X-ray irradiation of these samples at temperatures below 100 K creates oxygen vacancies (VOs) injecting Ti t 2g-electrons into the MES. At this temperature the oxygen out-diffusion is suppressed, and the VOs should appear mostly in the top STO layer. The x-ray generated MES demonstrates, however, a pronounced three-dimensional (3D) behavior as evidenced by variations of its experimental k F over different Brillouin zones. Identical to bare STO, this behavior indicates an unexpectedly large extension of the x-ray generated MES into the STO depth. The intrinsic MES in the standard LAO/STO samples annealed in situ, in contrast, demonstrates purely two-dimensional (2D) behaviour. The relevance of our ARPES data analysis is supported by model calculations to compare the intensity vs gradient methods of the k F determination as a function of the energy resolution ratio to the bandwidth. Based on self-interaction-corrected DFT calculations of the MES induced by VOs at the interface and in STO bulk, we discuss possible scenarios of the puzzling 3D-ity. It may involve either a dense ladder of quantum-well states formed in a long-range interfacial potential or, more likely, x-ray-induced bulk metallicity in STO accessed in the ARPES experiment through a short-range interfacial barrier. The mechanism of this metallicity may involve remnant VOs and photoconductivity-induced metallic states in the STO bulk, and even more exotic mechanisms such as x-ray induced formation of Frenkel pairs.

Giant and tunable Rashba spin splitting in MoS2/Bi2Te3 heterostructures

The study of the spin-orbit coupling (SOC) effect is an active research field in physics and it is of great interest for materials with large Rashba spin splitting (RSS) in spintronics applications. In this report, based on first-principles calculations, we propose the heterostructure of MoS2/Bi2Te3 with giant RSS duo to the lack of spatial inversion symmetry and the intrinsic electric field perpendicular to the heterostructure. Furthermore, it is found that the electronic and RSS can be tuned effectively by layers of MoS2 and Bi2Te3. When the Bi2Te3 thickness is less than 2QL, these MoS2/Bi2Te3 heterojunction systems exhibit semiconductor properties. The magnitude of the RSS in these MoS2/Bi2Te3 heterojunctions changes with the thickness, and the largest band splitting is found in the (MoS2)1(Bi2Te3)2 heterostructure with a Rashba coefficient of ~2.5 eV Å, which is a very large value among two-dimensional (2D) materials. While the interlayer distance and charge transfer remain stable at about 3.5 Å and 0.1 e, respectively. Through layer-projected band structure analysis, it is proven that the electronic states of these quantum well states (QWSs) are mainly contributed by Bi2Te3, while the MoS2 layer only plays an inductive role and does not contribute to the QWSs electrons. In addition, strain only plays a minor role in the Rashba effect in the MoS2/Bi2Te3 heterojunction, which is mainly caused by the breaking of the spatial inversion symmetry. The giant and tunable Rashba-type SOC of the MoS2/Bi2Te3 heterostructure suggests that it is a type of promising materials for spintronic applications.

Electron Transport in Double-Barrier Semiconductor Heterostructures for Thermionic Cooling

We investigate electron transport in asymmetric double-barrier ($\mathrm{Al},\mathrm{Ga})\mathrm{As}/\mathrm{Ga}\mathrm{As}$ thermionic cooling heterostructures. Measurements of temperature-dependent current-voltage characteristics confirm that the dominant electron transport is a sequential process of resonant tunneling injection into and thermionic emission from the quantum-well (QW) cooling layer. The thermal activation energy of the current is found to be strongly dependent on the bias voltage. Furthermore, instead of showing a simple thermal activation behavior, the current exhibits rather complicated temperature and voltage dependence, particularly when the thermionic emission barrier is low. To establish a quantitative understanding, we develop an intuitive analytical model for sequential electron transport that explicitly takes into account scattering effects in the thermionic emission process from the two-dimensional QW states to the three-dimensional above-barrier states. The observed temperature-dependent sequential current is well explained by the present theory.

