Controllable valley splitting in silicon quantum devices

Abstract

Silicon has many attractive properties for quantum computing, and the quantum dot architecture is appealing because of its controllability and scalability. However, the multiple valleys in the silicon conduction band are potentially a serious source of decoherence for spin-based quantum dot qubits. Only when these valleys are split by a large energy does one obtain well-defined and long-lived spin states appropriate for quantum computing. Here we show that the small valley splittings observed in previous experiments on Si/SiGe heterostructures result from atomic steps at the quantum well interface. Lateral confinement in a quantum point contact limits the electron wavefunctions to several steps, and enhances the valley splitting substantially, up to 1.5 meV. The combination of electronic and magnetic confinement produces a valley splitting larger than the spin splitting, which is controllable over a wide range. These results improve the outlook for realizing spin qubits with long coherence times in silicon-based devices.The fundamental unit of quantum information is the qubit. Qubits can be constructed from the quantum states of physical objects like atomic ions [1], quantum dots [2,3,4,5,6,7] or superconducting Josephson junctions [8]. A key requirement is that these quantum states should be well-defined and isolated from their environment. An assemblage of many qubits into a register and the construction of a universal set of operations, including initialization, measurement, and single and multi-qubit gates, would enable a quantum computer to execute algorithms for certain difficult computational problems like prime factorization and database search far faster than any conventional computer [9].The solid state affords special benefits and challenges for qubit operation and quantum computation. State-ofthe-art fabrication techniques enable the positioning of electrostatic gates with a resolution of several nanometers, paving the way for large scale implementations. On the other hand, the solid state environment provides numerous pathways for decoherence to degrade the computation [10]. Spins in silicon offer a special resilience against decoherence because of two desirable materials properties [11,12]: a small spin-orbit coupling and predominately spin-zero nuclei. Isotopic purification could essentially eliminate all nuclear decoherence mechanisms.Silicon, however, also has a property that potentially can increase decoherence. Silicon has multiple conduction band minima or valleys at the same energy. Unless this degeneracy is lifted, coherence and qubit operation will be threatened. In strained silicon quantum wells there are two such degenerate valleys [13] whose quantum numbers and energy scales compete directly with the spin degrees of freedom. In principle, sharp confinement potentials, like the quantum well interfaces, couple these two valleys and lift the degeneracy, providing a unique ground state if the coupling is strong enough [14,15]. Theoretical analyses for noninteracting electrons in perfectly f...

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

“…The effective Landé factor is g = 2. 44,89 Other material parameters read c l = 9150 m/s (for LA phonons), c t = 5000 m/s (for TA phonons), ρ = 2330 kg/m 3 , and ε = 11.9ε 0 . 90 The choice of deformation potential constants is not unique, 83,84,91 and we use d = 5 eV and u = 9 eV according to Ref.…”

“…This remaining degeneracy is further split if the perpendicular confinement is asymmetric, resulting in an energy difference called the ground-state gap. [42][43][44][45][46][47][48][49] As the valley degeneracy is believed to be the main obstacle for silicon-based quantum computation, 46,50,51 a large valley splitting is desired. If this is the case, the multivalley system can be reduced to an effective single-valley qubit, a potentially nuclear-spin-free analog to the well-known GaAs counterpart.…”

Coherent electrical rotations of valley states in Si quantum dots using the phase of the valley-orbit coupling

“…The multiplicity of the Hilbert space brought about by the existence of equivalent valleys has been shown to hamper spin QC. [71][72][73][74][75] At the same time, the interface potential gives rise to a valley-orbit coupling, which has been studied extensively in recent years, both experimentally [76][77][78][79][80][81] and theoretically. [82][83][84][85][86][87][88][89][90] Addressing specific valley eigenstates is a profound, challenging and unresolved problem.…”

Valley Phase and Voltage Control of Coherent Manipulation in Si Quantum Dots

“…Because there is no external control of the valley quantum number, complications include difficulty in well-defined initialization and enhanced spin decoherence at valley relaxation "hotspots" [7]. Experimental measurements of the magnitude of the valley splitting between the lowest two valley states include spinvalley "hotspots" [8] and valley splitting magnitude tunable with electric field [7] [9]. The experimental work most relevant for our study is Shi et al [10], which showed experimentally a shift in the single-triplet splitting J for two electrons on a single dot, where J is dominated by the energy difference between single-particle ground and excited valley-orbit states in Si/SiGe.…”

“…Since the valley phase in Equation 6 arises from the vertical height of the interface, at first glance one might think that moving the dot vertically into the Si substrate might have a strong effect on ∆φ; although a vertical electric field has strong effect on the magnitude of the coupling [9]− [21] , it has a small effect on ∆φ [15], at least for a flat interface. However, due to the strong dependence of the valley phase on the exact local realization of the interface roughness, using Overall, Figure 3 shows this possibility: the upper panel shows the effect on ∆φ of using a lateral gate voltage to move both dots laterally with a constant separation, for both a sinusoidal interface (∆λ = 0) and random interface (∆λ = 10).…”