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[93] S. Samanta, Study of systematic trends in electronic and optical properties within ZnM2O4 (M = Co, Rh, Ir) family by FPLAPW method with PBE and TB-mBJ potentials, Opt. Mater. (Amst). 45 (2015) 141–147. https://doi.org/10.1016/j.optmat.2015.03.024. [94] E. Antoini, Sintering of LixNi1− xO solid solutions at 1200 °C, J. Mater. Sci. 27 (1992) 3335–3340. http://link.springer.com/article/10.1007/BF01116034. [95] J. Van Elp, H. Eskes, P. Kuiper, G.A. Sawatzky, Electronic structure of Li-doped NiO,
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excitonic photoluminescence and band-gap engineering of wide-gap p-type oxychalcogenide epitaxial films of LnCuOCh (Ln = La, Pr, and Nd; Ch = S or Se) semiconductor alloys, J. Appl. Phys. 94 (2003) 5805–5808. https://doi.org/10.1063/1.1618932. [149] B. Medasani, M.L. Sushko, K.M. Rosso, D.K. Schreiber, S.M. Bruemmer, Temperature Dependence of Self-diffusion in Cr2O3 from First Principles, The Journal of Physical
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https://doi.org/10.1063/1.1584074. [179] A.N. Banerjee, C.K. Ghosh, K.K. Chattopadhyay, Effect of excess oxygen on the electrical properties of transparent p-type conducting CuAlO2+x thin films, Sol. Energy Mater. Sol. Cells 89 (2005) 75–83. https://doi.org/10.1016/j.solmat.2005.01.003. Figure 1. Band gap engineering of TCO material. Visible photons don't have enough energy to excite electrons directly from the valence band to conduction band. Still, they have sufficient
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excite electrons directly from the valence band to conduction band. Still, they have sufficient energy to excite electrons from donor level to conduction band (in n-type TCO) or holes from the acceptor level to valence band (in p-type TCO). The symbol (✓) and (×) represents the allowed and forbidden transition. Figure 2. Transmittance spectrum of TCO material. Figure 3. Band structure overview of n-type and p-type material with degenerate doping,
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Figure 3. Band structure overview of n-type and p-type material with degenerate doping, illustrating the BM-shift, Fermi-level (EFL), vacuum level (EVL), fundamental band gap (Eg), and secondary band gap (Esg). The dark blue shading portion represents the occupied energy states, while empty one is unoccupied energy levels. Figure 4. Schematic overview of CMVB technique [42]. Energy levels are not to scale. Figure 5. Evolution of publications on p-type TCO materials.
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Figure 5. Evolution of publications on p-type TCO materials. Figure 6. Variation in electrical conductivity of Mg-doped CuScO2+y thin film as a function of oxygen intercalation pressures [67]. Figure 7. Variation in electrical conductivity (σ), carrier concentration (n) and mobility (μ) of ZnCo2O4 thin films as a function of oxygen partial pressure ratio [86]. Figure 8. Resistivity, mobility, and carrier concentration of NiO thin films with varying Cu- content [98].
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content [98]. Figure 9. Changes in electrical resistivity, carrier type and carrier concentration of Ga-doped SnO2 thin films [62]. Figure 10. Changes in resistivity (ρ), Hall mobility (μ), and carrier concentrations of Eu-doped SnO2 thin films with varying Eu molar concentration [130]. (a) (b) Figure 11. (a) Resistivity and hole density and (b) mobility of Cu2O thin films with LTB-Cu2O
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Figure 11. (a) Resistivity and hole density and (b) mobility of Cu2O thin films with LTB-Cu2O as a function of oxygen flow rates. Figure 12. Optical transmission spectra of (a) Cr2O3, (b) Mg:Cr2O3, and (c) Mg,N:Cr2O3 thin films deposited with precursor ratios of Cr:Mg 9:1 and Cr:N 1:4. The inset shows a cross-section SEM image to measure film thickness [152]. Figure 13. The room temperature electrical conductivity of Cr2O3 thin films (deposited from