Scaling law for Rashba-type spin splitting in quantum-well films

We use laser-based spin- and angle-resolved photoemission spectroscopy (laser-SARPES) with high resolution and experimentally determine, for the first time, the Rashba parameters of quantum-well states (QWSs) systematically changing with the film thickness and the quantum numbers, through the observation of the Ag films grown on an Au(111) substrate. The data are very well reproduced by the theoretical calculations based on the density functional theory. Most importantly, we find a scaling law for the Rashba parameter (${\ensuremath{\alpha}}_{\mathrm{R}}$) that the magnitude of ${\ensuremath{\alpha}}_{\mathrm{R}}$ is scaled by the charge density at the interface and the spin-orbit coupling ratio between the film and the substrate, and it is expressed by a single straight line regardless of the film thickness and the quantum numbers. The new finding not only is crucial to understand the Rashba effect in QWSs but also gives a foundation of film growth engineering to fine-tune the spin splitting in 2D heterostructure systems.

Higher-order topological insulator in cubic semiconductor quantum wells

The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion. We show that the appearance of corner states does not depend solely on the crystallographic orientation of the meeting edges, but also on the growth orientation of the quantum well. Our theoretical results significantly extend the application potential of topological quantum wells based on IV, II–VI and III–V semiconductors with diamond or zinc-blende structures.

Equally Spaced Quantum States in van der Waals Epitaxy-Grown Nanoislands.

Pursuing the confinement of linearly dispersive relativistic Fermions is of interest in both fundamental physics and potential applications. Here, we report strong STM evidence for the equally spaced, strikingly sharp, and densely distributed quantum well states (QWSs) near Fermi energy in Pb(111) nanoislands, van der Waals epitaxially grown on graphitized 6H-SiC(0001). The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially "simulate" the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry-Pérot fittings based on the relativistic Fermions. First-principles calculations further reveal that the spin-orbit coupling strengthens the relativistic nature of electrons near Fermi energy. Our finding uncovers the unique equally spaced quantum states in electronic systems beyond Landau levels and may inspire future studies on confined relativistic quasiparticles in flourishing topological materials and applications in structurally simpler quantum cascade laser.

Direct Visualization and Manipulation of Tunable Quantum Well State in Semiconducting Nb2SiTe4.

Quantum well states (QWSs) can form at the surface or interfaces of materials with confinement potential. They have broad applications in electronic and optical devices such as high mobility electron transistor, photodetector, and quantum well laser. The properties of the QWSs are usually the key factors for the performance of the devices. However, direct visualization and manipulation of such states are, in general, challenging. In this work, by using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy/spectroscopy (STM/STS), we directly probe the QWSs generated on the vacuum interface of a narrow band gap semiconductor Nb2SiTe4. Interestingly, the position and splitting of QWSs could be easily manipulated via potassium (K) dosage onto the sample surface. Our results suggest Nb2SiTe4 to be an intriguing semiconductor system to study and engineer the QWSs, which has great potential in device applications.

The effects of external fields on double GaAs/AlGaAs quantum well with Manning potential

In this paper, we calculated the electronic and optical absorption coefficient of the Manning-like double quantum well under the external applied electric and magnetic fields. To calculate the linear and third-order nonlinear optical absorption coefficients is used two-level approach in the density matrix expansion. The findings show that the electronic structure can be adjusted by changing the well and barrier widths, the well depth, the coupling between the wells as well as applied external field intensities. In addition, direct and indirect exciton states in asymmetric double quantum wells with Manning-like potential under electric field are compared with experimental studies. From the obtained results, it is concluded that the Manning-like potential is an excellent strategy for modeling electronic states in asymmetric double quantum wells with steep potential barriers and also the Manning-like potential allows modeling interdiffusion effects at the interfaces of multiple heterostructures.

Extremely low-energy ARPES of quantum well states in cubic-GaN/AlN and GaAs/AlGaAs heterostructures

