Planar germanium heterostructures are promising hosts for hybrid quantum devices due to their compatibility with superconductors, low material disorder, and relaxed fabrication constraints. Also, the potentially low density of nuclear spins and strong spin-orbit interaction make germanium attractive for coherent spin physics. However, recent microwave spectroscopy experiments were unable to resolve a spin-splitting of bound states in germanium Josephson junctions, the prerequisite for defining and controlling Andreev spin qubits. Here, we argue that compressive strain is the key mechanism suppressing spin splitting in current devices. Furthermore, we propose unstrained and tensile-strained heterostructures, fully compatible with state-of-the-art growth technology, that significantly enhance the relevant spin-orbit effect. By numerically simulating ballistic Josephson junctions, we predict spin splittings comfortably in the GHz range, more than 2 orders of magnitude larger than compressively strained cases, and all-electric quantum gates in a hundred nanoseconds. Our results establish strain engineering as a key design principle for realizing Andreev spin qubits in germanium-based devices.
Strain engineering has proven to be vital for germanium-based photonics, in particular light emission. However, applying a large permanent biaxial strain to germanium has been a challenge. We present a simple, CMOS-compatible technique to conveniently induce a large, spatially homogenous strain in microdisks patterned within ultrathin germanium nanomembranes. Our technique works by concentrating and amplifying a pre-existing small strain into the microdisk region. Biaxial strains as large as 1.11% are observed by Raman spectroscopy and are further confirmed by photoluminescence measurements, w…
We demonstrate that a lightly-strained germanium channel ($\varepsilon_{//}$ = -0.41%) in an undoped Ge/Si$_{0.1}$Ge$_{0.9}$ heterostructure field effect transistor supports a 2D hole gas with mobility in excess of 1$\times$10$^{6}$ cm$^{2}$/Vs and percolation density less than 5$\times$10$^{10}$ cm$^{-2}$. This low disorder 2D hole system shows tunable fractional quantum Hall effect at low density and low magnetic field. The low-disorder and small effective mass (0.068$m_e$) defines lightly-strained germanium as a basis to tune the strength of the spin-orbit coupling for fast and coherent qua…
This work investigates the effect of the uniaxial strain on the tunneling conductance in a strained graphene superconductor where strain is applied in the armchair direction. Based on the Tight-Binding model, applying strain in the armchair direction gives rise to the asymmetric massless fermions as the carriers. Their velocities depend on their directions controlled by strain. Using the BTK theory, the conductances of strained graphene N/S junctions can be determined. As a result, we find that the current flowing perpendicular to the direction of strain depends linearly on strain, with the po…
We theoretically investigate the properties of holes in a Si$_{x}$Ge$_{1-x}$/Ge/ Si$_{x}$Ge$_{1-x}$ quantum well in a perpendicular magnetic field that make them advantageous as qubits, including a large ($>$100~meV) intrinsic splitting between the light and heavy hole bands, a very light ($\sim$0.05$\, m_0$) in-plane effective mass, consistent with higher mobilities and tunnel rates, and larger dot sizes that could ameliorate constraints on device fabrication. Compared to electrons in quantum dots, hole qubits do not suffer from the presence of nearby quantum levels (e.g., valley states) that…
Planar Josephson junctions comprising semiconductors with strong spin-orbit interaction (SOI) are promising platforms to host Majorana bound states (MBSs). Previous works on MBSs in planar Josephson junctions have focused on electron gases, where SOI is linear in momentum. In contrast, a two-dimensional hole gas in planar germanium (Ge) exhibits SOI that is cubic in momentum. Nevertheless, we show here that due to the particularly large SOI, Ge is a favorable material. Using a discretized model, we numerically simulate a Ge planar Josephson junction and demonstrate that also cubic SOI can lead…
Tailoring Germanium Heterostructures for Quantum Devices with Machine Learning