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Figure 13. The room temperature electrical conductivity of Cr2O3 thin films (deposited from various sources) measured at different post-annealing oxygen pressures [153]. Figure 14. Optical transmittance spectra of Al2O3 substrate and V2O3 thin films of varying thicknesses. The inset illustrates the images of the Al2O3 substrate and V2O3 thin films with different thicknesses [169]. Figure 15. ABO2 crystal lattice: (a) stoichiometric structure. (b & c) non-stoichiometric with
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Figure 15. ABO2 crystal lattice: (a) stoichiometric structure. (b & c) non-stoichiometric with excess oxygen: (b) occupying A and B cation sites (creates four holes, p-type), (c) occupying interstitial sites (forms O2-, creates two holes, p-type). Table 1: Cu-based materials as p-type TCO and their respective optoelectronic parameters. Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity
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Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility (cm2/V-s) Reference CuAlO2 PLD 500 Sapphire 70 3.5 1 1.3 × 1017 10.4 [42] CuGaO2 PLD 500 Sapphire 80 3.6 0.063 1.7 × 1018 0.23 [49] Sn: CuInO2 PLD 280 Sapphire < 50 3.9 3.8×10-3 - - [46] Ca: CuInO2 PLD 170 Sapphire < 50 ~3.9 2.83×10-3 - - [46] CuScO2+x Sputtering 110 Silica 40 3.3 15-30 - - [47] CuY1-xCaxO2 Thermal co-
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- - [46] CuScO2+x Sputtering 110 Silica 40 3.3 15-30 - - [47] CuY1-xCaxO2 Thermal co- evaporation 240 MgO 40-50 3.5 1 - - [48] CuCr1-xMgxO2 RF- sputtering 250 Quartz 30 3.1 220 - - [45] Cu-deficient CuCrO2 spray pyrolysis 80 Glass 55 3 1-12 - 0.006 [70] Mg, N: CuCrO2 RF- sputtering 150 Quartz 69.1 3.52 277.7 1.18×1021 0.006 [71] Sn:CuNi1- xSbxO2 RF- sputtering 150-200 Fused silica 60 3.4 0.05 - - [72] K-doped SrCu2O2 PLD 200
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RF- sputtering 150-200 Fused silica 60 3.4 0.05 - - [72] K-doped SrCu2O2 PLD 200 SiO2 glass ⁓ 70 3.3 4.8×10-2 6.13×1017 0.46 [50] CuCrO2+x Combustion 75 ITO 80-90 3.0 0.14 3.8 × 1018 0.23 [73] CuCrO2 CVD 75-85 Boro aluminosilicate glass 60-65 3.2 50 9.3 × 1018 -1.5 × 1016 0.65-5 [74] CuGaO2 RF- sputtering 200 Fused quartz 60-70 3.47 0.0167 - - [75] CuAlO2 Magnetron Sputtering 400 Sapphire 75 3.85 1.05 2.5 × 1019 0.254 [76]
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Magnetron Sputtering 400 Sapphire 75 3.85 1.05 2.5 × 1019 0.254 [76] Table 2: Ag-based materials as p-type TCO and their respective optoelectronic parameters. Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility Reference AgGaO2 PLD 200 Sapphire 50 4.12 3.2×10-4 - - [77] AgCr1-xMgxO2 Spin Coating
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Reference AgGaO2 PLD 200 Sapphire 50 4.12 3.2×10-4 - - [77] AgCr1-xMgxO2 Spin Coating 120 Sapphire 60 3.66 67.7×10-3 1.25×1017 50 [79] Ag-deficient AgInGaO2 Reactive Evaporation - Glass substrate 25 3.77 61 2.2×1018 0.017 [80] Table 3: Spinel materials as p-type TCO and their respective optoelectronic parameters. Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical
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(nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility (cm2/V-s) Reference NiCo2O4 Spin Casting 100 Sapphire 90 - 16.7 - - [81] ZnRh2O4 RFMS - Silica glass - 2.1 0.7 - - [82] ZnCo2O4 RFMS 400 Silica glass 55 2.63 1.2 2.81×1020 0.2 [86] ZnIr2O4 PLD 100-300 Quartz and sapphire 60 2.97 2.09-3.39 - - [82] ZnCo2O4 PLD 100-200 Sapphire - 2.3 21.8 2.6×1016-
