Perturbing ValleytronicMaterials to make them Relevant to Ground-State Quantum Computing

Y. Hsu, A. Vaezi, M. Fischer

PARADIM theorists have recognized that lightly hole-doped transition metal dichalcogenides (TMDs) are natural candidates for the long sought odd-parity topological superconductor vital for ground-state topological quantum computing. An interface materials strategy is considered that will cause a band of spin-polarized electrons to pair into an odd-parity superconductor.

The strategy exploits the unique valley band structure of TMDs where valleys occur at K and K’ just like graphene, but unlike graphene, TMDs have a special type of large spin-orbit coupling. These topological valley qubits are theorized to form in a hole-doped single-monolayer-thick TMD thin film synthesized on a strong ferromagnetic substrate. From theory the intra-valley pairing should have Chern number C=±1, whereas the inter-valley pairing should have C=2. The intra-valley pairing that can be promoted by a strong magnetic field coming from an underlying active substrate, will give rise to an odd-parity topo-logical superconductor with protected Majorana zero modes.

Y.-T. Hsu et al., Nature Communications 8 (2017) 14985.


Technical details: 

This strategy builds on the proposal by Fu and Kane [Physical Review Letters 100 (2008) 096407] to create an odd-parity topological superconductor at the interface between a topological insulator and an s‑wave superconductor.  Fu and Kane recognized that “spinless fermions” are bound to be topological and the surface states of topological insulators are “spinless” in that the spin-degeneracy is split in position-space (r-space):  the two degenerate Dirac surface states with opposite spin-textures are spatially separated to the two opposite surfaces of a sample.  While the proposal of Fu and Kane splits the spin degeneracy in real space, the new opportunity suggested by PARADIM theorists is to split the spin degeneracy of fermions in momentum space (K‑space).  The idea is to take a time-reversal-invariant non-centrosymmetric system with a pair of Fermi surfaces centered at opposite momenta, ±K0, with oppositely spin-polarized electrons.  This is precisely the “valley” band structure possessed by the spin-split hole bands of monolayer TMDs.  p-doped TMDs are hexagonal multi-valley systems with six bands that cut the Fermi surface, consisting of three pairs with hole pockets at ±K0.   The orbital-selective spin-orbit coupling leaves the conduction bands nearly degenerate, but splits the spin of the valence bands near the two valleys in a way that leaves the system time-reversal invariant.  When such a spin-valley-locked band structure is endowed with repulsive interactions, conventional pairing will be suppressed.

The materials-specific embodiment that PARADIM theorists have proposed is a monolayer of hole-doped (p-type) WSe2 epitaxially grown on a ferromagnetic substrate.  Superconductivity in electron-doped TMDs is well established, for example in MoS2 with Tc=10.8 K.  Unfortunately, electron-doped TMD systems do not have the needed spin-polarized Fermi surface, which is why WSe2, which has been hole-doped, is the target of the PARADIM experimental work that we are currently gearing up to do.