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Register a new userZeeman tunability of Andreev bound states in van-der-Waals tunnel barriers
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Quantum dots proximity-coupled to superconductors are attractive research platforms due to the intricate interplay between the single-electron nature of the dot and the many body nature of the superconducting state. These have been studied mostly using nanowires and carbon nanotubes, which allow a combination of tunability and proximity. Here we report a new type of quantum dot which allows proximity to a broad range superconducting systems. The dots are realized as embedded defects within semiconducting tunnel barriers in van-der-Waals layers. By placing such layers on top of thin NbSe$_2$, we can probe the Andreev bound state spectra of such dots up to high in-plane magnetic fields without observing effects of a diminishing superconducting gap. As tunnel junctions defined on NbSe$_2$ have a hard gap, we can map the sub-gap spectra without background related to the rest of the junction. We find that the proximitized defect states invariably have a singlet ground state, manifest in the Zeeman splitting of the sub-gap excitation. We also find, in some cases, bound states which converge to zero energy and remain there. We discuss the role of the spin-orbit term, present both in the barrier and the superconductor, in the realization of such topologically trivial zero-energy states.
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We study Andreev reflection and Andreev levels $varepsilon$ in Zeeman-split superconductor/Rashba wire/Zeeman-split superconductor junctions by solving the Bogoliubov de-Gennes equation. We theoretically demonstrate that the Andreev levels $varepsilon$ can be controlled by tuning either the strength of Rashba spin-orbit interaction or the relative direction of the Rashba spin-orbit interaction and the Zeeman field. In particular, it is found that the magnitude of the band splitting is tunable by the strength of the Rashba spin-orbit interaction and the rength of the wire, which can be interpreted by a spin precession in the Rashba wire. We also find that if the Zeeman field in the superconductor has the component parallel to the direction of the junction, the $varepsilon$-$phi$ curve becomes asymmetric with respect to the superconducting phase difference $phi$. Whereas the Andreev reflection processes associated with each pseudospin band are sensitive to the relative orientation of the spin-orbit field and the exchange field, the total electric conductance interestingly remains invariant.
Tunnel junctions, a well-established platform for high-resolution spectroscopy of superconductors, require defect-free insulating barriers with clean engagement to metals on both sides. Extending the range of materials accessible to tunnel junction fabrication, beyond the limited selection which allows high-quality oxide formation, requires the development of alternative fabrication techniques. Here we show that van-der-Waals (vdW) tunnel barriers, fabricated by stacking layered semiconductors on top of the transition metal dichalcogenide (TMD) superconductor NbSe$_2$, sustain a stable, low noise tunneling current, and exhibit strong suppression of sub-gap tunneling. We utilize the technique to measure the spectra of bulk (20 nm) and ultrathin (3- and 4-layer) devices at 70 mK. The spectra exhibit two distinct energy gaps, the larger of which decreases monotonously with thickness and $T_C$, in agreement with BCS theory. The spectra are analyzed using a two-band model modified to account for depairing. We show that in the bulk, the smaller gap exhibits strong depairing in an in-plane magnetic field, consistent with a high Fermi velocity. In the few-layer devices, depairing of the large gap is negligible, consistent with out-of-plane spin-locking due to Ising spin-orbit coupling. Our results demonstrate the utility of vdW tunnel junctions in mapping the intricate spectral evolution of TMD superconductors over a range of magnetic fields.
In transition metal dichalcogenides, defects have been found to play an important role, affecting doping, spin-valley relaxation dynamics, and assisting in proximity effects of spin-orbit coupling. Here, we study localized states in $mathrm{WS}_2$ and how they affect tunneling through van der Waals heterostructures of h-BN/graphene/$mathrm{WS}_2$/metal. The obtained conductance maps as a function of bias and gate voltage reveal single-electron transistor behavior (Coulomb blockade) with a rich set of transport features including excited states and negative differential resistance regimes. Applying a perpendicular magnetic field, we observe a shift in the energies of the quantum levels and information about the orbital magnetic moment of the localized states is extracted.
We calcuate electronic spin susceptibility and spin-lattice relaxation rate in singlet superconductor near a pairbreaking surface, or in a domain wall of the order parameter. We directly link presence of high-density Andreev bound states in the inhomogeneous region, combined with coherence factors, to enhancement of the susceptibility above the normal states value for certain $bf q$ vectors. Beside the dominant peak at ferromagnetic vector $q=0$, we find significant enhancement of antiferromagnetic correlations at vectors $qlesssim 2 k_f$, with $bf q$ $along$ the domain wall in $S$-wave superconductor, and $across$ domain wall in $D$-wave (nodes along the wall). These features are destroyed by applying moderate Zeeman field that splits the zero-energy peak. We solve Bogoliubov-de Gennes equations in momentum space and our results deviate from the lattice models investigated previously. Large enhancement of the spin-lattice relaxation rate $T_1^{-1}$ at the domain wall provides clear signature of the quasiparticle bound states, and is in good agreement with recent experiment in organic superconductor $kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$.
The interest in ferroelectric van der Waals crystals arises from the potential to realize ultrathin ferroic systems owing to the reduced surface energy of these materials and the layered structure that allows for exfoliation. Here, we quantitatively unravel giant negative electrostriction of van der Waals layered copper indium thiophosphate (CIPS), which exhibits an electrostrictive coefficient Q33 as high as -3.2 m4/C2 and a resulting bulk piezoelectric coefficient d33 up to -85 pm/V. As a result, the electromechanical response of CIPS is comparable in magnitude to established perovskite ferroelectrics despite possessing a much smaller spontaneous polarization of only a few uC/cm2. In the paraelectric state, readily accessible owing to low transition temperatures, CIPS exhibits large dielectric tunability, similar to widely-used barium strontium titanate, and as a result both giant and continuously tunable electromechanical response. The persistence of electrostrictive and tunable responses in the paraelectric state indicates that even few layer films or nanoparticles will sustain significant electromechanical functionality, offsetting the inevitable suppression of ferroelectric properties in the nanoscale limit. These findings can likely be extended to other ferroelectric transition metal thiophosphates and (quasi-) two-dimensional materials and might facilitate the quest towards novel ultrathin functional devices incorporating electromechanical response.
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