Spin filling of valley-orbit states in a silicon quantum dot

How Valley-Orbit States in Silicon Quantum Dots Probe Quantum Well Interfaces

The energies of valley-orbit states in silicon quantum dots are determined by an as yet poorly understood interplay between interface roughness, orbital confinement, and electron interactions. Here, we report measurements of one- and two-electron valley-orbit state energies as the dot potential is modified by changing gate voltages, and we calculate these same energies using full configuration interaction calculations. The results enable an understanding of the interplay between the physical contributions and enable a new probe of the quantum well interface.

An Operation Guide of Si-MOS Quantum Dots for Spin Qubits

In the last 20 years, silicon quantum dots have received considerable attention from academic and industrial communities for research on readout, manipulation, storage, near-neighbor and long-range coupling of spin qubits. In this paper, we introduce how to realize a single spin qubit from Si-MOS quantum dots. First, we introduce the structure of a typical Si-MOS quantum dot and the experimental setup. Then, we show the basic properties of the quantum dot, including charge stability diagram, orbital state, valley state, lever arm, electron temperature, tunneling rate and spin lifetime. After that, we introduce the two most commonly used methods for spin-to-charge conversion, i.e., Elzerman readout and Pauli spin blockade readout. Finally, we discuss the details of how to find the resonance frequency of spin qubits and show the result of coherent manipulation, i.e., Rabi oscillation. The above processes constitute an operation guide for helping the followers enter the field of spin qubits in Si-MOS quantum dots.

Electron beam lithography with negative tone resist for highly integrated silicon quantum bits

Process technologies have been developed for electron-beam (EB) lithography aimed at silicon quantum devices and their large-scale integration. It is necessary to understand the proximity effect and construct a method for its correction to perform EB lithography of fine and complicated structures. In this study, we investigate the lithography of Si quantum devices with a point-beam EB system and a maN 2401 negative tone resist, in order to correspond to various types of device structures. We optimize temperatures for specialized pre- and post-exposure bakes for forming ∼20 nm fine patterns with small line-edge roughness. Further, we demonstrated the fabrication of Si-on-insulator device patterns that have some tiny dots connected with many large wires/pads in the layout, with the careful tuning of the dose assignment. In this tuning, we used the EB process simulation to estimate the cumulative dose distribution effectively. In addition, we reproduced the experimentally obtained resist patterns via the EB process simulation after considering the mid-range effect, which is a factors in the proximity effect but is not yet deeply understood. The results of this study are expected to provide useful process technologies for EB lithography, which will help drastically accelerate the research on Si quantum devices with a high degree of freedom.

Giant Anisotropy of Spin Relaxation and Spin-Valley Mixing in a Silicon Quantum Dot

In silicon quantum dots (QDs), at a certain magnetic field commonly referred to as the "hot spot," the electron spin relaxation rate (T_{1}^{-1}) can be drastically enhanced due to strong spin-valley mixing. Here, we experimentally find that with a valley splitting of 78.2±1.6  μeV, this hot spot in spin relaxation can be suppressed by more than 2 orders of magnitude when the in-plane magnetic field is oriented at an optimal angle, about 9° from the [100] sample plane. This directional anisotropy exhibits a sinusoidal modulation with a 180° periodicity. We explain the magnitude and phase of this modulation using a model that accounts for both spin-valley mixing and intravalley spin-orbit mixing. The generality of this phenomenon is also confirmed by tuning the electric field and the valley splitting up to 268.5±0.7  μeV.

Theory of valley-resolved spectroscopy of a Si triple quantum dot coupled to a microwave resonator

We theoretically study a silicon triple quantum dot (TQD) system coupled to a superconducting microwave resonator. The response signal of an injected probe signal can be used to extract information about the level structure by measuring the transmission and phase shift of the output field. This information can further be used to gain knowledge about the valley splittings and valley phases in the individual dots. Since relevant valley states are typically split by several [Formula: see text], a finite temperature or an applied external bias voltage is required to populate energetically excited states. The theoretical methods in this paper include a capacitor model to fit experimental charging energies, an extended Hubbard model to describe the tunneling dynamics, a rate equation model to find the occupation probabilities, and an input-output model to determine the response signal of the resonator.

Coherent spin control of s-, p-, d- and f-electrons in a silicon quantum dot

Once the periodic properties of elements were unveiled, chemical behaviour could be understood in terms of the valence of atoms. Ideally, this rationale would extend to quantum dots, and quantum computation could be performed by merely controlling the outer-shell electrons of dot-based qubits. Imperfections in semiconductor materials disrupt this analogy, so real devices seldom display a systematic many-electron arrangement. We demonstrate here an electrostatically confined quantum dot that reveals a well defined shell structure. We observe four shells (31 electrons) with multiplicities given by spin and valley degrees of freedom. Various fillings containing a single valence electron-namely 1, 5, 13 and 25 electrons-are found to be potential qubits. An integrated micromagnet allows us to perform electrically-driven spin resonance (EDSR), leading to faster Rabi rotations and higher fidelity single qubit gates at higher shell states. We investigate the impact of orbital excitations on single qubits as a function of the dot deformation and exploit it for faster qubit control.

