Selective tuning of spin-orbital Kondo contributions in parallel-coupled quantum dots

Open Access

Selective tuning of spin-orbital Kondo contributions in parallel-coupled quantum dots

Heidi Potts, Martin Leijnse, Adam Burke, Malin Nilsson, Sebastian Lehmann, Kimberly A. Dick, and Claes Thelander

Phys. Rev. B 101, 115429 – Published 30 March 2020

Abstract

We use cotunneling spectroscopy to investigate spin, orbital, and spin-orbital Kondo transport in a strongly confined system of InAs double quantum dots that are parallel coupled to source and drain. In the one-electron transport regime, the higher-symmetry spin-orbital Kondo effect manifests at orbital degeneracy and no external magnetic field. We then proceed to show that the individual Kondo contributions can be isolated and studied separately: either by orbital detuning in the case of spin Kondo transport or by spin splitting in the case of orbital Kondo transport. By varying the interdot tunnel coupling, we show that lifting of the spin degeneracy is key to confirming the presence of an orbital degeneracy and to detecting a small orbital hybridization gap. Finally, in the two-electron regime, we show that the presence of a spin-triplet ground state results in spin Kondo transport at zero magnetic field.

Received 11 December 2019
Accepted 9 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.115429

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Kondo effect

Double quantum dots

Scanning electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Heidi Potts ^1,*, Martin Leijnse¹, Adam Burke ¹, Malin Nilsson¹, Sebastian Lehmann¹, Kimberly A. Dick^1,2, and Claes Thelander^1,†

¹Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
²Centre for Analysis and Synthesis, Lund University, SE-221 00 Lund, Sweden

^*heidi.potts@ftf.lth.se
^†claes.thelander@ftf.lth.se

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 101, Iss. 11 — 15 March 2020

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Top: Schematic of the nanowire and conduction-band alignment. Bottom: $45^{\circ}$ tilted SEM image of a representative device. (b) Conductance ( $G$ ) as a function of sidegate voltages at $B$ = 1 T. The electron populations on the left and right QD ( $N_{left}, N_{right}$ ) after subtracting $2 N$ electrons are indicated. Important gate vectors are shown in red, green, and orange.
Reuse & Permissions
Figure 2
Spin-orbital and isolated orbital Kondo transport in the one-electron regime. (a) Measurement of $d I / d V_{sd}$ vs $V_{sd}$ along the green gate vector indicated in Fig. 1 for $B = 0$ . A zero-bias peak can be observed in the $1 e, 2 e$ , and $3 e$ regimes. (b) Corresponding measurement in the $1 e$ regime when detuning the orbitals along the red gate vector. The dashed lines represent the sidegate voltages where the temperature sweeps are performed. (c) Schematic representation of the electron energy levels and resulting onset of cotunneling when detuning the QD orbitals (assuming $t = 0$ ). (d) Temperature dependence of the zero-bias conductance peak at orbital degeneracy. Blue and dashed black lines show the fit using Eq. (1) and the parameters for SU(2) and SU(4) Kondo scaling, respectively. (e) Temperature dependence and SU(2) Kondo fit of the zero-bias conductance peak in the (0,1) state. (f)–(i) Corresponding measurements and schematic for $B = 1 T$ . The spin degeneracy is lifted, but the orbital degeneracy at zero detuning in the $1 e$ regime remains. (j) Same as (f), but for different temperatures (only $1 e$ regime). (k) Conductance as a function of sidegate voltages $(V_{sd} = 25 μ V)$ for 70 mK and 1 K ( $1 e$ regime).
Reuse & Permissions
Figure 3
The effect of a finite tunnel coupling between the QDs in another orbital crossing. (a) Overview measurement with the electron number on the left and right QD ( $N_{left}, N_{right}$ ) indicated. (b),(c) Measurement of $d I / d V_{sd}$ vs $V_{sd}$ recorded along the pink gate vector at $B = 0 T$ and $B = 1 T$ . (d) Schematic representation of the energy levels and resulting onset of cotunneling when detuning the QD orbitals, assuming finite tunnel coupling between the two QD levels.
Reuse & Permissions
Figure 4
Kondo transport in the two-electron regime. (a) Measurement of $d I / d V_{sd}$ vs $V_{sd}$ recorded along the orange gate vector at $B = 0 T$ , showing a Kondo resonance in (1,1). (b) Corresponding measurement at $B = 1 T$ . The ground-state degeneracy is lifted and an additional onset of cotunneling is observed with an energy of $\sim 350 μ eV$ higher than the first-excited state. (c) Magnetic field sweep in the center of (1,1). (d) Schematic representation of the $2 e$ state energies and resulting onset of cotunneling as a function of the $B$ field. The triplet GS Zeeman splits into $T_{+}, T_{0}$ , and $T_{-}$ . At finite $B$ field, $T_{+}$ is the GS, and we observe transitions to $T_{0}$ and to the singlet state $S$ . (e) Temperature dependence of the zero-bias conductance peak in the center of (1,1) at $B = 0 T$ .
Reuse & Permissions
Figure 5
(a) Conductance as a function of sidegate voltages. The red and green squares indicate the orbital crossings that are studied. (b) Magnified conductance plot of the red orbital crossing, where relevant gate vectors are indicated. (c) Differential conductance vs source-drain voltage recorded along the red gate vector at $B = 1 T$ . (d) Differential conductance as a function of voltage across the device measured at the sidegate voltages corresponding to the dashed line in (c). The data are fitted with Eq. (B1) [44]. (e),(f) Transport recorded in the $3 e$ regime along the cyan gate vector at $B = 0 T$ and $B = 1 T$ , respectively. (g) Conductance $G$ at zero bias along the green gate vector. (h) Schematic representation of the orbital crossing and the different transport mechanisms at $B = 0 T$ .
Reuse & Permissions
Figure 6
(a) Differential conductance vs source-drain voltage as a function of gate vector through the unperturbed left and right QD levels [solid and dashed orange gate vector in Fig. 5] for $B = 0 T$ . (c) Corresponding measurement along the yellow gate vector for $B = 1 T$ . (d),(e) Conductance as a function of gate voltage for sequential tunneling through the left and right QD [purple and pink gate vector in Fig. 5]. The data is fitted using Eq. (D1) to extract $Γ$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics