One-dimensional Hole Gas Research Articles

Two-band description of the strong ‘spin’-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire

The low-energy effective Hamiltonian of the strong ‘spin’-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire in the presence of a strong magnetic field is studied both numerically and analytically. Basing on the Luttinger–Kohn Hamiltonian in the spherical approximation, we show this strong ‘spin’-orbit coupled one-dimensional hole gas can be accurately described by an effective two-band Hamiltonian , as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic field dependent expressions of the ‘spin’-orbit coupling and the effective g-factor are given. When the magnetic field is applied in an arbitrary direction, the two-band Hamiltonian description is still a good approximation.

Electrical manipulation of a hole ‘spin’–orbit qubit in nanowire quantum dot: The nontrivial magnetic field effects

Strong ‘spin’–orbit coupled one-dimensional hole gas is achievable in a Ge nanowire in the presence of a strong magnetic field. The strong magnetic field lifts the two-fold degeneracy in the hole subband dispersions, so that the effective low-energy subband dispersion exhibits strong spin–orbit coupling. Here, we study the electrical spin manipulation in a Ge nanowire quantum dot for both the lowest and second lowest hole subband dispersions. Using a finite square well to model the quantum dot confining potential, we calculate exactly the level splitting of the spin–orbit qubit and the Rabi frequency in the electric-dipole spin resonance. The spin–orbit coupling modulated longitudinal g-factor g so is not only non-vanishing but also magnetic field dependent. Moreover, the spin–orbit couplings of the lowest and second lowest subband dispersions have opposite magnetic dependences, so that the results for these two subband dispersions are totally different. It should be noticed that we focus only on the properties of the hole ‘spin’ instead of the real hole spin.

Searching strong ‘spin’-orbit coupled one-dimensional hole gas in strong magnetic fields

We show that a strong ‘spin’-orbit coupled one-dimensional hole gas is achievable via applying a strong magnetic field to the original two-fold degenerate (spin degeneracy) hole gas confined in a cylindrical Ge nanowire. Both strong longitudinal and strong transverse magnetic fields are feasible to achieve this goal. Based on quasi-degenerate perturbation calculations, we show the induced low-energy subband dispersion of the hole gas can be written as , a form exactly the same as that of the electron gas in the conduction band. Here the Pauli matrices σ z,x represent a pseudo spin (or ‘spin’), because the real spin degree of freedom has been split off from the subband dispersions by the strong magnetic field. Also, for a moderate nanowire radius R = 10 nm, the induced effective hole mass and the ‘spin’-orbit coupling α (0.35 ∼ 0.8 eV Å) have a small magnetic field dependence in the studied magnetic field interval 1 < B < 15 T, while the effective g-factor of the hole ‘spin’ only has a small magnetic field dependence in the large field region.

Low-energy subband wave-functions and effective g-factor of one-dimensional hole gas

One-dimensional (1D) hole gas confined in a cylindrical Ge nanowire has potential applications in quantum information technologies. Here, we analytically study the low-energy properties of this 1D hole gas. The subbands of the hole gas are two-fold degenerate. The low-energy subband wave-functions are obtained exactly, and the degenerate pairs are related to each other via a combination of the time-reversal and the spin-rotation transformations. In evaluating the effective g-factor of these low-energy subbands, the orbital effects of the magnetic field are shown to contribute as strongly as the Zeeman term. Also, near the center of the k z space, there is a sharp dip or a sharp peak in the effective g-factor. At the site k z = 0, the longitudinal g-factor g l is much less than the transverse g-factor g t for the lowest subband, while away from the site k z = 0, g l can be comparable to g t.

Gate Tunable Hole Charge Qubit Formed in a Ge/Si Nanowire Double Quantum Dot Coupled to Microwave Photons.

A controllable and coherent light-matter interface is an essential element for a scalable quantum information processor. Strong coupling to an on-chip cavity has been accomplished in various electron quantum dot systems, but rarely explored in the hole systems. Here we demonstrate a hybrid architecture comprising a microwave transmission line resonator controllably coupled to a hole charge qubit formed in a Ge/Si core/shell nanowire (NW), which is a natural one-dimensional hole gas with a strong spin-orbit interaction (SOI) and lack of nuclear spin scattering, potentially enabling fast spin manipulation by electric manners and long coherence times. The charge qubit is established in a double quantum dot defined by local electrical gates. Qubit transition energy can be independently tuned by the electrochemical potential difference and the tunnel coupling between the adjacent dots, opening transverse (σ x) and longitudinal (σ z) degrees of freedom for qubit operation and interaction. As the qubit energy is swept across the photon level, the coupling with resonator is thus switched on and off, as detected by resonator transmission spectroscopy. The observed resonance dynamics is replicated by a complete quantum numerical simulation considering an efficient charge dipole-photon coupling with a strength up to 2π × 55 MHz, yielding an estimation of the spin-resonator coupling rate through SOI to be about 10 MHz. The results inspire the future researches on the coherent hole-photon interaction in Ge/Si nanowires.