Quantum well (QW) heterostructures have been extensively used for the realization of a wide range of optical and electronic devices. Exploiting their potential for further improvement and development requires a fundamental understanding of their electronic structure. So far, the most commonly used experimental techniques for this purpose have been all-optical spectroscopy methods that, however, are generally averaging in momentum space. Additional information can be gained by angle-resolved photoelectron spectroscopy (ARPES), which measures the electronic structure with momentum resolution. Here we report on the use of extremely low-energy ARPES (photon energy ~ 7 eV) to increase depth sensitivity and access buried QW states, located at 3 nm and 6 nm below the surface of cubic-GaN/AlN and GaAs/AlGaAs heterostructures, respectively. We find that the QW states in cubic-GaN/AlN can indeed be observed, but not their energy dispersion, because of the high surface roughness. The GaAs/AlGaAs QW states, on the other hand, are buried too deep to be detected by extremely low-energy ARPES. Since the sample surface is much flatter, the ARPES spectra of the GaAs/AlGaAs show distinct features in momentum space, which can be reconducted to the band structure of the topmost surface layer of the QW structure. Our results provide important information about the samples’ properties required to perform extremely low-energy ARPES experiments on electronic states buried in semiconductor heterostructures.

Momentum and energy dissipation of hot electrons in a Pb/Ag(111) quantum well system

The band structure of multilayer systems plays a crucial role for the ultrafast hot carrier dynamics at interfaces. Here, we study the energy- and momentum-dependent quasiparticle lifetimes of excited electrons in a highly ordered Pb monolayer film on Ag(111) prior and after the adsorption of a monolayer of 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA). Using time-resolved two-photon momentum microscopy with femtosecond visible light pulses, we show that the electron dynamics of the Pb/Ag(111) quantum well system is largely dominated by two types of scattering processes: (i) isotropic intraband scattering processes within the quantum well state (QWS) and (ii) isotropic interband scattering processes from the ${p}_{z}$-like QWS into the Pb ${p}_{x/y}$ band. In the latter case, the Pb QWS acts as an electron source for the momentum space refilling process of the Pb ${p}_{x/y}$ band. This conclusion is confirmed by the modification of the band structure and the quasiparticle dynamics of the Pb/Ag(111) bilayer film after the adsorption of PTCDA. We find both an adsorption-induced suppression of the QWS itself as well as of the refilling process into the Pb ${p}_{x/y}$ band. Our study hence demonstrates the isotropic nature of the momentum-dependent scattering processes of metallic bilayer systems and uncovers a new possibility to selectively tune and control scattering processes occurring in quantum (well) materials by the adsorption of organic molecules.

Pb/Bi heterostructure as a versatile platform to realize topological superconductivity

Abstract Realization of topological superconductors (TSCs) hosting Majorana fermions is an exciting challenge in materials science. Majorana fermions are predicted to emerge at vortex cores of two-dimensional (2D) TSCs and at both ends of one-dimensional (1D) TSCs; these two types of TSCs have been explored independently in different materials. Here, a system which has a potential to access both 1D and 2D TSCs in a single platform, Pb(111)/Bi(111) heterostructure, is proposed. One to twenty bilayers (BLs) of Bi(111) ultra-thin films are epitaxially fabricated on TlBiSe$_2$, and an intriguing evolution of electronic states upon variation of Bi-layer thickness is revealed by angle-resolved photoemission spectroscopy. The metallic quantum-well states at 1–2BLs are found to turn into the Rashba states at 5–20BLs, via the semiconducting states at 3BL. Fabrication of a Pb(111) film on 20BL Bi(111) enables observation of the proximity-induced superconductivity in Bi(111) as evident from a 1 meV energy gap at 5 K; these energy and temperature scales are considerably larger than those of Rashba superconductors. The Pb/Bi heterostructure serves as a versatile platform to study the interplay among proximity-induced superconductivity, band structure, and topology.

Theoretical proposals to measure resonator-induced modifications of the electronic ground state in doped quantum wells

Recent interest in the physics of non-perturbative light-matter coupling led to the development of solid-state cavity quantum electrodynamics setups in which the interaction energies are comparable with the bare ones. In such a regime the ground state of the coupled system becomes interaction-dependent and is predicted to contain a population of virtual excitations which, notwithstanding having been object of many investigations, remain still unobserved. In this paper we investigate how virtual electronic excitations in quantum wells modify the ground-state charge distribution, and propose two methods to measure such a cavity-induced perturbation. The first approach we consider is based on spectroscopic mapping of the electronic population at a specific location in the quantum well using localised defect states. The second approach exploits instead the photonic equivalent of a Kelvin probe to measure the average change distribution across the quantum well. We find both effects observable with present-day or near-future technology. Our results thus provide a route toward a demonstration of cavity-induced modulation of ground-state electronic properties.