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sapphire 60 2.97 2.09-3.39 - - [82] ZnCo2O4 PLD 100-200 Sapphire - 2.3 21.8 2.6×1016- 1.49×1020 0.12-0.6 [91] ZnCo2O4 Spin coating 120 Glass 55 3.95-3.99 0.4×10-3- 0.6×10-2 5.57×1012- 4.29 ×1014 - [89] ZnGa2O4 MOCVD 100 Sapphire 80 5.1 7.6×10-4 1.6 ×1015 7-10 [90] Table 4: Binary oxide materials as p-type TCO and their respective optoelectronic parameters. Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%)
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Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility (cm2/V-s) Reference NiO Magnetron Sputtering 110 glass 40 3.8 7.2 1.3×1019 - [5] NiO RFMS 100 glass 69 - 9.09 8.8×1018 6.12 [96] K:NiO PLD 100 glass 60 3.73- 3.88 4.25 7.18×1019 0.37 [97] Cu-NiO Reactive Sputtering 500 Silicon - 2.41 8.34 4.22×1020 1 [98] SnxNiyOz
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[97] Cu-NiO Reactive Sputtering 500 Silicon - 2.41 8.34 4.22×1020 1 [98] SnxNiyOz RFMS 100 InP - 2.9 0.071 2.04×1017 7.7 [101] Mn:NiO spray pyrolysis 200 glass 84 3.61 1.19 - - [102] Zn:NiO spray pyrolysis 200 glass 73 3.67 3.79 - - [102] ZnO PLD 700-1400 Fused Silica 80 - 0.5 5.6×1018 0.1 [107] SnO PLD 110 YSZ - 2.7 - 2.5×1017 2.4 [121] SnOx RFMS 200 glass 85 2.8 0.1-0.01 1017-1018 4.8 [123] SnO RFMS 200-300 Soda lime glass
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RFMS 200 glass 85 2.8 0.1-0.01 1017-1018 4.8 [123] SnO RFMS 200-300 Soda lime glass 57 2.7-2.9 1.16 45.7×1017 1.6 [124] Ga-SnO RFMS 200-300 Soda lime glass 65 2.7-2.9 3.71 62.4×1017 3.6 [124] Na-SnO RFMS 200-300 Soda lime glass 50 2.7-2.9 90.9 469×1017 11.3 [124] Ga:SnO2 DC magnetron sputtering 200 Quartz 85 3.8 0.021 8.84×1018 0.0146 [129] Eu-doped SnO2 spray pyrolysis 700 Si (100) and glass 70-80 3.68- 3.73 0.02-0.06 9.12×1019
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SnO2 spray pyrolysis 700 Si (100) and glass 70-80 3.68- 3.73 0.02-0.06 9.12×1019 57.1-2.71 [130] Cu2O PLD 100 MgO - - - 1020 90 [140] Cu2O Thermal Evaporation 223 ITO and glass - 2.0 2.74×10-3 2.8×1015 6.1 [142] Table 5: Chalcogen-based materials as p-type TCO and their respective optoelectronic parameters. Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity
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Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility (cm2/V-s) Reference La1-xSrxCuOS RF Sputtering 130 Silica glass >70 3.1 0.26 - - [53] LaCuOS1-x Sex Reactive Solid phase 150 MgO - - 24 ⁓1018 8 [54] Mg-LaCuOSe Reactive Solid phase 40 MgO 70 2.8 140 2.2×1020 3.5 [56] (La1-xSrxO)CuS RF Sputtering 150 SiO2 >60 - 20 - - [56] La1−xYxCuOS Spin coating 250 Quartz ⁓70 3
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RF Sputtering 150 SiO2 >60 - 20 - - [56] La1−xYxCuOS Spin coating 250 Quartz ⁓70 3 89.3 6.6×1020 0.85 [147] La1-xSrxCuOS RF Sputtering 130 Silica glass >70 3.1 0.26 - - [53] Table 6: Cr-based materials as p-type TCO and their respective optoelectronic parameters. Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility
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Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility (cm2/V-s) FOM (μS) Reference Mg,N:Cr2O3 Spray pyrolysis 150 Glass 10-65 3.1 0.06 1019 0.1 7.2 [152] Ni:Cr2O3 PLD 150 Sapphire 40 - 28 - - 110 [154] Cr2O3 PLD 75 Sapphire 80 3.64 0.008 1.93×1018 0.1 0.29 [155] Mg:Cr2O3 PLD 75 Sapphire 70 3.54 0.4 2.04×1018 0.4 8.16 [155] Al:Cr2O3 PLD 75 Sapphire 81 3.59 0.009 1.90×1018 0.11 0.33 [155] Ni:Cr2O3 PLD
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[155] Al:Cr2O3 PLD 75 Sapphire 81 3.59 0.009 1.90×1018 0.11 0.33 [155] Ni:Cr2O3 PLD 75 Sapphire 78 3.49 1.17 7.24×1018 2 34.62 [156] Sr-LaCrO3 MBE 50 STO 42.3 1.9 54 7.5×1021 0.04 3050 [158] La0.75Sr0.25CrO3 Spin coating 45 STO and LAO 67 - 1 - - - [159] Mg,N:Cr2O3 Spray pyrolysis 150 Glass 10-65 3.1 0.06 1019 0.1 7.2 [152] Table 7: Some other oxide materials as p-type TCO and their respective optoelectronic parameters. Material Deposition