Spin-Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas.

Low dimensional semiconducting structures with strong spin–orbit interaction (SOI) and induced superconductivity attracted great interest in the search for topological superconductors. Both the strong SOI and hard superconducting gap are directly related to the topological protection of the predicted Majorana bound states. Here we explore the one-dimensional hole gas in germanium silicon (Ge–Si) core–shell nanowires (NWs) as a new material candidate for creating a topological superconductor. Fitting multiple Andreev reflection measurements shows that the NW has two transport channels only, underlining its one-dimensionality. Furthermore, we find anisotropy of the Landé g-factor that, combined with band structure calculations, provides us qualitative evidence for the direct Rashba SOI and a strong orbital effect of the magnetic field. Finally, a hard superconducting gap is found in the tunneling regime and the open regime, where we use the Kondo peak as a new tool to gauge the quality of the superconducting gap.

Vertical Ge/Si Core/Shell Nanowire Junctionless Transistor.

Vertical junctionless transistors with a gate-all-around (GAA) structure based on Ge/Si core/shell nanowires epitaxially grown and integrated on a ⟨111⟩ Si substrate were fabricated and analyzed. Because of efficient gate coupling in the nanowire-GAA transistor structure and the high density one-dimensional hole gas formed in the Ge nanowire core, excellent P-type transistor behaviors with Ion of 750 μA/μm were obtained at a moderate gate length of 544 nm with minimal short-channel effects. The experimental data can be quantitatively modeled by a GAA junctionless transistor model with few fitting parameters, suggesting the nanowire transistors can be fabricated reliably without introducing additional factors that can degrade device performance. Devices with different gate lengths were readily obtained by tuning the thickness of an etching mask film. Analysis of the histogram of different devices yielded a single dominate peak in device parameter distribution, indicating excellent uniformity and high confidence of single nanowire operation. Using two vertical nanowire junctionless transistors, a PMOS-logic inverter with near rail-to-rail output voltage was demonstrated, and device matching in the logic can be conveniently obtained by controlling the number of nanowires employed in different devices rather than modifying device geometry. These studies show that junctionless transistors based on vertical Ge/Si core/shell nanowires can be fabricated in a controlled fashion with excellent performance and may be used in future hybrid, high-performance circuits where bottom-up grown nanowire devices with different functionalities can be directly integrated with an existing Si platform.

Enhanced efficiency of p-type doping by band-offset effect in wurtzite and zinc-blende GaAs/InAs-core-shell nanowires

Using first principles calculation based on density-functional theory, we investigated p-type electronic structures and the doping mechanism in wurtzite (WZ) and zinc-blende (ZB) GaAs/InAs-core-shell nanowires (NWs) along the [0001] and [111] directions, respectively. Comparing the doping in WZ and ZB core-shell NWs, we found it is easier and more stable to realize dopant in WZ NWs. Due to the type I band-offset, p-type doping in the GaAs-core of GaAscore/InAsshell for both WZ and ZB NWs makes that the valence band-edge electrons in the InAs-shell can spontaneously transfer to the impurity states, forming one-dimensional hole gas. In particular, this process accompanies with a reverse transition in WZ core-shell nanowire due to the existence of antibonding and bonding states.

The Role of Atomic Hydrogen in Ge/Si Core–Shell Nanowires

We investigate the role of atomic hydrogen in Ge/Si core–shell nanowires with first-principles calculations and present that the hole doping in the Ge/Si heterointerface is achievable through interstitial hydrogen mediated remote doping. This atomic hydrogen induced hole doping could generate one-dimensional hole gas in Ge/Si core–shell nanowires. Hydrogen prefers to be incorporated in the Si shell due to the lattice strain effect. As the charge transition energy level of the interstitial hydrogen in Si is lower than the valence band maximum of the Ge band, the electrons in the Ge core prefer to move toward the Si shell and become trapped by the interstitial hydrogen. This unique hydrogen energy level in the Ge/Si heterostructure between the Ge and Si valence band edges drives the electron transfer from the Ge core and induces holes states in the Ge core through remote hole doping. We also perform a quantum transport simulation and show that a high conductive hole channel in the Ge core can be generated when hydrogen is incorporated into the Si shell. Our investigation on the role of atomic hydrogen in the Ge/Si core–shell nanowire opens the possibility of manipulating the hole concentration by tuning the process conditions.