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克研究所和卡弗里纳米科学研究所）；Department of Materials Science and Engineering, Delft University of Technology（代尔夫特理工大学材料科学与工程系）；Climate Safety and Security Centre, TU Delft The Hague Campus, Delft University of Technology（代尔夫特理工大学海牙校区气候安全与安保中心）
Complementary to the development of highly three-dimensional (3D) integrated circuits in the continuation of Moore's law, there has been a growing interest in new 3D deformation strategies to improve device performance. To continue this search for new 3D deformation techniques, it is essential to explore beforehand - using computational predictive methods - which strain tensor leads to the desired properties. In this work, we study germanium (Ge) under an isotropic 3D strain on the basis of first-principle methods. The transport and optical properties are studied by a fully ab initio Boltzmann…
We fabricate Josephson field-effect-transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a tra…
Elastic strain distributions in SiGe heterostructures with quantum dots have been simulated with the use of the finite element method. The effect of a non-uniform germanium distribution in the nanoislands on the spatial dependence and the magnitude of elastic fields was studied. It is shown that quantum dots with a uniform component content are more strained in comparison with non-uniform nanoislands
The integration of efficient, miniaturized group IV lasers into CMOS architecture holds the key to the realization of fully functional photonic-integrated circuits. Despite several years of progress, however, all group IV lasers reported to date exhibit impractically high thresholds owing to their unfavorable bandstructures. Highly strained germanium with its fundamentally altered bandstructure has emerged as a potential low-threshold gain medium, but there has yet to be any successful demonstration of lasing from this seemingly promising material system. Here, we demonstrate a low-threshold, …
We report experimental evidence of ballistic hole transport in one-dimensional quantum wires gate-defined in a strained SiGe/Ge/SiGe quantum well. At zero magnetic field, we observe conductance plateaus at integer multiples of 2e^2/h. At finite magnetic field, the splitting of these plateaus by Zeeman effect reveals largely anisotropic g-factors, with absolute values below 1 in the quantum-well plane, and exceeding 10 out of plane. This g-factor anisotropy is consistent with a heavy-hole character of the propagating valence-band states, in line with a predominant confinement in the growth dire…
Buried germanium quantum well proximitised by magnetic field-resilient superconducting platinum iridium germanosilicide
Delft University of Technology（代尔夫特理工大学）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子纳米科学夸夫泰克研究所）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学夸夫泰克纳米科学研究所）；Catalan Institute of Nanoscience and Nanotechnology – ICN2 (CSIC and BIST)（加泰罗尼亚纳米科学与技术研究所）；ICREA（加泰罗尼亚高级研究学院）
Electrons and holes confined in quantum dots define an excellent building block for quantum emergence, simulation, and computation. In order for quantum electronics to become practical, large numbers of quantum dots will be required, necessitating the fabrication of scaled structures such as linear and 2D arrays. Group IV semiconductors contain stable isotopes with zero nuclear spin and can thereby serve as excellent host for spins with long quantum coherence. Here we demonstrate group IV quantum dot arrays in silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe) and strained g…
The quiet quantum environment of holes in solid-state devices has been at the core of increasingly reliable architectures for quantum processors and memories.1-6 However, due to the lack of scalable materials to properly tailor the valence band character and its energy offsets, the precise engineering of light-hole (LH) states remains a serious obstacle toward coherent photon-spin interfaces needed for a direct mapping of the quantum information encoded in photon flying qubits to stationary spin processor.4-9 Herein, to alleviate this long-standing limitation we demonstrate an all-group IV low…