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Material Deposition technique used Thickness (nm) Substrate used Average optical Transmittance (%) Optical band gap (eV) Electrical conductivity (S/cm) Carrier conc (/cm3) Hall Mobility (cm2/V-s) FOM (μS) Reference Ca3Co4O9 Spin coating 100 Quartz 67 3 18 - - 151 [163] Bi2Sr2Co2Oy PLD 50 LAO 51 3.14 181.8 5,17×1020 2.2 1350 [166] In2O3-Ag2O RF Sputtering 300 Glass 20 - 113.6 4.2×1019 17 - [167] In2O3-MoO3 Spin coating 80 Glass 80-88 3.8
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Glass 20 - 113.6 4.2×1019 17 - [167] In2O3-MoO3 Spin coating 80 Glass 80-88 3.8 400 2.1×1020 11.9 - [168] V2O3 PLD 7-58 Sapphire 40-78 3.6 400-2122 >1022 0.14-0.24 12992 [169] V2O3 Spray pyrolysis 60 Sapphire 32 - 1079 2.86×1022 0.24 5699 [170] ZnMgAlO Spray Pyrolysis 200 Borosilicate glass 87.1 3.34 1 ⁓1018 3.5 - [171] Cu-Mg (OH)2 Electro- chemical 1000-2000 ITO coated glass 90 4 1×10-5 - - - [172] La1-xSrxVO3 PLD 12 LSAT
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chemical 1000-2000 ITO coated glass 90 4 1×10-5 - - - [172] La1-xSrxVO3 PLD 12 LSAT 53.9–70.1 3.5 742.3–872 1.72×1021 2.1 2507- 6776 [174]
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Ballast charges for semiconductor spin qubits Yujun Choi,1, 2, ∗ John M. Nichol,3 and Edwin Barnes1, 2 1Department of Physics, Virginia Tech, Blacksburg, VA 24061, United States 2Virginia Tech Center for Quantum Information Science and Engineering, Blacksburg, VA 24061, United States 3Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, United States (Dated: May 24, 2024) Semiconductor spin qubits are an attractive platform for quantum computing, but their perfor-
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Semiconductor spin qubits are an attractive platform for quantum computing, but their perfor- mance is degraded primarily by fluctuating electromagnetic environments. We introduce the concept of ballast charges, which are induced charges on the surface of an additional screening layer situated below the qubits. The counteractive behavior of these charges can significantly reduce the power spectral density associated with fluctuations from two-level systems that contribute to charge noise.
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Our simulations show that the dephasing time of a spin qubit in a Si/SiGe device increases by a factor of 4 to 6 on average when using this method. We also discuss the physical implementation and potential challenges of this approach. Introduction — Spin qubits in semiconductor quan- tum dots (QD) are a promising platform for quantum computing [1]. They have reached the fidelities needed for fault-tolerant operation [2–5] and are also compatible with CMOS manufacturing infrastructure [6, 7]. One of
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with CMOS manufacturing infrastructure [6, 7]. One of the main bottlenecks for practical quantum computing with spin qubits is pure dephasing, which typically oc- curs on a time scale that is orders of magnitude shorter than the spin relaxation time [8]. This dephasing is pri- marily due to environmental noise, particularly hyperfine noise from nearby nuclear spins of spinful isotopes and charge noise due to random fluctuations of background charges in QD devices [9]. Charge noise, which typically
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charges in QD devices [9]. Charge noise, which typically has a 1/f power spectrum [10, 11], is the dominant noise source in silicon devices, where isotopic enrichment can significantly reduce the density of spinful isotopes, mit- igating hyperfine noise [12, 13]. The physical origin of charge noise is not yet fully understood [14], but there is evidence that two-level systems (TLSs) associated with charge traps in an oxide layer or on the surface of a semi- conductor layer are responsible [15–17].
