Topological states at exceptional points

We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of topologically distinct systems. We discuss that topological states appear even in closed systems. We explore dynamical robustness of exceptional edge states.     

Pump-induced exceptional points in lasers

We demonstrate that the above-threshold behavior of a laser can be strongly affected by exceptional points which are induced by pumping the laser nonuniformly. At these singularities, the eigenstates of the non-Hermitian operator which describes the lasing modes coalesce. In their vicinity, the laser may turn off even when the overall pump power deposited in the system is increased. Such signatures of a pump-induced exceptional point can be experimentally probed with coupled ridge or microdisk lasers.     

Many-body exceptional points in colliding condensates

ABSTRACT

Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.     

Topological confinement in bilayer graphene

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics.     

Two-body exceptional points in open dissipative systems

We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation.Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation,we show that the non-Hermitian effective Hamiltonian of the master equation gives rise to two-body scattering states with state-and interaction-dependent parity-time transition.The resulting two-body exceptional points can be extracted from the trace-preserving density-matrix dynamics of the same dissipative system with three atoms.Our results not only demonstrate the interplay of parity-time symmetry and interaction on the exact few-body level,but also serve as a minimal illustration on how key features of non-Hermitian few-body physics can be probed in an open dissipative many-body system.     

Properties of exceptional points in some many body models

The Lipkin model is a popular toy model, first used in nuclear physics, to understand quantum phase transitions including symmetry breaking. However, the thermodynamic limit, that is the limit of large particle numbers, appears rather elusive. The pattern of the exceptional points of the model, in particular their behavior with increasing particle numbers, is presented. They may give a clue as to the properties of the Lipkin Hamiltonian in the thermodynamic limit. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Strong absorption near exceptional points in plasmonic waveguide arrays

We investigate the exceptional points (EPs) in plasmonic waveguide arrays, including metallic waveguide arrays (MWAs) and graphene sheet arrays (GSAs). The EPs emerge at the boundary of strong and weak coupling ranges in both systems. The cross conversion of Bloch modes and variation of geometric phase can be observed by encircling an EP in the parametric space. We also show the Bloch modes exhibit strong absorption in the vicinity of EPs in GSAs, which originates from the enhanced longitude electric field along the propagation direction. The abnormal absorption and field enhancement also arise in ultrathin MWAs and disappear when the thickness of metal film increases. Our results may find applications in optical switches and sensors at the nanoscale.     

Supercurrent switching effect in zigzag graphene nanoribbons

The lattice dynamics in the CuIr₂S₄ system have been investigated through Raman spectroscopy and the induced-pressure effect. Four Raman active modes are observed experimentally. Upon cooling, these Raman spectra undergo changes due to the Peierls-like phase transition. In addition, the substitution of Ag for Cu affects the amplitude of the Raman spectra while keeping their wave number unchanged. Furthermore, the positive and negative pressure effects are induced by shrinking and expanding the lattice. It is suggested that the pressure effect is an effective proof of the orbital-induced Peierls state mechanism.     

Topological vortices in chiral gauge theory of graphene

Generation mechanism of energy gaps between conductance and valence bands is at the centre of the study of graphene material. Recently, Chamon, Jackiw et al. proposed a mechanism of using a Kekulé distortion background field φ and its induced gauge potential A_i to generate energy gaps. In this paper, various vortex structures inhering in this model are studied. Regarding φ as a generic background field rather than a fixed Nielson-Oleson type distribution, we have found two new types of vortices on the graphene surface—the velocity field vortices and the monopole-motion induced vortices—from the inner structure of the potential A_i. These vortex structures naturally arise from the motion of the Dirac fermions instead of from the background distortion field.     

Photoresistivity and optical switching of graphene with DNA lattices

We present the photon induced conductivity of 2D DNA lattices with and without graphene and demonstrate the switching current responses controlled by light irradiation. The conductivity in the DNA lattices with protein streptavidin controlled by blue and white lights shows significant enhancement with the addition of graphene. An optical pulse response of a graphene immobilized DNA lattice is encouraging and may lead to various bio-sensing applications such as immunological assays, DNA forensics, and toxin detection.     

New electromagnetic mode in graphene

A new, weakly damped, transverse electromagnetic mode is predicted in graphene. The mode frequency omega lies in the window 1.667<[see text]omega/micro < 2, where micro is the chemical potential, and can be tuned from radio waves to the infrared by changing the density of charge carriers through a gate voltage.     

Electro‐optic switching with liquid crystal graphene

Graphene oxide (GO) particles in aqueous dispersions can form liquid crystal (LC) phases at extremely low concentrations due to the extremely high aspect ratio of the flakes and noticeably, they possess an extremely large Kerr coefficient attractive for low power consumption electro‐optic devices. Reduced graphene does not easily form LC phases in water due to its hydrophobic nature but here we show that stable dispersions of reduced graphene oxide can be realized with surfactants and that they exhibit birefringence upon shearing as well as under application of electric fields. The performance of the system is largely superior to GO LC possessing longer time stability and drastically improved electro‐optic properties with an induced birefringence twice as large at the same field strength thanks to the almost recovery of graphene properties upon reduction. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Electrical switching effect in a photochromic molecule between two graphene electrodes

We propose a single-molecule electrical switches consisting of a photochromic dimethyldihydropyrene/cyclophanediene molecule sandwiched between two graphene electrodes and investigate the electronic transport by using density-functional theory and nonequilibrium Green's function methods. The “open” and “closed” isomers of the photochromic molecule are shown to have electrical switching behavior and negative differential resistance effect. Moreover, it is also found that the switching ratio between two different conductive states depends on the ambient temperature, and the device behaves as a stable electrical switch around room temperature, which is in agreement with a recent experimental study of another photochromic molecule diarylethene reported by Jia et al. (2016) [17].     

Ultrafast mode switching based on a micro-ring laser

Injection locking and multi-mode switching characteristics of a semiconductor ring laser with the radius of 10 μm are investigated based on a nonlinear time domain multimode rate-equation model. The stable injection locking regions for different target modes are studied as the function of detuning frequency and injection power ratio. The results show that ultra-wide detuning range of ∼100 GHz wide at 5 dB injection power ratio and ultra-low switching power ratio of −27 dB can be realized for this micro-ring laser device. Optimal detuning value and high injection power lead to the minimal switching time. An ultrafast response time of 10 ps indicates that a 10 μm-radius SRL can be utilized for ultrafast all-optical scenarios and high-speed tunable lasers.     

Charge response function and a novel plasmon mode in graphene

Polarizability of noninteracting 2D Dirac electrons has a 1/square root(qv-omega) singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N-->infinity, where N is the "color" degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the nth order ladder term to the same order random phase approximation contribution is ln(n)|qv-omega|/N(n). We perform an analytical summation of the infinite series of ladder diagrams which describe the excitonic effect. Beyond the threshold, qv>omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.     

Topological quantization of disclination points in three—dimensional liquid crystals

Using the φ-mapping method and topological current theory, we study the inner structure of disclination points in three-dimensional liquid crystals. By introducing the strength density and the topological current of many disclination points, it is pointed out that the disclination points are determined by the singularities of the general director field and they are topologically quantized by the Hopf indices and Brouwer degrees.