Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise [1][2][3][4][5][6] . Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly 7,8 , like a state-flip or the accumulation of a geometric phase 9,10 . Experiments dedicated to this issue could already successfully explore the topological structure of exceptional points [11][12][13] , but a full dynamical encircling and the breakdown of adiabaticity inevitably associated with it 14-21 remained out of reach of any measurement so far. Here we

Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ∼1.5 × 106 m s−1 in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a ‘necklace state’. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

We investigate the effect of spatially correlated disorder on two-dimensional topological insulators and on the quantum spin Hall effect which the helical edge states in these systems give rise to. Our work expands the scope of previous investigations which found that uncorrelated disorder can induce a nontrivial phase called the topological Anderson insulator (TAI). In extension of these studies, we find that spatial correlations in the disorder can entirely suppress the emergence of the TAI phase. We show that this phenomenon is associated with a quantum percolation transition and quantify it by generalizing an existing effective medium theory to the case of correlated disorder potentials. The predictions of this theory are in good agreement with our numerics and may be crucial for future experiments.

We investigate the presence of percolating states in disordered two-dimensional topological insulators. In particular, we uncover a close connection between these states and the so-called topological Anderson insulator (TAI), which is a topologically non-trivial phase induced by the presence of disorder. The decay of this phase could previously be connected to a delocalization of bulk states with increasing disorder strength. In this work we identify this delocalization to be the result of a percolation transition of states that circumnavigate the hills of the bulk disorder potential.