Characterization of dot-specific and tunable effective $g$ factors in a GaAs/AlGaAs double quantum dot single-hole device

A. Padawer-Blatt, J. Ducatel, M. Korkusinski, A. Bogan, L. Gaudreau, P. Zawadzki, D. G. Austing, A. S. Sachrajda, S. Studenikin, L. Tracy, J. Reno, and T. Hargett

Phys. Rev. B 105, 195305 – Published 11 May 2022

Abstract

Difference in $g$ factors in multidot structures can form the basis of dot-selective spin manipulation under global microwave irradiation. Employing electric dipole spin resonance facilitated by strong spin-orbit interaction (SOI), we observe differences in the extracted values of the single-hole effective $g$ factors of the constituent quantum dots of a GaAs/AlGaAs double quantum dot device at the level of $\sim 5 % - 10 %$ . We examine the continuous change in the hole $g$ factor with electrical detuning over a wide range of interdot tunnel couplings and for different out-of-plane magnetic fields. The observed tendency of the quantum dot effective $g$ factors to steadily increase on decreasing the interdot coupling or on increasing the magnetic field is attributed to the impact on the SOI of changing the dot confinement potential and heavy-hole light-hole mixing.

Received 12 November 2021
Revised 3 March 2022
Accepted 25 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.195305

Physics Subject Headings (PhySH)

Quantum information architectures & platforms Spin blockade Spin-orbit coupling

III-V semiconductors Quantum dots

Electron spin resonance

Quantum Information, Science & Technology

Authors & Affiliations

A. Padawer-Blatt and J. Ducatel

Emerging Technologies Division, National Research Council of Canada, Ottawa, Ontario, Canada K1A0R6 and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

M. Korkusinski, A. Bogan, L. Gaudreau, P. Zawadzki, D. G. Austing, A. S. Sachrajda, and S. Studenikin ^*

Emerging Technologies Division, National Research Council of Canada, Ottawa, Ontario, Canada K1A0R6

L. Tracy

Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

J. Reno and T. Hargett

Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

^*Author to whom correspondence should be addressed: sergei.studenikin@nrc-cnrc.gc.ca

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Vol. 105, Iss. 19 — 15 May 2022