Semiconductor superlattices have been extensively investigated for thermoelectric applications, to explore the effects of compositions, interface structures, and lattice strain environments on the reduction of thermal conductivity, and improvement of efficiency. Most studies assumed that their electronic properties remain unaffected compared to their bulk counterparts. However, recent studies demonstrated that electronic properties of silicon (Si)/germanium (Ge) superlattices show significant variations depending on compositions and growth substrates. These studies used a constant relaxation t…
Buried-channel semiconductor heterostructures are an archetype material platform to fabricate gated semiconductor quantum devices. Sharp confinement potential is obtained by positioning the channel near the surface, however nearby surface states degrade the electrical properties of the starting material. In this paper we demonstrate a two-dimensional hole gas of high mobility ($5\times 10^{5}$ cm$^2$/Vs) in a very shallow strained germanium channel, which is located only 22 nm below the surface. This high mobility leads to mean free paths $\approx6 μm$, setting new benchmarks for holes in shal…
A split gate technique is used to form a lateral quantum dot in a two-dimensional electron gas of a modulation-doped silicon/silicon-germanium heterostructure. e-beam lithography was employed to produce split gates. By applying negative voltages to these gates the underlying electron gas is depleted and a lateral quantum dot is formed, the size of which can be adjusted by the gate voltage. We observe single-electron operation with Coulomb blockade behavior below 1K. Gate leakage currents are well controlled, indicating that the recently encountered problems with Schottky gates for this type of…
Hole-spin qubits in germanium beyond the single-particle regime
CNR-Istituto Nanoscienze（意大利国家研究委员会纳米科学研究所）；Università di Milano（米兰大学）；Università degli Studi di Modena e Reggio Emilia（摩德纳和雷焦艾米利亚大学）；University of Basel（巴塞尔大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；Delft University of Technology（代尔夫特理工大学）
We design, fabricate, and study a hole bilayer in a strained germanium double quantum well. Magnetotransport characterisation of double quantum well field-effect transistors as a function of gate voltage reveals the population of two hole channels with a high combined mobility of 3.34$\times$10$^5$ cm$^2$/Vs and a low percolation density of 2.38$\times$10$^{10}$ cm$^{-2}$. We resolve the individual population of the channels from the interference patterns of the Landau fan diagram. At a density of 2.0$\times$10$^{11}$ cm$^{-2}$ the system is in resonance and we observe an anti-crossing of the …
Gate-controllable spin-orbit coupling is often one requisite for spintronic devices. For practical spin field-effect transistors, another essential requirement is ballistic spin transport, where the spin precession length is shorter than the mean free path such that the gate-controlled spin precession is not randomized by disorder. In this letter, we report the observation of a gate-induced crossover from weak localization to weak anti-localization in the magneto-resistance of a high-mobility two-dimensional hole gas in a strained germanium quantum well. From the magneto-resistance, we extract…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CEA（法国原子能和替代能源委员会）；IRIG-MEM-L_Sim；Quantum Advanced Research Center (QuARC) - Consejo Superior de Investigaciones Científicas (CSIC)（量子先进研究中心（QuARC）- 西班牙高等科学研究理事会（CSIC））；Instituto de Ciencia de Materiales de Madrid (ICMM) - Consejo Superior de Investigaciones Científicas (CSIC)（马德里材料科学研究所（ICMM）- 西班牙高等科学研究理事会（CSIC））
The lifting of the two-fold degeneracy of the conduction valleys in a strained silicon quantum well is critical for spin quantum computing. Here, we obtain an accurate measurement of the splitting of the valley states in the low-field region of interest, using the microwave spectroscopy technique of electron valley resonance (EVR). We compare our results with conventional methods, observing a linear magnetic field dependence of the valley splitting, and a strong low-field suppression, consistent with recent theory. The resonance linewidth shows a marked enhancement above $T\simeq 300$ mK.
