Probing Single and Bilayer Graphene Field Effect Transistors By Raman Spectroscopy

This article is a review of our work related to Raman studies of single layer and bilayer graphenes as a function Fermi level shift achieved by electrochemically top gating a field effect transistor. Combining the transport and in situ Raman studies of the field effect devices, a quantitative understanding is obtained of the phonon renormalization due to doping of graphene. Results are discussed in the light of time dependent perturbation theory, with electron phonon coupling parameter as an input from the density functional theory. It is seen that phonons near and Gamma and K points of the Brillouin zone are renormalized very differently by doping. Further, Gamma-phonon renormalization is different in bilayer graphene as compared to single layer, originating from their different electronic band structures near the zone boundary K-point. Thus Raman spectroscopy is not only a powerful probe to characterize the number of layers and their quality in a graphene sample, but also to quantitatively evaluate electron phonon coupling required to understand the performance of graphene devices.

Supersolid Phase in One-Dimensional Bose-Hubbard Model With Extended Range Interactions: DMRG And Field Theoretic Study at Different Densities

We use the Density Matrix Renormalization Group and the Abelian bosonization method to study the effect of density on quantum phases of one-dimensional extended Bose-Hubbard model. We predict the existence of supersolid phase and also other quantum phases for this system. We have analyzed the role of extended range interaction parameters on solitonic phase near half-filling. We discuss the effects of dimerization in nearest neighbor hopping and interaction as well as next nearest neighbor interaction on the plateau phase at half-filling.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

Spatially dependent zero-frequency response functions and correlation functions in the Kondo model

We present the details of a formalism for calculating spatially varying zero-frequency response functions and equal-time correlation functions in models of magnetic and mixed-valence impurities of metals. The method is based on a combination of perturbative, thermodynamic scaling theory [H. R. Krishna-murthy and C. Jayaprakash, Phys. Rev. B 30, 2806 (1984)] and a nonperturbative technique such as the Wilson renormalization group. We illustrate the formalism for the spin-1/2 Kondo problem and present results for the conduction-spin-density�impurity-spin correlation function and conduction-electron charge density near the impurity. We also discuss qualitative features that emerge from our calculations and discuss how they can be carried over to the case of realistic models for transition-metal impurities.

The concentration dependent cooperative friction coefficient of dilute polymer solutions at the theta point

We combine multiple scattering and renormalization group methods to calculate the leading order dimensionless virial coefficient k(s) for the friction coefficient of dilute polymer solutions under conditions where the osmotic second virial coefficient vanishes (i.e., at the theta point T-theta). Our calculations are formulated in terms of coupled kinetic equations for the polymer and solvent, in which the polymers are modeled as continuous chains whose configurations evolve under the action of random forces in, the velocity field of the solvent. To lowest order in epsilon=4-d, we find that k(s) = 1.06. This result compares satisfactorily with existing experimental estimates of k(s), which are in the range 0.7-0.8. It is also in good agreement with other theoretical results on chains and suspensions at T-theta. Our calculated k(s) is also found to be identical to the leading order virial coefficient of the tracer friction coefficient at the theta point. We discuss possible reasons for the difficulties encountered when attempting to evaluate k(s) by extrapolating prior renormalization group calculations from semidilute concentrations to the infinitely dilute limit. (C) 1996 American Institute of Physics.

Quantum-confinement effects on the ordering of the lowest-lying excited states in conjugated chains

The symmetrized density-matrix renormalization-group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation delta) to study the ordering of the lowest one-photon (1(1)B(u)(-)) and two-photon (2(1)A(g)(+)) states in one-dimensional conjugated systems with chain lengths N up to N = 80 sites. Three different types of crossovers are studied, as a function of U/t, delta, and N. The ''U crossover'' emphasizes the larger ionic character of the 2A(g) state compared to the lowest triplet excitation. The ''delta crossover'' shows strong dependence on both N and U/t. the ''N crossover'' illustrates the more localized nature of the 2A(g) excitation relative to the 1B(u) excitation at intermediate correlation strengths.

