Session D39: Semiconductor Qubits II

Electron g-factor renormalization in SiGe superlattice quantum wells

An electron g-factor of g ~ 1.6 has been observed in a SiGe superlattice quantum well with a periodic Ge concentration ranging from 0% to 9% within a supercell of length L ~ 1.8 nm. This shift from g_o = 2 represents a g-factor renormalization one to two orders of magnitude larger than what may be naively expected based on the material composition of the quantum well. We present a model that attributes this strong renormalization to the coupling of the conduction band minima to states with strong spin-orbit coupling.  More specifically, the periodic potential arising from the Ge concentration oscillations couples the conduction band minima near the X-point to states near the zone center of the Brillouin zone. In contrast to the conduction band minima, which have a spectral weight dominated by p_z orbitals, the states near the Brillouin zone center have significant contributions from all three p orbital species, which gives rise to strong spin-orbit coupling and g-factor renormalization. This g-factor renormalization may be useful in manipulation of qubit spin resonance without the use of micromagnets.    

Anomalous g-factor in a Si/SiGe heterostructure with oscillatory Ge concentration

We measure an electron g-factor of 1.6 in a quantum well consisting of predominately silicon with an oscillating varying concentration of Ge that oscillates in space between 0% and 9% with a period of 1.8 nm.  This result is surprising, because bulk materials at all compositions of

Si_x Ge_1-x in this range have g-factors very close to 2.  This unexpected g-factor is a sign that strong spin-orbit coupling is present in this quantum well, which has been shown to host quantum dots andwith have large valley splitting [1], and which is useful for electrically-driven electron spin resonance.  We hypothesize that the high spatial frequency changes in Ge concentration present in this sample lead to contributions to the electronic states from points in the Brillouin zone far from the conduction band minimum –regions that play very little role in the physics of conventional, pure-Si quantum wells.   

Increasing the valley splitting in Si/SiGe heterostructures by exploiting atomic concentration fluctuations

We present a theory of how alloy disorder affects the intervalley coupling and valley splitting in quantum dot qubits in Si/SiGe heterostructures. We show that this theory is in good agreement with experiments as well as the NEMO-3D 20-band strain-dependent sp³d⁵s^* tight-binding model. We find that, for realistic devices, alloy disorder is the dominant source of variation in the valley splitting.  Moreover, we show that increasing the alloy disorder increases the spread of the intervalley coupling, thereby increasing the average valley splitting. These results lead to a new and counterintuitive strategy for engineering quantum wells with large average valley splittings: increasing the alloy disorder. We find that adding just 5% Ge to the bottom of the quantum well enhances valley splittings substantially, achieving splittings larger than 100 μeV over 95% of the time. This strategy runs counter to the prevailing strategy of making devices with little disorder and very sharp interfaces.     

Cryogen-free scanning gate microscope for the characterization of Si/Si0.7Ge0.3 quantum devices at milli-Kelvin temperatures

The conduction band of bulk Si exhibits a six-fold valley degeneracy, which may adversely impact the performance of silicon quantum devices [1]. The spatial characterization of valley states in Si remains limited; especially in functional quantum devices. We describe here a cryogen-free scanning gate microscope for the characterization of Si/Si_0.7Ge_0.3 quantum devices at mK temperatures. The microscope is based on the Pan-walker design, with coarse positioning piezo stacks and a fine scanning piezo tube [2]. To reduce the pulse tube noise, we utilize both active and passive vibration isolation mechanisms, and achieve a root-mean-square noise in z of ∼ 2 nm [3]. As a proof of concept, we use the microscope to manipulate the charge occupation of a Si quantum dot, opening up a range of possibilities for the exploration of quantum devices and materials

[1] Zwanenburg et al., Rev. Mod. Phys. 85, 961 (2013)

[2] Pan et al., Rev. Sci. Instrum. 70, 1459 (1999)

[3] Pelliccione et al., Rev. Sci. Instrum. 84, 033703 (2013)   

Scanning-gate-driven photon assisted tunneling in a Si/Si0.7Ge0.3 double quantum dot

 

The scanning tip of an atomic force microscope was coupled to electrons confined in a gate-defined double quantum dot (DQD) fabricated on a Si/SiGe heterostructure. Even though the electrons in the accumulation-mode heterostructure are confined beneath the metallic gates, the lever arm of the tip is large enough to change the DQD charge occupation by moving the tip around or changing the tip bias voltage [1, 2]. We map resonance lines of the tip-interaction potential by measuring the currents through the DQD and a proximal charge sensor dot. By applying a microwave tone to the tip we are able to perform excited state spectroscopy via photon-assisted tunneling [3].

[1] Pioda et al., PRL 93, 216801 (2004)

[2] Fallahi et al., Nano Lett. 5, 223 (2004)

[3] Wang et al., PRL 111, 046801 (2013)   

Simulating electron densities obtained in scanning gate microscopy of Si/SiGe quantum dot devices

Silicon-based quantum devices are a serious contender for scalable quantum computing, enabling coherent and highly controllable semiconductor spin qubits [1]. However, the six-fold “valley-degeneracy” of bulk Si [2] poses a challenge to silicon-based spin qubits [3]. Progress in understanding what limits valley splitting has been limited by the lack of high throughput measurements, calling for the development of new measurement techniques. A cryogen-free scanning gate microscope (SGM), compatible with Si/Si_0.7Ge_0.3 quantum dot devices and operating at milli-Kelvin temperatures, was recently demonstrated [4]. The microscope has the potential to enable spatial mapping of the valley splitting in silicon-based quantum dot devices. Here, we report recent efforts on quantum dot device simulations to investigate the influence of the tip bias in a SGM on the electronic occupation of a Si/SiGe quantum dot.