Band-offset effect on localization of carriers and p-type doping of InAs/GaAs core–shell nanowires

The electronic properties and p-type doping mechanism of InAs/GaAs core–shell nanowires are studied by using the first-principles calculations within density-functional theory. The core–shell structure of nanowires creates one-dimensional band offset at the InAs/GaAs interface. The magnitude of band offset depends on the sizes of core and shell. We find that a highly efficient p-type doping in InAs/GaAs core–shell nanowires can be achieved by introducing the Cd-impurity into the GaAs shell, utilizing the band-offset effect. It is because the valence-band electrons can spontaneously transfer to the Cd-impurity level, resulting in one-dimensional hole gas in the InAs core of nanowires.

Enhanced doping efficiency of the remotely p-doped InAs/InP core-shell nanowires: A first principles study

We investigated the electronic properties of Zn-doped InAs/InP core-shell nanowires by using first principles calculations. It is found that efficient p-type doping of InAs nanowires can be achieved by remotely doping the InP shell. The activation energy of Zn dopant is zero since the valence band offset and one-dimensional hole gas is created in the InAs core without thermal activation. Moreover, the separation between the free carrier and ionized dopant may result in higher carrier mobility due to the reduced scattering. Our results provide insights for the efficient p-type doping of nanodevices based on III−V nanowires.

Charge localization in [1 1 2] Si/Ge and Ge/Si core–shell nanowires

We report a first-principles study of Ge/Si and Si/Ge core/shell nanowires (NWs) along the [1 1 2] direction with a diameter of ∼20 Å using density-functional theory. Our results show that for both NW structures the band gaps are indirect and are significantly larger than the gaps of the bulk crystalline Si and Ge. The quantum well confinement effect in these NWs is found to be modified by a type II lineup of band structures. Moreover, the carriers on the conduction band minimum are strongly localized in the Si region while the carriers on the valence band maximum are located mainly in the Ge region. The charge separation and localization characters make the NWs good candidates for nanochannels in field effect devices, solar cells with higher efficiency and high mobility heterostructures due to the spatial separation of one-dimensional electron gas and one-dimensional hole gas.

Multiple subband crossing in a one-dimensional hole gas with enhanced g-factors

We have measured the transport properties of one-dimensional ballistic constrictions defined in a two-dimensional hole gas. The conductance quantization of the constrictions switches between even and odd multiples of e 2/ h as a function of a parallel magnetic field, as spin-splitting causes the subbands of the 1D channel to cross repeatedly. The in-plane g-factors of the 1D subbands are measured from the low field data. We find them to increase as the number of occupied 1D subbands decreases and attribute this enhancement of the g-factor to Coulomb interactions. The quantization at high fields shows that the subbands have crossed four times; in this regime the system is highly magnetized and exchange effects should be of particular importance.

Enhanced g factors of a one-dimensional hole gas with quantized conductance

We have measured the transport properties of quasi-one-dimensional ballistic constrictions defined on a high-mobility two-dimensional hole gas. The conductance quantization of the constrictions is changed from even to odd multiples of ${\mathrm{e}}^{2}$/h as a function of the magnetic field in the plane of the heterojunction, as spin splitting causes the subbands of the one-dimensional (1D) channel to cross. We calculate the in-plane g factors of the 1D subbands using the magnetic fields at which crossing occurs and find that they increase as the number of occupied 1D subbands decreases. We attribute this enhancement of the g factor to Coulomb interactions.

Influence of dimensionality and statistics on the Coulomb coupling between electron gases or electron-and-hole gases.

Mutual Coulomb scattering between a one-dimensional electron gas (1DEG) and an i-dimensional electron gas (i=1,2,3), separated by a finite distance l, or a one-dimensional hole gas is considered. The gases can have the same or different statistics. The momentum and energy relaxation frequencies are evaluated using a drifted Fermi-Dirac distribution function and taking into account dynamical screening. For a degenerate 1DEG the main contribution to these frequencies comes from processes involving small momentum changes and backscattering. The screening of the first process can be significant even for a weakly nonideal 1DEG. The contribution of backscattering vanishes at large separations l. The phase-space restrictons imposed by the conservation laws render the scattering rate between two strongly degenerate 1DEG's exponentially small everywhere except for narrow ranges of the concentrations. The dependences of the scattering rates on the temperature, the carrier concentrations, and the distance l are evaluated analytically and numerically for a number of realistic cases.