Spin splitting, Kondo correlation and singlet-doublet quantum phase transition in a superconductor-coupled InSb nanosheet quantum dot

Abstract: We realize a superconductor-coupled quantum dot (QD) in an InSb nanosheet, a 2D platform promising for studies of topological superconductivity. The device consists of a superconductor-QD-superconductor junction, where a bottom bilayer gate defines the QD and allows tuning of its coupling to the superconducting leads. The QD exhibits large $g$-factors and strong spin-orbit coupling. Transport measurements reveal Coulomb diamond-shaped differential conductance features with even-odd alternating sizes and pronounced conductance lines associated with the superconducting gap, confirming a few-electron, superconductor-coupled regime. At an odd electron occupation, Kondo signatures emerge, including a zero-bias peak that splits with magnetic field and is logarithmically suppressed at elevated temperatures. We further observe a doublet-singlet quantum phase transition, manifested by a clear change of Andreev bound states from crossing to anticrossing as the coupling strength increases. These results underscore the rich physics of InSb nanosheet QDs and their promise for topological quantum devices.

• The paper demonstrates the fabrication and transport characterization of a superconductor-coupled InSb nanosheet QD, showing clear Coulomb blockade and quantum confinement effects.
• The study quantifies spin splitting with variable g-factors, robust Kondo resonances, and spin-orbit induced level mixing using magnetic field and temperature-dependent measurements.
• The work uncovers gate-tunable singlet-doublet quantum phase transitions via Andreev bound state spectroscopy, highlighting its potential for topological quantum device engineering.

Spin Splitting, Kondo Correlation, and Singlet-Doublet Quantum Phase Transition in a Superconductor-Coupled InSb Nanosheet Quantum Dot

Introduction and Motivation

Quantum dots (QDs) in proximity to superconductors have gained attention as building blocks for topological quantum devices, largely due to their pivotal role in realizing Majorana zero modes and facilitating quantum information readout in configurations such as Josephson junctions and artificial Kitaev chains. Materials exhibiting strong spin-orbit coupling (SOC) and sizable $g$-factors, notably InSb, are crucial for these applications. While prior research has primarily focused on InSb nanowire QDs, this paper (2602.06573) demonstrates the realization and comprehensive transport characterization of a superconductor-coupled QD in an InSb nanosheet—a two-dimensional platform offering superior geometric versatility for topological circuitry.

Device Architecture and Fabrication

The device architecture is centered on a bilayer electrostatic gate stack patterned on a Si/SiO$_2$ substrate, with an InSb nanosheet transferred atop for QD formation. Superconducting Ti/Al electrodes are deposited on this sheet, yielding a QD Josephson junction. The bilayer gate configuration affords advanced control over QD confinement and coupling, enabling exploration of the few-electron regime with high fidelity. Importantly, the fabrication avoids processing steps directly on the InSb nanosheet, mitigating interface deterioration and preserving material quality.

Figure 1: False-colored SEM and schematic cross-section of the InSb nanosheet QD device, highlighting the bilayer gate stack and superconducting contacts.

Transport Signatures: Coulomb Blockade, Spin Splitting, and Spin-Orbit Coupling

Low-temperature transport measurements reveal Coulomb diamonds with distinct even-odd alternation, indicative of few-electron regimes and strong electron-electron interactions. The extracted charging energy ($U \sim 4.4$ meV) and lever arm ($\alpha \sim 0.08$) align with expectations for highly confined systems. Magnetic field sweeps allow extraction of quantum level-dependent $g$-factors ($|g_1^*|=32$, $|g_2^*|=40$, $|g_3^*|=55$), with variances attributed to SOC-induced level mixing.

Figure 2: Transport spectroscopy showing Coulomb diamonds, magnetic-field-induced peak splitting, and anticrossing attributed to spin-orbit interactions.

An anticrossing between ground and excited states, observed in field-dependent conductance, enables quantification of the spin-orbit energy ($\Delta_{\text{SO}} = 186\,\mu$eV), notably smaller than the mean level spacing ($\Delta E = 2.4$ meV), yet sufficient to induce sizable $g$-factor fluctuations across levels.

Kondo Physics in Superconductor-Coupled InSb QDs

The odd-electron Coulomb diamonds exhibit robust Kondo resonances—a hallmark of spin-1/2 impurity screening in the presence of strong electron correlations. A zero-bias Kondo ridge is detected, splitting linearly with magnetic field, and suppressed at elevated temperatures ($T > 0.45$ K). Fitting to empirical scaling yields Kondo temperatures ($T_{K}$) on the order of $0.94$–$1.06$ K within a single diamond, with higher $T_{K}$ near charge-degeneracy points.

Figure 3: Detailed spectroscopy of Kondo ridges, magnetic-field-induced splitting, and temperature-dependent conductance showing logarithmic suppression characteristic of Kondo physics.

Additionally, an integer-spin Kondo-like enhancement is observed in adjacent diamonds upon increased field, suggesting transition to an $S=1$ spin-triplet configuration under the Zeeman effect.

Singlet-Doublet Quantum Phase Transition and Andreev Spectroscopy

Modulation of superconductor-QD coupling strength ($\Gamma$) via gate voltage resolves signatures of a quantum phase transition between doublet ($S=1/2$) and singlet ($S=0$) ground states, as predicted by theory for intermediate occupation ($-1 < \varepsilon_0/U < 0$). Andreev bound state (ABS) spectroscopy, employing a soft-gap probe, reveals bias resonance loop structures crossing at zero energy, which shrink and ultimately anticross as $\Gamma$ increases. The phase diagram demarcates domains of singlet and doublet ground states directly linked to subgap ABS crossings.

Figure 4: Phase diagram and ABS spectroscopy; bias resonance loops highlight singlet-doublet transition and evolution as coupling strength is tuned.

The soft-gap nature, often attributed to nonideal superconductor-semiconductor interfaces, remains a persistent obstacle. In situ epitaxial contacts, previously shown to induce hard gaps, are proposed as a future optimization strategy.

Implications and Outlook

The demonstrated ability to engineer and probe superconductor-coupled QDs with large $g$-factors, strong SOC, and gate-tunable coupling in planar InSb platforms enables systematic exploration of correlated mesoscopic phenomena, including Kondo screening, quantum phase transitions, and subgap bound-state physics. These advancements are relevant not only for topological quantum computation schemes leveraging Majorana zero modes but also for operational refinement of multiterminal Josephson junctions and phase-tuned superconducting networks.

Theoretical models governing ABS structure and ground-state transitions in hybrid QDs are corroborated by empirical spectroscopic signatures, reinforcing the practical and conceptual links between mesoscopic physics and topological device engineering. Future work will likely focus on interface engineering to achieve hard superconducting gaps, integration of nanosheet QDs into complex circuit architectures, and detailed exploration of Majorana signatures in multiterminal geometries.

Conclusion

This paper reports the successful realization and characterization of a superconductor-coupled QD in a planar InSb nanosheet. Key findings include large and fluctuating $g$-factors, clear SOC-induced level mixing, Kondo correlations (spin-1/2 and integer-spin), and gate-tunable singlet-doublet phase transitions probed via ABS spectroscopy. The results substantiate InSb nanosheets as promising platforms for the next generation of topological quantum devices, with practical and theoretical implications for quantum computation and mesoscopic condensed matter physics.