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conductor layer are responsible [15–17]. In quantum computing, there are many approaches to combatting environmental noise. One of them is to en- code logical information into many physical qubits uti- lizing quantum error correction codes, which is neces- sary for fault-tolerant quantum computation [18, 19]. More near-term methods involve quantum error miti- gation techniques implemented at the algorithmic level, such as zero-noise extrapolation, probabilistic error can-
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such as zero-noise extrapolation, probabilistic error can- cellation, etc. [20, 21]. Other near-term error mitigation techniques include dynamical decoupling and dynami- cally corrected gates, decoherence-free subspaces, active feedforward loops, and tuning to sweet spots in the pa- rameter space of a particular qubit device [22–25]. In this Letter, we introduce an alternative approach to reducing the effect of charge noise in QD spin qubits that makes use of ballast charges in the device. The con-
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that makes use of ballast charges in the device. The con- cept of ballast charges originates from the idea of ballast water used for maritime vessels. In that context, bal- last water is used to control the buoyant force acting on vessels to improve their stability and maneuverability in various maritime conditions; for example, the loading of heavy ballast water can provide added stability when bad weather is expected [26]. Analogously, our central idea is to use ballast charges to make spin qubits less
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idea is to use ballast charges to make spin qubits less susceptible to charge noise, leading to an increase in the dephasing time of the qubits. The underlying principle of ballast charges relies on electrostatic induction, where in- duced charges are redistributed to counteract the change in electric fields that are external to the charges. Hence, the ballast charges for spin qubits should be a kind of induced charge that can move freely to compensate for the fluctuations of TLSs.
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induced charge that can move freely to compensate for the fluctuations of TLSs. This approach can also be regarded as leveraging the screening effect of additional electrons in the device. A recent experimental study indirectly exhibits the screen- ing effect by adding electrons to a charge sensor close to a QD [27]. Other studies show that the coherence of a spin qubit can be enhanced when the qubit is de- fined with multiple electrons in a QD [28, 29]. In such
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fined with multiple electrons in a QD [28, 29]. In such a scheme, however, we can only expect a small screening effect from induction because the electrons are strongly confined within the QD. Furthermore, the extra electrons complicate gate operations due to the inherent complex- ity (large Hilbert space) of the multi-electron qubit. This suggests that ballast charges should be extrinsic to the QD and to the qubit itself. One possible way to introduce more mobile ballast
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QD and to the qubit itself. One possible way to introduce more mobile ballast charges is to insert a metallic layer below the quantum well (QW) in which the 2D electron gas (2DEG) that is used to form the qubits resides. This is a natural choice in terms of electrostatic induction. Alternatively, an ad- ditional 2DEG can also be used for this purpose, as this would also allow electrons to move freely. For now, we suppose that there is an additional layer in the device
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suppose that there is an additional layer in the device that can host ballast charges, and the merits and draw- backs of different physical implementations will be dis- cussed later. A schematic diagram for ballast charges in a Si/SiGe QD device is shown in Fig. 1(a). A screening layer is arXiv:2405.14027v1 [cond-mat.mes-hall] 22 May 2024 2 QD TLS Ballast charges SiGe SiGe Oxide Gate 𝑥𝑥 𝑧𝑧 TLS SiGe Oxide Gate 𝑥𝑥 𝑧𝑧 Image TLS (a) (b) SiGe SiGe SiGe 𝐵𝐵𝑄𝑄 𝐸𝐸𝑥𝑥 𝐸𝐸𝑧𝑧 QD Si QW 𝑧𝑧 = 0 𝑑𝑑 Si QW
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TLS SiGe Oxide Gate 𝑥𝑥 𝑧𝑧 Image TLS (a) (b) SiGe SiGe SiGe 𝐵𝐵𝑄𝑄 𝐸𝐸𝑥𝑥 𝐸𝐸𝑧𝑧 QD Si QW 𝑧𝑧 = 0 𝑑𝑑 Si QW FIG. 1. Schematic diagrams for ballast charges in a Si/SiGe quantum dot device. (a) Ballast charges are induced charges due to TLSs (red ±) and gate voltages (orange ±). The ballast charges are on the surface of the additional screening layer below thin Si quantum well and SiGe layers. (b) Different viewpoint for ballast charges using the method of image charges. The
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electric fields (Ex and Ez) at the QD position come from TLSs (solid arrows) and their image TLSs (dashed arrows). The diagrams are not to scale. Si cap between the SiGe and oxide layers and micromagnets on top of the gate layer are not shown. inserted below a thin SiGe layer that confines a QD in the Si QW. The QD plane is defined as z = 0, and the distance between the QD plane and the screening layer is d. There are two kinds of ballast charges on the surface of
