Dirac particles, massless relativistic entities, obey linear energy dispersions and hold important implication in particle physics. Recent discovery of Dirac fermions in condensed matter systems including graphene and topological insulators raises gr
eat interests to explore relativistic properties associated with Dirac physics in solid-state materials. In addition, there are stimulating research activities to engineer Dirac paricles to eludicte their physical properties in a controllable setting. One of the successful platforms is the ultracold atom-optical lattice system, whose dynamics can be manipulated in a clean environment. A microcavity exciton-polariton-lattice system provides an alternative route with an advantage of forming high-orbital condensation in non-equilibrium conditions, which enables to explore novel quantum orbital order in two dimensions. Here we directly map the liner dispersions near the Dirac points, the vertices of the first hexagonal Brillouin zone from exciton-polariton condensates trapped in a triangular lattice. The associated velocity values are ~ 0.9 - 2*10^8 cm/s, which are consistent with the theoretical estimate 1*10^8 cm/s with a 2 mu m-lattice constant. We envision that the exciton-polariton condensates in lattices would be a promising solid-state platform, where the system order parameter can be accesses in both real and momentum spaces. We furthermore explore unique phenomena revealing quantum bose nature such as superfluidity and distinct features analogous to quantum Hall effect pertinent to time-reversal symmetry.
We addressed the inconsistency between the electron mass anisotropy ratios determined by the far-infrared experiments and DC conductivity measurements. By eliminating possible sources of error and increasing the sensitivity and resolution in the far-
infrared reflectivity measurement on the single crystalline and on the polycrystalline La1.84Sr0.16CuO4, we have unambiguously identified that the source of the mass anisotropy problem is in the estimation of the free electron density involved in the charge transport and superconductivity. In this study we found that only 2.8 % of the total doping-induced charge density is itinerant at optimal doping. Our result not only resolves the mass anisotropy puzzle but also points to a novel electronic structure formed by the rest of the electrons that sets the stage for the high temperature superconductivity.
A positive definite even Hermitian lattice is called emph{even universal} if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields $Q{-m}$ for all positive
square-free integers $m$ and we list optimal criterions on even universality of Hermitian lattices over $Q{-m}$ which admits even universal binary Hermitian lattices.
We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over $mathbb{Q}(sqrt{-m})$ for all m. For each imaginary quadratic field $mathbb{Q}(sqrt{-m})$, we obtain a criterion on universality of Hermitian latt
ices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13,14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneebergers fifteen theorem and ours is the number 13.
We investigate the response of dense and hot holographic QCD (hQCD) to a static and baryonic electric field E using the chiral model of Sakai and Sugimoto. Strong fields with E>(sqrtlambda M_{KK})^2 free quark pairs, causing the confined vacuum and m
atter state to decay. We generalize Schwingers QED persistence function to dense hQCD. At high temperature and density, Ohms law is derived generalizing a recent result by Karch and OBannon to the chiral case.
We present a simple method to create an in-plane lateral potential in a semiconductor microcavity using a metal thin-film. Two types of potential are produced: a circular aperture and a one-dimensional (1D) periodic grating pattern. The amplitude of
the potential induced by a 24 nm-6 nm Au/Ti film is on the order of a few hundreds of ueV measured at 6 ~ 8 K. Since the metal layer makes the electromagnetic fields to be close to zero at the metal-semiconductor interface, the photon mode is confined more inside of the cavity. As a consequence, the effective cavity length is reduced under the metal film, and the corresponding cavity resonance is blue-shifted. Our experimental results are in a good agreement with theoretical estimates. In addition, by applying a DC electric voltage to the metal film, we are able to modify the quantum well exciton mode due to the quantum confined Stark effect, inducing a ~ 1 meV potential at ~ 20 kV/cm. Our method produces a controllable in-plane spatial trap potential for lower exciton-polaritons (LPs), which can be a building block towards 1D arrays and 2D lattices of LP condensates.
We consider the diffusion of a non-relativistic heavy quark of fixed mass M, in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT duality. The Greens function constructed around a static string embedded in a background with
a moving horizon, is identified with the noise correlation function in a Langevin approach. The (electric) noise decorrelation is of order 1/T(tau) while the velocity de-correlation is of order MD(tau)/T(tau). For MD>1, the diffusion regime is segregated and the energy loss is Langevin-like. The time dependent diffusion constant D(tau) asymptotes its adiabatic limit 2/pisqrt{lambda} T(tau) when tau/tau_0=(1/3eta_0tau_0)^3 where eta_0 is the drag coefficient at the initial proper time tau_0.
In the context of holographic QCD we analyze Sakai-Sugimotos chiral model at finite baryon density and zero temperature. The baryon number density is introduced through compact D4 wrapping S^4 at the tip of D8-bar{D8}. Each baryon acts as a chiral po
int-like source distributed uniformly over R^3, and leads a non-vanishing U(1)_V potential on the brane. For fixed baryon charge density n_B we analyze the bulk energy density and pressure using the canonical formalism. The baryonic matter with point like sources is always in the spontaneously broken phase of chiral symmetry, whatever the density. The point-like nature of the sources and large N_c cause the matter to be repulsive as all baryon interactions are omega mediated. Through the induced DBI action on D8-bar{D8}, we study the effects of the fixed baryon charge density n_B on the pion and vector meson masses and couplings. Issues related to vector dominance in matter in the context of holographic QCD are also discussed.
We investigate cold dense matter in the context of Sakai and Sugimotos holographic model of QCD in the Wigner-Seitz approximation. In bulk, baryons are treated as instantons on S^3times R^1 in each Wigner-Seitz cell. In holographic QCD, Skyrmions are
instanton holonomies along the conformal direction. The high density phase is identified with a crystal of holographic Skyrmions with restored chiral symmetry at about 4 Mkk^3/pi^5. As the average density goes up, it approaches to uniform distribution while the chiral condensate approaches to p-wave over a cell. The chiral symmetry is effectively restored in long wavelength limit since the chiral order parameter is averaged to be zero over a cell. The energy density in dense medium varies as n_B^{5/3}, which is the expected power for non-relativistic fermion. This shows that the Pauli exclusion effect in boundary is encoded in the Coulomb repulsion in the bulk.