Excited States in Bilayer Graphene Quantum Dots

We report ground- and excited-state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different from quantum dots in carbon nanotubes, where the two-particle ground state is a spin-singlet state. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35 meV and measure a valley and spin g factor of 36 and 2, respectively.

Dispersively Detected Pauli Spin-Blockade in a Silicon Nanowire Field-Effect Transistor

We report the dispersive readout of the spin state of a double quantum dot formed at the corner states of a silicon nanowire field-effect transistor. Two face-to-face top-gate electrodes allow us to independently tune the charge occupation of the quantum dot system down to the few-electron limit. We measure the charge stability of the double quantum dot in DC transport as well as dispersively via in situ gate-based radio frequency reflectometry, where one top-gate electrode is connected to a resonator. The latter removes the need for external charge sensors in quantum computing architectures and provides a compact way to readout the dispersive shift caused by changes in the quantum capacitance during inter-dot charge transitions. Here, we observe Pauli spin-blockade in the high-frequency response of the circuit at finite magnetic fields between singlet and triplet states. The blockade is lifted at higher magnetic fields when intra-dot triplet states become the ground state configuration. A line shape analysis of the dispersive phase shift reveals furthermore an intra-dot valley-orbit splitting Δvo of 145 μeV. Our results open up the possibility to operate compact complementary metal-oxide semiconductor (CMOS) technology as a singlet-triplet qubit and make split-gate silicon nanowire architectures an ideal candidate for the study of spin dynamics.

Hybrid spin and valley quantum computing with singlet-triplet qubits

The valley degree of freedom in the electronic band structure of silicon, graphene, and other materials is often considered to be an obstacle for quantum computing (QC) based on electron spins in quantum dots. Here we show that control over the valley state opens new possibilities for quantum information processing. Combining qubits encoded in the singlet-triplet subspace of spin and valley states allows for universal QC using a universal two-qubit gate directly provided by the exchange interaction. We show how spin and valley qubits can be separated in order to allow for single-qubit rotations.

Spin blockade and exchange in Coulomb-confined silicon double quantum dots

Electron spins confined to phosphorus donors in silicon are promising candidates as qubits because of their long coherence times, exceeding seconds in isotopically purified bulk silicon. With the recent demonstrations of initialization, readout and coherent manipulation of individual donor electron spins, the next challenge towards the realization of a Si:P donor-based quantum computer is the demonstration of exchange coupling in two tunnel-coupled phosphorus donors. Spin-to-charge conversion via Pauli spin blockade, an essential ingredient for reading out individual spin states, is challenging in donor-based systems due to the inherently large donor charging energies (∼45 meV), requiring large electric fields (>1 MV m(-1)) to transfer both electron spins onto the same donor. Here, in a carefully characterized double donor-dot device, we directly observe spin blockade of the first few electrons and measure the effective exchange interaction between electron spins in coupled Coulomb-confined systems.

Few-electron edge-state quantum dots in a silicon nanowire field-effect transistor

We investigate the gate-induced onset of few-electron regime through the undoped channel of a silicon nanowire field-effect transistor. By combining low-temperature transport measurements and self-consistent calculations, we reveal the formation of one-dimensional conduction modes localized at the two upper edges of the channel. Charge traps in the gate dielectric cause electron localization along these edge modes, creating elongated quantum dots with characteristic lengths of ∼10 nm. We observe single-electron tunneling across two such dots in parallel, specifically one in each channel edge. We identify the filling of these quantum dots with the first few electrons, measuring addition energies of a few tens of millielectron volts and level spacings of the order of 1 meV, which we ascribe to the valley orbit splitting. The total removal of valley degeneracy leaves only a 2-fold spin degeneracy, making edge quantum dots potentially promising candidates for silicon spin qubits.

Detection of a large valley-orbit splitting in silicon with two-donor spectroscopy

We measure a large valley-orbit splitting for shallow isolated phosphorus donors in a silicon gated nanowire. This splitting is close to the bulk value and well above previous reports in silicon nanostructures. It was determined using a double dopant transport spectroscopy which eliminates artifacts induced by the environment. Quantitative simulations taking into account the position of the donors with respect to the Si/SiO2 interface and electric field in the wire show that the values found are consistent with the device geometry.

Valley-based noise-resistant quantum computation using Si quantum dots

We devise a platform for noise-resistant quantum computing using the valley degree of freedom of Si quantum dots. The qubit is encoded in two polarized (1,1) spin-triplet states with different valley compositions in a double quantum dot, with a Zeeman field enabling unambiguous initialization. A top gate gives a difference in the valley splitting between the dots, allowing controllable interdot tunneling between opposite valley eigenstates, which enables one-qubit rotations. Two-qubit operations rely on a stripline resonator, and readout on charge sensing. Sensitivity to charge and spin fluctuations is determined by intervalley processes and is greatly reduced as compared to conventional spin and charge qubits. We describe a valley echo for further noise suppression.