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Figure 1
(a) Scanning electron micrograph of DQD device. A global top gate on an insulating material is also present (not shown). Voltages $V_{L}$ and $V_{R}$ , respectively, on the left (L) and right (R) plunger gates regulate the number of holes on the left and right QDs. Voltage $V_{C}$ on the center (C) gate controls the interdot coupling. The crossed boxes represent Ohmic contacts. Current $I$ flows through the DQD in response to an applied source-drain bias $V_{SD}$ . Microwaves (MWs) are applied to the right plunger gate. Scale bar: 500 nm. (b) Schematic showing quantum molecular levels when system is in an energy blockaded condition in the absence of MWs. MW modulation is shown as exciting a spin-down hole trapped predominantly on the right QD onto the first excited state, spin-up also predominantly on the right QD, from where the hole can exit to the drain (D). (c) Single-hole high-bias transport triangle for weak interdot coupling (condition WC1) at $B = 1.8$ T with MWs applied at frequency $f = 35.3$ GHz and power $P = - 12$ dBm. $d I / d V_{L}$ , in arbitrary units, is plotted as a function of $V_{L}$ and $V_{R}$ , and $V_{SD} = - 0.5$ mV which corresponds to holes flowing from left to right in (b). The dotted line identifies the base of the bias triangle. The black arrow (asterisk) marks the EDSR signal for positive (negative) detuning $ɛ$ . In subsequent measurements $V_{L}$ and $V_{R}$ are simultaneously scanned so as to sweep $ɛ$ and cut through the EDSR features outside of the bias triangle—see dashed arrow, for example. (d) Calculated eigenenergies as a function of detuning for model parameters $B = 2.0$ T, $t_{N} = 16.7 μ eV, t_{F} = 13.0 μ eV, g_{L}^{*} = 0.8$ , and $g_{R}^{*} = 1.6$ . GS, ES1, ES2, and ES3 correspond, respectively, to the ground and first three excited states. Black (red) identifies spin-down (spin-up). Green (blue) vertical lines identify examples of predominantly spin excitations in the left (right) QD. In the vicinity of the ES1-ES2 anticrossings the spin is hybrid spin-up and spin-down, and transitions from GS are hybrid spin-charge transitions. We stress that for illustration we have grossly exaggerated the difference in g factor between the two dots. The actual difference is typically 5%–10%. Note in (b) and (d), and henceforth in this article, for convenience, the positive direction of the energy axis corresponds to increasing hole energies.
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Figure 2
(a) Frequency $f$ dependence of the measured EDSR signal in $d I / d ɛ$ (arbitrary units) as a function of detuning $ɛ$ for intermediate interdot coupling (condition IC1) at $B = 2.0$ T and $V_{SD} = + 1$ mV. Two branches corresponding to the $G S \to E S 1$ and $G S \to E S 2$ MW excitations are visible. The plot is built up from three adjoining blocks of data captured consecutively: The MW power is stepped up from $- 20$ to $- 15$ dBm at $f = 15$ GHz and then finally to $- 6$ dBm at $f = 22$ GHz. (b) Frequency dependence of extracted EDSR peak position as a function of detuning for strong interdot coupling (condition SC) at $B = 2.0$ T and $V_{SD} = + 1$ mV. $P$ is set to 0 dBm. Only points for the $G S \to E S 1$ branch could be extracted (the $G S \to E S 2$ branch is out of range). (c) Frequency dependence of EDSR peak position as a function of detuning for intermediate interdot coupling (condition IC1) extracted from the plot in (a). Data points for the $G S \to E S 1$ ( $G S \to E S 2$ ) branch are colored blue (red). (d) Frequency dependence of extracted EDSR peak position as a function of detuning for weak interdot coupling (condition WC1) at $B = 2.0$ T and $V_{SD} = - 0.5$ mV. $P$ is set to $- 28$ ( $- 12$ ) dBm below (above) 23 GHz. For (b)–(d), blue and red dashed lines are fits to the data according to the two– $g$ -factor model. The fitted values for $g_{L}^{*}$ and $g_{R}^{*}$ are also indicated, and for convenience, a right axis scale is included to show directly $g_{eff} = h f / μ_{B} B$ .
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Figure 3
Frequency dependence of extracted EDSR peak position as a function of detuning for interdot coupling conditions: (a) IC2 at $B = 1.8$ T and $V_{SD} = + 0.5$ mV ( $P = - 12$ dBm); (b) WC1 at $B = 1.8$ T and $V_{SD} = - 0.5$ mV ( $P = - 12$ dBm); and (c) WC2 at $B = 1.864$ T and $V + SD = - 0.5$ mV ( $P = - 5$ dBm). Of these three coupling conditions, IC2 (WC2) is the strongest (weakest). Data points for the $G S \to E S 1$ ( $G S \to E S 2$ ) branch are colored blue (red). For (a) and (b), blue and red dashed lines are fits to the data according to the two– $g$ -factor model. For (c), a fit to the data with the two– $g$ -factor model could not be reliably obtained. The fitted [estimated] values for $g_{L}^{*}$ and $g_{R}^{*}$ in (a) and (b) [(c)] are also indicated, and for convenience, a right axis scale is included to show directly $g_{eff}$ .
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Figure 4
Compilation of (a) tunneling elements $t_{N}$ (black symbols) and $t_{F}$ (red symbols), and (b) left QD $g$ factor $g_{L}^{*}$ extracted from the two– $g$ -factor model for strong (SC, squares), intermediate (IC1, circles), and weak (WC1, triangles) interdot coupling conditions as a function of magnetic field. MW power and source-drain voltage conditions may differ for data points at a given interdot coupling condition. Also, for IC1, the compilations consist of overlapping data sets.
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