[1] Yoneda et al., Nature Nano. 13, 102 (2018)

[2] Zwanenburg et al., Rev. Mod. Phys. 85, 961 (2013)

[3] Friesen et al., Phys. Rev. B 81, 115324 (2010)

[4] Oh et al., arXiv:2105.05684   

Reduced Disorder and Opportunities for Scalable, 2-Dimensional Gate Array Design Using the SLEDGE Architecture in Si/SiGe Exchange-Only Qubits

The recently-demonstrated Single-Layer Etch-Defined Gate-Electrode (SLEDGE) architecture in Si/SiGe exchange-only qubits enables flexible device design and fabrication by separating the front-end-of-line (FEOL) gate stack from the back-end-of-line (BEOL) interconnects [1]. For FEOL gates, moving from a lift-off to subtractive fabrication process with improved gate stack cleans decreases electrostatic disorder; we measure Hall bars with a reduced minimum electron density at which conduction occurs and quantum dot device gates with reduced variability in voltages at which electrons load and tunnel. BEOL routing enables scalable, 2-dimensional gate array designs of the FEOL, instead of 1-dimensional arrays or ring-like designs, but requires good electrical connections between vias and gates. We show that if a via is poorly-connected to a gate, the gate behaves as an unwanted quantum dot (coined “parasitic metal dot,” PMD). With design and fabrication improvements, we measure drastically reduced PMD prevalence. We further show SLEDGE devices can be used for coherent operation of high-performance qubits.

 

[1] Ha et al. arXiv:2107.10916   

28Si/SiGe heterostructures with engineered semiconductor/dielectric interface

Advancing the materials science of quantum information devices plays an essential role in the pursuit of larger spin-based quantum processors with more functionality. Previously, we demonstrated ²⁸Si/SiGe heterostructures that hosted quantum processors with two-qubit gate fidelities above 99\% [1][2]. We build on these results and present ²⁸Si/SiGe heterostructures with an engineered semiconductor/dielectric interface to reduce remote impurities and improve device uniformity on a wafer scale. We characterize the heterostructures by magnetotransport and show a two-fold reduction of the standard deviation for key transport metrics such as peak mobility,  percolation density, and quantum lifetime. We correlate the results of quantum transport with studies of charge noise in quantum dots fabricated on the same heterostructures.

[1] Xue, X et al., arXiv:2107.00628 (2021)

[2] Noiri, A et al., arXiv:2108.02626 (2021)   

Quantitative strain mapping in Si0.7Ge0.3/Si/ Si0.7Ge0.3 heterostructures for spin qubits

We present laterally resolved maps of the lattice strains around spin qubits housed in Si/SiGe heterostructures and demonstrate that that material related inhomogeneities must be taken into account in the optimization and design for scaled CMOS-compatible quantum processors. 

The Si/SiGe material system is promising for large-scale integration of solid state qubits due to the demonstration of high coherence times and multi-qubit algorithms. One key requirement for realizing large arrays of qubits with shared gate control is a high degree of homogeneity of the lattice strains. Here, we leverage Scanning Xray Diffraction Microscopy (SXDM) at ID01/ESRF to investigate non-destructively the lattice homogeneity in Si/SiGe heterostructures. We map the strain tensor in a 10 nm thick Si QW with a lateral resolution below 50 nm and determine local strain variations larger than 1e-4. Based on the experimental data, we perform Finite Element Method (FEM) thermomechanical simulations to calculate the strain distribution at low temperature. Furthermore, the strain maps are translated into spatially resolved profiles for the energy of the conduction band valley state, the variation of which is found to be of the magnitude as the charging energy of an electrostatic quantum dot of approx. 1 meV   

Observation of disorder-induced decoherence for individual electron spins in moving quantum dots

Controlled electron displacement has been identified as one possible strategy to convey on-chip quantum information in semiconductor quantum circuits. Understanding the mechanisms limiting the transfer fidelity is therefore an important task to validate this quantum information conveyer procedure.

In this presentation, we demonstrate the observation of disorder-induced decoherence for individual electron spins in moving quantum dots. Using our ability to transfer individual electrons on fast timescales with an unprecedented control [1, 2], we study the mechanisms affecting the spin coherence during the electron displacement. We demonstrate that the main source of decoherence is a combination of Coulomb disorder and spin-orbit coupling, and study its fluctuations over milliseconds timescales.

[1] Bertrand, B., Hermelin, S., Takada, S. et al. Fast spin information transfer between distant quantum dots using individual electrons. Nature Nanotech 11, 672–676 (2016).

[2] Jadot, B., Mortemousque, PA., Chanrion, E. et al. Distant spin entanglement via fast and coherent electron shuttling. Nat. Nanotechnol. 16, 570–575 (2021).   

Quantum-well subband-degeneracy refrigeration with cascaded cryogenic solid-state heat pumps

Design for a solid-state heat pump to eventually replace dilution refrigerators is introduced based on the cyclic adiabatic expansion and compression of 2D electron gas subbands to achieve sub-Kelvin temperatures. With the one-shot version proposed by Rego & Kirczenow (APL, 1999), the proposed device cools by a factor of T_C/T_H = g₁/g₂ by decreasing the electric field in the quantum well via gates to increase the subband occupancy from g₁ to g₂. Narrow “throttle” gates to the left and right of the compression/expansion gates can selectively deplete a narrow strip of electrons, which electrically and thermally isolate the central electron reservoir alternately from the heat sink and from the cold load. Optimal materials selection and device design is supported by an analytical model of device function. A 1 cm² single-stage device is predicted to cool to 0.85 K with a 1 K heat sink and 1 MHz cycle frequency. Moreover, temperatures below 0.10 K can be achieved by a multi-stage cascaded device. Future generations of this device are intended to eventually supplant dilution refrigerators for cooling of solid-state quantum computers.