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

TL;DR

This work demonstrates a planar InSb nanosheet quantum dot strongly coupled to superconductors using a bilayer gate architecture, enabling precise tuning of dot–lead coupling and access to few-electron regimes. Transport reveals large $|g^{*}|$ factors and strong spin–orbit coupling, evidenced by Coulomb diamonds, a Kondo resonance that splits in a magnetic field, and ABS signatures in the superconducting regime. By modulating the coupling, the system exhibits a singlet–doublet quantum phase transition, manifested as ABS crossings evolving to anticrossings, highlighting sub-gap physics and Majorana-relevant phenomena in a 2D platform. These results position InSb nanosheet QDs as a versatile platform for exploring topological superconductivity and Majorana physics in planar architectures, with potential for scalable topological qubits.

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.

Figures (7)

• Figure 1: (a) False-colored scanning electron microscopy image of a QD in an InSb nanosheet. Two lithographically defined metallic gate layers, indicated by pink and orange dashed lines, lie beneath the nanosheet and are separated by $\text{Al}_{2}\text{O}_{3}$ dielectric. These gates are used to define a QD in the InSb nanosheet. The green superconducting contacts (S, D), positioned atop the InSb nanosheet, act as the source and drain electrodes, respectively. (b) Cross-sectional schematic of the layer structure of the nanosheet QD device. (c) Schematic energy diagram of a QD Josephson junction device as studied in (a). $\Delta$ is the superconducting gap, $\varepsilon_{0}$ represents the QD energy level relative to the chemical potential of the right SC $\mu_{s}$, $U$ is the QD charging energy, and $\Gamma_{LB}$ ($\Gamma_{RB}$) is the coupling strength of the QD with left (right) superconducting contact.
• Figure 2: (a) Differential conductance d$I$/d$V$ as a function of source-drain bias $V_{\text{sd}}$ and plunger gate voltage $V_{\text{PG}}$ at $T$ = 25 mK and $B$ = 0 T, showing Coulomb diamonds typical for the electron transport in a few-electron QD. Several white dotted lines have been superimposed to illustrate the onset of inelastic cotunneling. The dash-dotted lines denote the onset of tunneling through an excited state. (b) Source-drain current as a function of the plunger gate voltage $V_{\text{PG}}$ and magnetic field $B$ at $V_{\text{sd}}$ = 1.2 mV. Conductance enhancements are observed in the Coulomb blockade regime along the blue dashed lines. (c) Differential conductance d$I$/d$V$ along the red cut in (a) as a function of magnetic field $B$. The red lines denote fits from a two-level model incorporating the spin-orbit energy $\Delta_{\text{SO}}$.
• Figure 3: (a) Zoom-in of the $N=2n+5$ charge stability diamond in Figure 2(a) at zero magnetic field, which clearly reveals the spin-1/2 Kondo effect. (b) Kondo ridge at zero bias corresponding to (a). (c) Corresponding charge stability diamond measured at an in-plane magnetic field $B$ = 0.3 T, taken with respect to (a). (d) Differential conductance evolution in the Kondo regime as a function of an in-plane magnetic field at $V_{\text{PG}}$ = 1.71 V. The dashed line represents a linear fit to the maxima of the differential conductance for $B > 0.05$ T, which is used to extract the effective $g$-factor. (e) Kondo peak evolution as a function of temperature at $V_{\text{PG}}$ = 1.697 V. (f) Kondo peak conductance value as a function of temperature $T$ for different plunger gate voltages within the same Coulomb diamond. Solid circles represent the experimental data, while solid lines indicate the corresponding fits, yielding fitting Kondo temperatures of $T_{K} = 1.04$, $0.94$, and $1.06$ K for $V_{\text{PG}} = 1.688$, $1.697$, and $1.706$ V, respectively. The bottom-left schematic inset indicates the corresponding positions of the three plunger gate voltages within the Coulomb diamond.
• Figure 4: (a) Phase diagram of superconductor-coupled QD. (b) Schematic of the ABS spectroscopy measurements. A soft induced gap in the left probe is taken into account, resulting in a finite quasiparticle density of states near the Fermi level. (c) Source-drain current as a function of plunger gate voltage $V_{\text{PG}}$ and right barrier gate voltage $V_{\text{RB}}$ at a small bias $V_{\text{sd}} = 17.5~\mu V$, with $V_{\text{LB}}$ fixed at -0.2 V. (d) Voltage bias spectroscopy along four different $V_{\text{RB}}$ cuts in (c). The black dashed curves are guides for the crossing behavior of two ABSs resonances.
• Figure S1: Schematics of the measurement circuit setup for the voltage-biased configuration. The region enclosed by the dashed line denotes a voltage divider.