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Engineered Topological Superconductivity in van der Waals Heterostructures

Periodic Reporting for period 2 - TopSupra (Engineered Topological Superconductivity in van der Waals Heterostructures)

Reporting period: 2020-01-01 to 2021-06-30

The title of the ERC-Project “Engineered Topological Superconductivity in van der Waals Heterostructures” with acronym “TopSupra” refers to two aspects that receive high interest in today’s research: topological matter and two-dimensional (2D) van der Waals (vdW) materials.

Topological matter is a young research theme with great perspectives and potential applications in quantum computing and thermoelectrics. A topological material is a new material class. It is neither a metal, a semiconductor, or a conventional insulator. A topological insulator (TI) is an insulator with an inverted “negative” bandgap and a conducting surface state. In a TI in 3D, the conducting surface is 2D. In analogy, in a 2D TI, the 1D-edge is a conducting wire.

A prototype example is the quantum spin Hall (QSH) state, which has been discovered in HgTe quantum wells. Electrons in the QSH surface state are chiral and described by the Dirac equation. At each edge, there are two counter propagating channels, also known as helical edge-states, one for spin up and one for spin down. Without spin-scattering the edge-states are perfect quantum channels with maximal conductance.

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. In the simplest case, these particles are known as Majorana fermions. In 1D, the surface state of a TSC reduces to a pair of localized states that appear at opposite ends of the nanowire. It represents, at the same time, an electron and a hole and is distributed with equal weight on the left and right side of the nanowire. Although first indications of Majorana fermions were found in (quasi-) 1D nanowires, we think it is more convenient to work with 2D materials coupled to SCs. TopSupra aims to establish topological superconductivity in high-mobility graphene heterostructures. This has several advantages: the platform builds on graphene, a 2D van der Waals (vdW) material which is easy to handle compared to other 2D electron gases, has high mobility and can be combined with other layered materials to realize heterostructures with modified properties. For example, graphene can be combined with 2D SCs and 2D magnetic materials and it is easily gated with local gate-electrodes.
To obtain a topological superconducting state in graphene, one first must engineer graphene into a topological state. While the QSH state was originally proposed to be the ground-state of graphene, it soon was realized that the gap of this TI is way too small to be measured, due to the small spin-orbit interaction in graphene. However, by virtue of vdW heterostructures, large SOI can be induced by coupling graphene to TMDCs such as MoS2, WSe2 and others.

In TopSupra we aim to engineer topological nontrivial states in graphene by several means: by using a bipolar graphene bilayer in the quantum-Hall regime, by heterojunctions of stacked 2D vdW layers to induce the desired interaction into graphene by proximity, and by static fields and strain tuning.

The technology of stacking different 2D layers together has been developed with encapsulated graphene to such a perfection that more advanced material combinations, such as graphene-TMDC, graphene-FM, graphene-SC, can now be addressed. Using twisted graphene bilayers at small angles where flat bands appear is another direction to search for topological non-trivial states.
The goal of TopSupra is 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 with optical light.

Up to M36, work on all 5 axes have been conducted. We have achieved significant results. Out of those, we mention four highlights that are listed in the next subsection under progress beyond the state of the art.
We mention four highlights that go beyond the state of the art.

First, the discovery of the super-superlattice in encapsulated graphene, see L. Wang et al. Nano Lett. 19, 2371 (2019). It has been observed before that aligning graphene with hBN, which is used to encapsulate graphene, gives rise to a superlattice due to a small lattice difference between the two materials. If both the upper and lower hBN layer are aligned, one would think that in total two superlattices appear. However, we observed that the two superlattices themselves can generate a second generation superlattice. This “third” superlattice can have a much larger unit cell. The online media news was shared widely on the internet. See e.g. under “Super superlattices: The moiré patterns of three layers change the electronic properties of graphene”.

Second, the discovery of long-distance edge currents in few layers of WTe2, see A. Kononov et al. Nano Lett. 20, 4228 (2020). Theory has proposed that atomically thin layers of the semimetal WTe2 could be a 2nd-order TI, a material that conducts electrons along hinges. We have made two unexpected discoveries: (a) taking the normal metal Pd as a contact material to WTe2 turns this material into a superconductor, and (b), the current in superconducting junctions flows predominantly along edges and steps over long distances. This robustness supports the predication of a topological phase. Here, we come already very close to our target, namely a topological superconductor.

Third, the realization of a “Compact SQUID (superconducting quantum interference device) realized in a double layer graphene heterostructure”, Nano Lett. 20, 7129 (2020). This “double decker” SQUID consists of two graphene layers stacked on top of each other with a thin insulator of a few nanometers in thickness in between. A supercurrent can flow through both layers due to “source” and “drain” contacts made from a bulk superconductor that shunts the two layers some distance apart. This results in a superconducting loop with two parallel Josephson “weak links” formed by the upper and lower graphene. Due to the 2D nature of graphene, this is possibly the smallest SQUID with the strongest confined Josephson junctions that has ever been realized.

Forth, using our innovative approach to control strain, we could demonstrate that strain induces a scalar potential. We have found a conversion factor of 3.8 eV, which means that a uniaxial strain of 1% leads to a shift of the Fermi energy of 38 meV. This highlight received quite a media echo following the press release from the University under the heading "Stretching changes the electronic properties of graphene": See also on youtube: We currently finalize a unique measurements setup allowing the controlled straining at low temperatures.
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
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