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Register a new userThe emergent linear Rashba spin-orbit coupling offering the fast manipulation of hole-spin qubits in germanium
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The electric dipole spin resonance (EDSR) combining strong spin-orbit coupling (SOC) and electric-dipole transitions facilitates fast spin control in a scalable way, which is the critical aspect of the rapid progress made recently in germanium (Ge) hole-spin qubits. However, a puzzle is raised because centrosymmetric Ge lacks the Dresselhaus SOC, a key element in the initial proposal of the hole-based EDSR. Here, we demonstrate that the recently uncovered finite k-linear Rashba SOC of 2D holes offers fast hole spin control via EDSR with Rabi frequencies in excellent agreement with experimental results over a wide range of driving fields. We also suggest that the Rabi frequency can reach 500 MHz under a higher gate electric field or multiple GHz in a replacement by [110]oriented wells. These findings bring a deeper understanding for hole-spin qubit manipulation and offer design principles to boost the gate speed.
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In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain certain peculiarities in the electron spin resonance of two-dimensional semiconductors. Over the past thirty years, similar ideas have been leading to a vast number of predictions, discoveries, and innovative concepts far beyond semiconductors. The past decade has been particularly creative with the realizations of means to manipulate spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and with the discovery of new topological classes of materials. These developments reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures ranging from layered graphene-like materials to cold atoms. This review presents the most remarkable recent and ongoing realizations of Rashba physics in condensed matter and beyond.
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 can compete with spins as qubits. The strong spin-orbit coupling in Ge quantum wells may be harnessed to implement electric-dipole spin resonance, leading to gate times of several nanoseconds for single-qubit rotations. The microscopic mechanism of this spin-orbit coupling is discussed, along with its implications for quantum gates based on electric-dipole spin resonance, stressing the importance of coupling terms that arise from the underlying cubic crystal field. Our results provide a theoretical foundation for recent experimental advances in Ge hole-spin qubits.
Within an effective Dirac theory the low-energy dispersions of monolayer graphene in the presence of Rashba spin-orbit coupling and spin-degenerate bilayer graphene are described by formally identical expressions. We explore implications of this correspondence for transport by choosing chiral tunneling through pn and pnp junctions as a concrete example. A real-space Greens function formalism based on a tight-binding model is adopted to perform the ballistic transport calculations, which cover and confirm previous theoretical results based on the Dirac theory. Chiral tunneling in monolayer graphene in the presence of Rashba coupling is shown to indeed behave like in bilayer graphene. Combined effects of a forbidden normal transmission and spin separation are observed within the single-band n to p transmission regime. The former comes from real-spin conservation, in analogy with pseudospin conservation in bilayer graphene, while the latter arises from the intrinsic spin-Hall mechanism of the Rashba coupling.
Spin qubits composed of either one or three electrons are realized in a quantum dot formed at a Si/SiO_2-interface in isotopically enriched silicon. Using pulsed electron spin resonance, we perform coherent control of both types of qubits, addressing them via an electric field dependent g-factor. We perform randomized benchmarking and find that both qubits can be operated with high fidelity. Surprisingly, we find that the g-factors of the one-electron and three-electron qubits have an approximately linear but opposite dependence as a function of the applied dc electric field. We develop a theory to explain this g-factor behavior based on the spin-valley coupling that results from the sharp interface. The outer shell electron in the three-electron qubit exists in the higher of the two available conduction-band valley states, in contrast with the one-electron case, where the electron is in the lower valley. We formulate a modified effective mass theory and propose that inter-valley spin-flip tunneling dominates over intra-valley spin-flips in this system, leading to a direct correlation between the spin-orbit coupling parameters and the g-factors in the two valleys. In addition to offering all-electrical tuning for single-qubit gates, the g-factor physics revealed here for one-electron and three-electron qubits offers potential opportunities for new qubit control approaches.
Holes confined in semiconductor nanostructures realize qubits where the quantum mechanical spin is strongly mixed with the quantum orbital angular momentum. The remarkable spin-orbit coupling allows for fast all electrical manipulation of such qubits. We study an idealization of a CMOS device where the hole is strongly confined in one direction (thin film geometry), while it is allowed to move more extensively along a one-dimensional channel. Static electric bias and $ac$ electrical driving are applied by metallic gates arranged along the channel. In quantum devices based on materials with a bulk inversion symmetry, such as silicon or germanium, there exists different possible spin-orbit coupling based mechanisms for qubit manipulation. One of them, the $g$-tensor magnetic resonance ($g$-TMR), relies on the dependence of the effective $g$-factors on the electrical confinement. In this configuration the hole is driven by an $ac$ field parallel to the static electric field and perpendicular to the channel (transverse driving). Another mechanism, which we refer to here as iso-Zeeman electric dipole spin resonance (IZ-EDSR), is due to the Rashba spin-orbit coupling that leads to an effective time-dependent magnetic field experienced by the pseudo-spin oscillating along the quantum channel (longitudinal driving). We compare these two modes of operation and we describe the conditions where the magnitudes of the Rabi frequencies are the largest. Different regimes can be attained by electrical tuning where the coupling to the $ac$ electric field is made either weak or strong...
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