Magnetic-Field-Independent Subgap States in Hybrid Rashba Nanowires

Subgap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically nontrivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete subgap states in a long nanowire segment. In addition to subgap states with a standard magnetic field dependence, we find topologically trivial subgap states that are independent of the external magnetic field, i.e., that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates. This result constitutes an important step forward in the research on superconducting subgap states in nanowires, such as Majorana bound states.

Figure 1

(a) Energy diagram of the considered system, with a quantum dot (QD), a lead segment (LS) with discrete energy levels strongly coupled to a superconducting (SC) and a normal metal electrode (N). (b) False color scanning electron micrograph of a representative device, showing an zincblende InAs nanowire with an integrated QD (red) between two wurtzite tunnel barriers (green), located ${\ell }_{\mathrm{LS}}\approx 220\mathrm{nm}$ from SC (scale bar: 100 nm). The measurement setup is shown schematically on top. The external magnetic field, $B$, is applied perpendicular to the substrate. (c) Differential conductance, $G$, as a function of the backgate voltage, $V_{\mathrm{BG}}$, and the voltage bias, $V_{\mathrm{SD}}$, in the normal state ($B=50\mathrm{mT}$). LS resonances inside the Coulomb blockade diamonds of the QD are pointed out by white arrows, QD excited states (ES) by green arrows.

Figure 2

(a) $G$ vs $V_{\mathrm{BG}}$ and $V_{\mathrm{SD}}$ in the normal state ($B=50\mathrm{mT}$) and (b) in the superconducting state ($B=0$). QD resonances are indicated by red arrows and LS resonances by blue arrows in (a). White dashed lines are guides to the eye for the LS conductance features. (c)–(f) Detailed measurements of the regions labeled in (a) and (b), including cross sections at the constant $V_{\mathrm{BG}}$ indicated by a blue arrow.

Figure 3

$G$ vs $B$ and $V_{\mathrm{SD}}$ for (a) region $B$ ($V_{\mathrm{BG},B}=-6.418\mathrm{V}$) and (c) region $C$ ($V_{\mathrm{BG},C}=-6.312\mathrm{V}$). The dashed blue and red lines are the superimposed model spectra. (b) and (d) show waterfall plots of the same data. In both regions we find a subgap resonance at a constant energy $\pm E_1$, independent of $B$.

Figure 4

Schematic of the spin texture for a given injected spin for (a) a noncommensurate, ${\ell }_{\mathrm{LS}}<{\ell }_{\mathrm{so}}$, and (b) a commensurate case, ${\ell }_{\mathrm{LS}}={\ell }_{\mathrm{so}}$, in a NW LS of length ${\ell }_{\mathrm{LS}}$. (c),(e) Calculated spectra as a function of $B$ and $V_{\mathrm{SD}}$ for a commensurate case, reproducing the characteristics of (c) region $B$ at chemical potential ${\mu }_1$ and (e) for region $C$ at ${\mu }_2={\mu }_1+\mathrm{\Delta }\mu$, respectively. In the calculations, the chemical potentials are chosen as ${\mu }_{\mathrm{SC}}=100\mathrm{meV}$, ${\mu }_1=10.8\mathrm{meV}$, and ${\mu }_2=11.2\mathrm{meV}$. In both cases a subgap state is pinned to a constant energy $\pm E_1$, independent of $B$. Panels (d) and (f) show waterfall plots of the calculated DOS at the respective chemical potential using a resonance broadening of $40\mu \mathrm{eV}$.