More topology in quantum electronic circuits

In the framework of the French-German laboratory association between SPINTEC and the IFW Dresden (CNRS International Research Project « SPINMAT »), and in collaboration with the C2N institute and the university of Würzburg, a novel plateform was implemented to reveal the non-hermitian topology of scalable quantum electronic circuits. It opens some new perspectives to realize quantum simulators and highly-sensitive sensors protected by the circuit topology, also relevant for quantum spintronics.

Artistic view of a multi-connected quantum ring (10 pairs) and of the ballistic transport of edge states between contacts in the quantum Hall regime (centre), realizing a 1D chain quantum model (Hatano-Nelson). For an open chain, the intrinsic circuit topology leads to the asymmetric localization of states at it ends, as determined by the chirality of the system and the specific ground scheme (“topological skin effect”).


In quantum materials, the non-trivial band-structure topology generates some novel electronic states, being robust against perturbations. The most famous example is the quantum Hall effect in 2D systems, with 1D ballistic edge states induced by a large magnetic field.

Connecting such edge states in an electronic quantum ring, the team realized a quantum simulator mapping the 1D-chain Hatano-Nelson quantum model. The experimental results reveal the intrinsic topology of the circuit itself, specific to non-hermitian open quantum systems, known as the topological skin effect. This leads to the exponential localization of states at one end of the ring (a finite chain of ballistic conductors) in an open-boundary configuration. The extreme sensitivity of this asymmetric topological response to a change in the boundary conditions makes such circuits interesting for sensing. More generally, this plateform offer some new perspectives to realize and study other quantum models, with circuits based on connected 1D chiral edge states. In quantum spintronics, such states can be realized in zero magnetic field in the quantum anomalous Hall regime of magnetic topological insulators.

The experimental device was realized from an AlGaAs 2D electron gas patterned into a ring geometry with ten ohmic contacts on its outer edge, each with an additional arm for grounding purpose (see Figure). By applying a perpendicular magnetic field, the circuit is driven into the quantum Hall regime, so that charge transport occurs via ballistic chiral edge states, in between successive contacts. The device is equivalent to a chain of chiral conductors connected by dissipative contacts, realizing the 1D Hatano-Nelson quantum model describing a non-hermitian hamiltonian. The well-designed contact geometry allows one to tune electrically the boundary conditions, continuously from an open-boundary to a periodic-bounday chain, by adding a finite resistance to the single contact connected to the ground (partially open-chain geometry). By measuring the magnetic-field dependence of the circuit conductance matrix, it was shown that the topological invariant associated to the skin effect is best quantized in the quantum Hall regime, but also that it remains quantized in the diffusive regime. This device topology appears very robust, both in magnetic field and in temperature, as long as the chirality of the system is preserved. An intriguing extension of this work is to realize some similar studies with devices patterned from magnetic topological insulators, in the quantum anomalous Hall regime in zero magnetic field, with some potential applications in quantum spintronics and metrology.

Team: Topological spintronics

Collaboration: IFW Dresden, C2N, Würzburg University

Funding: H2020 FET Proactive project TOCHA (No. 824140); CNRS IRP SPINMAT

Further reading: Non-Hermitian topology in a multi-terminal quantum Hall device, K. Ochkan et al., Nat. Phys. 20, 395-401 (2024). Open access: hal-04115908

Contact: Romain Giraud

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