Density of states in graphene with vacancies: midgap power law and frozen multifractality

The density of states (DoS), $varrho(E)$, of graphene is investigated numerically and within the self-consistent T-matrix approximation (SCTMA) in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies, $n_text{A}$ and $n_text{B}$, in both sub-lattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The prediction of the non-linear sigma-model for this class is a Gade-type singularity $varrho(E) sim |E|^{-1}exp(-|log(E)|^{-1/x})$. Our numerical data is compatible with this result in a preasymptotic regime that gives way, however, at even lower energies to $varrho(E)sim E^{-1}|log(E)|^{-mathfrak{x}}$, $1leq mathfrak{x} < 2$. We take this finding as an evidence that similar to the case of dirty d-wave superconductors, also generic bipartite random hopping models may exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.

Experimental Observation of Stabilization and Lasing Death via Asymmetric Gain

Using a pair of coupled LRC cavities we experimentally demonstrate that instabilities and amplification action can be tamed by a spatially inhomogenous gain. Specifically we observe the counter-intuitive phenomenon of stabilization of the system even when the overall gain provided is increased. This behavior is directly related to lasing death via asymmetric pumping, recently proposed in [M. Liertzer {it et al}., Phys. Rev. Lett. {bf 108}, 173901 (2012)]. The stability analysis of other simple systems reveals the universal nature of the lasing death phenomenon.

PT-Symmetric Electronics

We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.

Bypassing the bandwidth theorem with PT symmetry

The beat time {tau}_{fpt} associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound {tau}_{fpt}sim 1/{delta}{omega}. We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time (PT) symmetry, bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference {delta}{omega}. Our results foster new design strategies which lead to (stable) pseudo-unitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.