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Engineered Topological Superconductivity in van der Waals Heterostructures

Periodic Reporting for period 4 - TopSupra (Engineered Topological Superconductivity in van der Waals Heterostructures)

Reporting period: 2023-01-01 to 2023-12-31

The ERC-Project “Engineered Topological Superconductivity in van der Waals Heterostructures” (TopSupra) addresses two aspects of high interest: topological matter and two-dimensional (2D) van der Waals (vdW) materials.
Topological matter is a young research theme with great perspectives. A topological insulator (TI) is a “strange” insulator with an inverted “negative” bandgap. Since the bandgap must be positive for the vacuum, it must cross zero at the surface. A characteristic feature of a TI is, therefore, a conducting surface state.

Alike a TI, a topological superconductor (TSC) is also gapped in the bulk and has a special surface state, which is pinned to zero-energy due to electron-hole symmetry. The in-gap quasiparticles live at zero energy and carry neither charge nor spin. But they have a special “non-Abelian” exchange statistics that can be used for quantum computing. Although first indications of a TSC were reported in 1D systems, TopSupra aimed to search for evidence for a TSC in vdW heterostructures.

This platform builds on graphene, a 2D material that is obtained by exfoliating graphite down to the monolayer (ML). It can be combined with other layered materials by stacking 2D materials on top of each other to realize heterostructures with novel properties. The technology of stacking different 2D layers together has been developed to such a perfection that also arbitrarily twisted heterostructures are studied today.

In TopSupra a large fraction of activity was devoted to searching for the fractional Josephson effect (FJE). The FJE can appear in Josephson junctions (JJs) made from TSCs. While there are multiple claims of evidence for the FJE in contemporary literature based on missing odd Shapiro steps, we could show that missing Shapiro steps can be generated even in the most basics non-topological JJ. Further on, we have conducted an intensive search for the fractional AC radiation. Although we have tested a series of potential candidates for a TSC we have not observed any evidence for the FJE. However, we often find signals at frequencies expected for the FJE due to spurious resonances that form in the environment: Phys. Rev. B 108, 94514 (2023).

In our studies of different vdW materials that are supposedly TIs, we have found one material that provided the largest degree of evidence for “topology”. This is WTe2. While MLs of WTe2 are QSH insulators, the few layers variant is a Weyl semimetal. In TopSupra we discovered strong edge currents, a breaking of inversion symmetry, and a surprisingly robust long distant supercurrent which led us to speculate that few-layer WTe2 may be a higher-order topological insulator (HOTI): “One-dimensional edge transport in few-layer WTe2”, Nano Lett. 20, 4228 (2020) and follow-up papers, J. of Appl. Phys. 129, 113903 (2021), Phys. Rev. Mat. 6, L081201 (2022), and “Current-phase relation of WTe2 Josephson JJs”, Nano Lett. 23, 4654 (2023).

Further on, we reported on the superconducting diode effect: Phys. Rev. Res. 5, 33131 (2023) and on “Charge-4e supercurrent in an InAs-Al superconductor-semiconductor heterostructure”, Comm. Phys. 7, 41 (2024).

Most recently, we were able to realize superconducting devices in magic-angle twisted trilayers of graphene. We measured the kinetic inductance in the intrinsic superconducting phase and found a huge value exceeding the highest known values by up to two orders of magnitude.

The project took quite a different path than initially anticipated. As time passed on, I got more and more skeptical regarding claims of topological superconductivity. I would also like to stress that a conventional shorter-term funding would not have allowed me to research to the same depth.
The goal of TopSupra was to engineer topological superconductivity in 2D vdW materials. We have proposed to proceed along five axes:

1. To take a 2D vdW superconductor (SC) with large intrinsic spin-orbit interaction, and
2. a known 2D vdW topological insulator (TI) and combine it with a SC.
3. To engineer a synthetic TI in a double-layer graphene stack.
4. To obtain new states in 2D vdW materials by controlling strain, and
5. to induce a topological phase by dressing the 2D electron-bands by optical light.

We have done significant work on all 1-5 axes, but also dived into new directions. An important new direction was the upcoming magic-angle twisted graphene, in which superconductivity appeared for certain twist angles “magically”. The materials that we researched on were different types of 2D van der Waals (vdW) material stacks consisting of graphene, MoS2, WSe2, WTe2, NbSe2, BN, Cd3As2 and a few other materials not of vdW type. We combined these materials with normal-metal and superconducting contacts, such as CrAu edge contacts, sputtered MoRe and Pd/Pt and encapsulated them where necessary to protect the devices from oxidation.
We mention a couple of highlights:

1. The discovery of the super-superlattice in encapsulated graphene, Nano Lett. 19, 2371 (2019), also highlighted in our university news.

2. The discovery of long-distance edge currents in few layers of WTe2, Nano Lett. 20, 4228 (2020). The long-distance and robustness of the supercurrent provides support that WTe2 might be a HOTI.

3. Using our innovative approach to control strain, we could demonstrate that strain induces a scalar potential, Comm. Phys. 4, 147 (2021). University news: "Stretching changes the electronic properties of graphene".

4. We were searching for signatures of topology by intending to measure the current-phase relation (CPR) in WTe2 using the asymmetric SQUID technique: M. Endres et al. Nano Lett. 23, 4654 (2023). We have found that one may strongly be misled by undetected large inductances arising at contacts.

5. A large fraction of our research throughout the whole project went into the development of AC Josephson radiation experiments. Here, a JJ is (quasi) DC voltage biased, which by virtue of the AC Josephson effect (JE) results in an AC supercurrent with frequencies in the microwave range: f=2eV/h, where f is the frequency, e the quantized charge, V the (quasi) DC voltage, and h the Planck constant. Since a topological SC can carry a supercurrent with single electrons the fundamental frequency is halved to f=eV/h. This is known as the “fractional JE” and the signal is a (possible) fingerprint for a TSC. We have searched in many materials including Cd3As2, HgTe, WTe2 and in conventional Al-based JJs. However, we were not able to find a sign of the fractional JE. This first paper, in which we describe the methodology and details of the analysis, has recently been published: Phys. Rev. B 108, 94514 (2023).

6. Motivated by the sudden appearance of interest in symmetry broken superconductivity, which can lead to the “superconducting diode effect”, we added a basic insight paper. Using an asymmetric SQUID realized in a proximitized InAs 2DEG we demonstrated that the diode effect requires a higher harmonic content in the CPR: Phys. Rev. Res. 5, 33131 (2023). We are quite confident that in most published results this mechanism is at hand.

7. Finally, we have investigated the kinetic inductance of the superconducting phase appearing in magic-angle twisted trilayer graphene. This work and further results are being written right now (Feb. 2024).
High kinetic inductance in the superconducting phase of magic-angle twisted triayer graphene
Picture shows the glovebox with stacking system used to fabricate stacks of 2D materials
An example of a six layer stack from which compact SQUID devices were made
Measurement of the AC Josephson radiation from a Dirac semimetal-based Josephson junction
Current-phase relation of WTe2 Josephson junctions
Installation of the low-temperature Raman system for attocube
Illustration of edge-dominated supercurrent in tungsten ditelluride
CAD design of the strain control unit for the low temperature Raman microscope
Tunnel spectroscopy into the van der Waals superconductor NbSe2