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d. There are two kinds of ballast charges on the surface of the screening layer: One is due to TLSs (red ±) and the other is due to applied gate voltages (orange ±) where ± denote positive and negative charges on the surface of the screening layer respectively. The ballast charges due to TLSs are the key to the suppression of charge noise since they compensate for the change in electric potential or field at the QD via redistribution. If a TLS is modeled as
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field at the QD via redistribution. If a TLS is modeled as a flipping electric dipole whose position and orientation are fixed, the ballast charges will change their signs as the TLS flips back and forth. The ballast charges due to gate voltages can be taken into account as offsets when calibrating and tuning the device in the first place. The role of ballast charges can be understood by the method of image charges as shown in Fig. 1(b). An im- age TLS corresponding to the TLS in the oxide layer is
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age TLS corresponding to the TLS in the oxide layer is illustrated as dashed red arrows. Assuming the screening layer is much larger than the size of the QD and TLS and exactly located at the QD plane, the horizontal compo- nents of the electric field due to the real and image TLSs perfectly cancel out, while the vertical component is dou- bled. This gives rise to zero detuning noise provided that there is an in-plane external magnetic field (BQ), and the
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there is an in-plane external magnetic field (BQ), and the dominant magnetic field gradients due to micromagnets are ∂BQ/∂x and ∂BQ/∂y. However, this is not what we want, because the qubit cannot be defined due to the equipotential surface along the QD plane. Moreover, it is not possible to make the screening layer at the QD plane in practice. Only partial cancellation of the charge noise will appear when the screening layer is a finite distance away from the QD plane (see Supplemental Material for
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away from the QD plane (see Supplemental Material for an analytical result on this). Results — Examples of simulated power spectral den- sities (PSDs) are shown for the electric potential and the spin qubit precession frequency in Figs. 2(a) and (b), respectively. TLSs are assumed to be at the interface of the oxide and gate layers (z = 50 nm) with random orientations. The orders of magnitude of the PSD for the spin qubit frequency agree well with the experimen-
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The orders of magnitude of the PSD for the spin qubit frequency agree well with the experimen- tal data in Ref. [13]. As expected, the reduction in the PSDs increases as the screening layer is located closer to the QD plane from z = −15 to z = −5 nm. For a 10 nm Si QW, which is a typical width for realistic devices, the PSD for the electric potential is decreased by about two orders of magnitude. If we make thin Si QW and SiGe layers of 5 nm thickness each [27], the PSD can be
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SiGe layers of 5 nm thickness each [27], the PSD can be reduced by about three orders of magnitude. The reduc- tion in the PSD for the spin qubit frequency is less than that for the electric potential, which is about two orders of magnitude for d = 5 nm. This can be attributed to the vector property of compensating electric fields that are more sensitive to the positions and orientations of the image TLSs in the device. The dephasing time of the qubit can be directly com-
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image TLSs in the device. The dephasing time of the qubit can be directly com- puted from the PSD for the spin qubit frequency as- 3 (a) (b) No sc. Sc. at z=-15 nm Sc. at z=-10 nm Sc. at z=-5 nm 10-5 10-4 10-3 10-2 10-1 10-14 10-11 10-8 10-5 PSD (V2/Hz) No sc. Sc. at z=-15 nm Sc. at z=-10 nm Sc. at z=-5 nm 10-5 10-4 10-3 10-2 10-1 107 1010 1013 1016 Frequency (Hz) PSD (Hz2/Hz) FIG. 2. An example of simulated power spectral densities for (a) electric potential and (b) spin qubit frequency for several
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(a) electric potential and (b) spin qubit frequency for several distances d between the QD and screening layer (Sc. at z = −d). The case of no screening layer (No sc.) is also shown. suming Gaussian noise [30]. The dephasing times for no screening, screening at z = −15 nm, z = −10 nm, and z = −5 nm are 2.1, 7.5, 11.7, and 25.2 µs, respectively. This enhancement can be understood from the relation T ∗ 2 ∼ 1/ �� S(ω)dω in the quasistatic limit [27]. The simulation parameters and details are given in the Sup-
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