We engineer planar Ge/SiGe heterostructures for low disorder and quiet hole quantum dot operation by positioning the strained Ge channel 55~nm below the semiconductor/dielectric interface. In heterostructure field effect transistors, we measure a percolation density for two-dimensional hole transport of $2.1\times10^{10}~\text{cm}^{-2}$, indicative of a very low disorder potential landscape experienced by holes in the buried Ge channel. These Ge heterostructures support quiet operation of hole quantum dots and we measure charge noise levels that are below the detection limit $\sqrt{S_\text{E}}…
We theoretically study scattering process and superconducting triplet correlations in a graphene junction comprised of ferromagnet-RSO-superconductor in which RSO stands for a region with Rashba spin orbit interaction. Our results reveal spin-polarized subgap transport through the system due to an anomalous equal-spin Andreev reflection in addition to conventional back scatterings. We calculate equal- and opposite-spin pair correlations near the F-RSO interface and demonstrate direct link of the anomalous Andreev reflection and equal-spin pairings arised due to the proximity effect in the pres…
Depth-Resolved Lattice Distortions in a Silicon-Germanium Qubit Host
Q-NEXT, Argonne National Laboratory（Q-NEXT，阿贡国家实验室）；Materials Science Division, Argonne National Laboratory（材料科学部，阿贡国家实验室）；Pritzker School of Molecular Engineering, University of Chicago（普里茨克分子工程学院，芝加哥大学）；Department of Physics, University of Wisconsin-Madison（物理学系，威斯康星大学麦迪逊分校）；Center for Nanoscale Materials, Argonne National Laboratory（纳米材料中心，阿贡国家实验室）
Granular aluminum induced superconductivity in germanium for hole spin-based hybrid devices
ISTA, Institute of Science and Technology Austria（奥地利科学技术研究所）；Quantum Advanced Research Center (QuARC), Consejo Superior de Investigaciones Científicas (CSIC)（西班牙高等科学研究理事会量子先进研究中心）；Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC)（西班牙高等科学研究理事会马德里材料科学研究所）
Solid-state single-photon emitters are attractive for realization of integrated quantum systems due to their experimental convenience and scalability. Unfortunately, however, their complex mesoscopic environments cause photons from different emitters to be spectrally distinguishable. Here we demonstrate spectral alignment of two solid-state single-photon emitters by utilizing the strain gradient. Multiple germanium vacancy (GeV) color centers in diamond are created in fabricated diamond microcantilevers using focused ion beam implantation. The strain response of the electronic energy levels of…
Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their inherent compatibility with standard semiconductor manufacturing. While early on it was recognized that holes may offer a multitude of favourable properties for fast and scalable quantum control, research thus far has remained almost exclusively restricted to the simpler electron system. However, recent developments with holes have led to separate demonstrations of single-shot readout and fast quantum logic, albeit only in the multi-hole regime. Here, we establish a single-hole spin qubit in germ…
In this paper we present NANOTCAD2D, a code for the simulation of the electrical properties of semiconductor-based nanoelectronic devices and structures in two-dimensional domains. Such code is based on the solution of the Poisson/Schrödinger equation with density functional theory and of the continuity equation of the ballistic current. NANOTCAD2D can be applied to structures fabricated on III-IV, strained-silicon and silicon-germanium heterostructures, CMOS structures, and can easily be extended to new materials. In particular, in the case of SiGe heterostructures, it computes the effects of…
In this study we numerically calculate the spatial profile of mechanical strain on self-assembled germanium (Ge) quantum dots (QDs) grown on a silicon (Si) substrate. Although the topic has been exhaustively studied, interesting features have not been explained or even mentioned in the literature yet. We studied the effect of the cap layer considering two cases: capped QDs (where a Si cap is present above the Ge QDs) and uncapped QDs (where no Si is present above the Ge QDs). We observed that Ge in the capped QDs is more strained compared with the the uncapped QDs. This expected effect is attr…
Striving for nanometer-sized solid-state single-photon sources, we investigate atom-like quantum emitters based on single germanium vacancy (GeV) centers isolated in crystalline nanodiamonds (NDs). Cryogenic characterization indicated symmetry-protected and bright (> 10^6 counts/s with off-resonance excitation) zero-phonon optical transitions with up to 6-fold enhancement in energy splitting of their ground states as compared to that found for GeV centers in bulk diamonds (i.e., up to 870 GHz in highly strained NDs vs 150 GHz in bulk). Utilizing lithographic alignment techniques, we demonstrat…
The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view graphene is special since it allows the creation of strong pseudo-magnetic fields due to strain. We show that in a Josephson junction made of strained graphene, Cooper pairs will diffuse into the strained region. The pair correlation function will be sub-lattice polarized due to the polarization of the local density of states in the zero pseudo-Landau level. We uncover …
