Observation of supersymmetric pseudo-Landau levels in strained microwave graphene

Matthieu Bellec,Henning Schomerus,Ulrich Kuhl,Fabrice Mortessagne,Charles Poli

doi:10.1038/s41377-020-00351-2

Abstract

Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory. In particular, we resolve the full sublattice polarisation of the anomalous 0th pseudo-Landau level, which reveals a deep connection to zigzag edge states in the unstrained case.

Highlights

Topological states enjoy intense attention, as they equip quantum systems with desirable robust properties
The unstrained system forms a honeycomb lattice with nearest-neighbour spacing a0 = 13.9 mm, combining two triangular lattices of A and B sites, where each vertex denotes the position of a dielectric microwave resonator with bare frequency ω0 = 6.653 GHz, while adjacent resonators are coupled at strength t0 = 21.5 MHz
We achieved the direct observation of the formation of pseudo-Landau levels in deformed honeycomb systems, both spectrally and in terms of their key spatial features

Summary

Introduction

Topological states enjoy intense attention, as they equip quantum systems with desirable robust properties. On the other hand, often invoke a third, somewhat deeper feature of topological states, which is connected to the anomalous expectation values of the underlying symmetry operators[3,4] In momentum space, this feature underpins, e.g., the unidirectional chiral currents around the edges of topological insulators, while in real space, it manifests itself, e.g., in the sublattice polarisation of defect states in bipartite lattice systems[5], as has been exploited in recent topological lasers or nonlinear limiters based on photonic Su-Schrieffer-Heeger structures[6,7,8,9]. A second example is a class of helical edge states in reciprocal systems, as observed, e.g., in zigzag terminated graphene[21,22] While these bulk and edge phenomena do not naturally fall into the scope of standard topological band structure theory[1], they are still intimately linked to wavefunctions with a characteristic sublattice polarisation. This association provides a promising perspective from which one can seek to develop very general unifying descriptions (see, e.g., Kunst et al.[23] for a recent approach utilising this perspective)

Methods

Results

Conclusion