Spin distributions in antiferromagnetically coupled Mn2+Cu2+ systems: from the pair to the infinite chain

Probably the most informative description of the ground slate of a magnetic molecular species is provided by the spin density map. Such a map may be experimentally obtained from polarized neutron diffraction (PND) data or theoretically calculated using quantum chemical approaches. Density functional theory (DFT) methods have been proved to be well-adapted for this. Spin distributions in one-dimensional compounds may also be computed using the density matrix renormalization group (DMRG) formalism. These three approaches, PND, DFT, and DMRG, have been utilized to obtain new insights on the ground state of two antiferromagnetically coupled Mn2+Cu2+ compounds, namely [Mn(Me-6-[14]ane-N-4)Cu(oxpn)](CF3SO3)(2) and MnCu(pba)(H2O)(3) . 2H(2)O, with Me-6-[14]ane-N-4 = (+/-)-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, oxpn = N,N'-bis(3-aminopropyl)oxamido and pba = 1,3-propylenebis(oxamato). Three problems in particular have been investigated: the spin distribution in the mononuclear precursors [Cu(oxpn)] and [Cu(pba)](2-), the spin density maps in the two Mn2+Cu2+ compounds, and the evolution of the spin distributions on the Mn2+ and Cu2+ sites when passing from a pair to a one-dimensional ferrimagnet.

Magnetization properties of some quantum spin ladders

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Hen we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZ model, We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat. [S0163-1829(99)303001-5].

Raman evidence for the superconducting gap and spin-phonon coupling in the superconductor Ca( Fe0.95Co0.05)(2)As-2

Inelastic light scattering studies on a single crystal of electron-doped Ca(Fe0.95Co0.05)(2)As-2 superconductor, covering the tetragonal-to-orthorhombic structural transition as well as the magnetic transition at T-SM similar to 140 K and the superconducting transition temperature T-c similar to 23 K, reveal evidence for superconductivity-induced phonon renormalization. In particular, the phonon mode near 260 cm(-1) shows hardening below T-c, signaling its coupling with the superconducting gap. All three Raman active phonon modes show anomalous temperature dependence between room temperature and T-c, i.e. the phonon frequency decreases with lowering temperature. Further, the frequency of one of the modes shows a sudden change in temperature dependence at TSM. Using first-principles density functional theory based calculations, we show that the low temperature phase (T-c < T < T-SM) exhibits short-ranged stripe antiferromagnetic ordering, and estimate the spin-phonon couplings that are responsible for these phonon anomalies.

The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low- and high-temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, such as the quantum Brownian motion of a panicle in a periodic potential and impurity problems, are pointed out.

Driven Heisenberg magnets: Nonequilibrium criticality, spatiotemporal chaos and control

We drive a d-dimensional Heisenberg magnet using an anisotropic current. The continuum Langevin equation is analysed using a dynamical renormalization group and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be controlled in a robust manner to target spatially periodic steady states with helical order.

Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in 2+2epsilon dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an epsilon expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in 2+2epsilon dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action (theta term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as nu and p, control not only the scaling behavior of the conductances sigma(xx) and sigma(xy) at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat (c(v)proportional toT(p)). To extract the numerical values of nu and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.

Two-channel Kondo physics in odd impurity chains

We study odd-membered chains of spin-1/2 impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong interimpurity coupling, a residual chain spin-1/2 moment experiences a renormalized effective coupling to the leads, while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models in which the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular, the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is nonzero and determined solely by the ``excess'' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where interlead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization-group techniques are used to obtain a detailed understanding of these problems.

Griffiths phase-like behavior and spin-phonon coupling in double perovskite Tb(2)NiMnO(6)

The Griffiths phase-like features and the spin-phonon coupling effects observed in Tb(2)NiMnO(6) are reported. The double perovskite compound crystallizes in monoclinic P2(1)/n space group and exhibits a magnetic phase transition at T(c) similar to 111 K as an abrupt change in magnetization. A negative deviation from ideal Curie-Weiss law exhibited by 1/chi(T) curves and less-than-unity susceptibility exponents from the power-law analysis of inverse susceptibility are reminiscent of Griffiths phase-like features. Arrott plots derived from magnetization isotherms support the inhomogeneous nature of magnetism in this material. The observed effects originate from antiferromagnetic interactions that arise from inherent disorder in the system. Raman scattering experiments display no magnetic-order-induced phonon renormalization below Tc in Tb(2)NiMnO(6), which is different from the results observed in other double perovskites and is correlated to the smaller size of the rare earth. The temperature evolution of full-width-at-half-maximum for the stretching mode at 645 cm(-1) presents an anomaly that coincides with the magnetic transition temperature and signals a close connection between magnetism and lattice in this material. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3671674]