Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ?) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ₀ · exp(? (T ₀/T)^1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2. An expression for the thermopower in the hopping regime is derived and evaluated.     

Theory of hopping and multiple-trapping transport in disordered systems

We present a general theory to describe equilibrium as well as nonequilibrium transport properties of systems in which the carriers perform an incoherent motion that can be described by means of a set of master equations. This includes hopping as well as trapping in the localized energy region of amorphous or perturbed crystalline semiconductors. Employing the mathematical analogy between the master equations and the tight binding problem we develop approximation schemes using methods of many-particle physics to derive expressions for the averaged propagator of the carriers and the conductivity tensor. The calculated conductivity and Hall conductivity of hopping systems compare extremely well to computer simulations over the whole range of frequency, density, and temperature. We are able to derive expressions for dispersive transport in hopping as well as trapping systems that contain the results of earlier theories of Scher, Montroll and Noolandi, Schmidlin as special cases and establish criteria for the occurrence of dispersive transport in such systems. We find that in principle hopping can lead to dispersive transport if the times and densities are very low, but actual experimental data are more easily explained in terms of multiple trapping.     

Theory for slightly doped antiferromagnetic mott insulators

New trial wave functions, constructed explicitly from the unique Mott insulating state with antiferromagnetic order, are proposed to describe the ground state of a Mott insulator slightly doped with holes or electrons. A rigid band is observed as charged quasiparticles with well-defined momenta being realized in these states. These states have much less superconducting correlations than previously studied ones. Small Fermi patches obtained are consistent with recent experiments on high T(c) cuprates doped lightly with holes or electrons.     

Strong photon nonlinearities and photonic mott insulators

We show that photon nonlinearities in an electromagnetically induced transparency can be at least 1 order of magnitude larger than predicted in all previous approaches. As an application we demonstrate that in this regime they give rise to very strong photon-photon interactions which are strong enough to make an experimental realization of a photonic Mott insulator state feasible in arrays of coupled ultrahigh-Q microcavities.     

Temperature dependence of dispersive hopping transport and diffusion in disordered solids

The time- and temperature-dependent drift mobility μ_d for dispersive transients in disordered solids is $\text{μ}{}_{\mathrm{d}}\text{(T,t) =}\text{L}\text{Et}{}_{\mathrm{T}}$ in terms of distance L, field E and transit time t_T. Since current I ∝ tsu?(1?α) for t <_Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that $\text{μ}{}_{\mathrm{d}}\text{(T) = α[μ}{}_{\mathrm{d}}\text{(T,t)]}{}^{\mathrm{\alpha }}\text{(}\text{L}\text{Eτ}\text{)}{}^{\mathrm{1?\alpha }}$ where τ≈ 10^?13s is estimated. Further $\text{μ}{}_{\mathrm{d}}\text{(T) ∝ exp (}\text{?Δ}{}_0\text{KT}\text{)}$ and the activation energy Δ₀ is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As₂Se₃ is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μ_d(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As₂Se₃ as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ t^α?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ₀+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10^?13?10^?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν₀(t/τ)^α?1 exp(frsol|?Δ₀/KT) which applies also to bimolecular recombination.     

Exotic gapless mott insulators of bosons on multileg ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.     

Multiphonon hopping in disordered semiconductors

Equations of motion for the nonequilibrium single-frequency density matrix are used to obtain a balance equation describing the kinetics of electron hopping between localized states in disordered semiconductors. Conclusions are drawn about the applicability of the theory of multiphonon processes to systems with a small nonadiabaticity. The decoupling used is a generalization of one used earlier to the multiphonon case. The balance equation found in the Markov approximation for the average number of sites occupied in an electric field contains the field dependence of the multiphonon-transition probability, tending to the well-known weak-field limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.2, pp.35–42, February, 1976.In conclusion the author is grateful to V. L. Bonch-Bruevich and A. G. Mironov for discussing this work.     

Resonant two-magnon Raman scattering and photoexcited States in two-dimensional mott insulators

We investigate the resonant two-magnon Raman scattering in two-dimensional (2D) Mott insulators by using a half-filled 2D Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the Raman intensity is enhanced when the incoming photon energy is not near the optical absorption edge but well above it, being consistent with experimental data. The absence of resonance near the gap edge is associated with the presence of background spins, while photoexcited states for resonance are found to be characterized by the charge degree of freedom. The resonance mechanism is different from those proposed previously.     

Theory of hopping conductivity in disordered semiconductors

The bond percolation method is used to investigate the conditions under which a linear (and not exponential) temperature dependence of hopping conductivity can be observed.Translated from Izvestiya Vysshikh Uchbenykh Zavedenii, Fizika, No.2, pp. 52–62, February, 1976.     

Theory of hopping transfer in disordered systems

The problem of hopping conduction in a system with randomly distributed impurity centers at low temperatures has been considered in terms of the linearized balance equation. The Gochanour-Andersen-Fayer diagram technique has been used to obtain a self-consistent expression for the configuration-averaged Green’s function, which describes the charge transfer in a disordered system with inclusion of Fermi correlations. In the framework of the developed formalism, a relationship has been derived for hopping conductivity as a function of the temperature with a power law of the density of states. The results obtained agree well with the percolation approach and, in the static limit, lead to the Mott’s law.     

Particle-hole asymmetry in doped mott insulators: implications for tunneling and photoemission spectroscopies

We use exact sum rules for the one-particle spectral function to quantify the idea that it is more difficult to add an electron than to extract one in a system with strong local repulsion. Our results explain the striking asymmetry in the tunneling spectra of underdoped cuprates which increases with underdoping. We also propose a novel method, based on ratios of sum rules, to estimate local density variations in inhomogeneous materials. Using a variational approach, we show that the origin of the particle-hole asymmetry lies in the incoherent spectral weight.     

Nature of spin excitations in two-dimensional mott insulators: undoped cuprates and other materials

We investigate the excitation spectrum of a two-dimensional resonating valence bond (RVB) state. Treating the pi-flux phase with antiferromagnetic correlations as a variational ground state, we recover the long wavelength magnon as an "RVB exciton." However, this excitation does not exhaust the entire spectral weight and the high-energy spectrum is dominated by fermionic excitations. The latter can be observed directly by inelastic neutron scattering, and we predict their characteristic energy scales along different high symmetry directions in the magnetic Brillouin zone. We also interpret experimental results on two magnon Raman scattering and midinfrared absorption within this scenario.     

Correlated insulated phase suggests bond order between band and mott insulators in two dimensions

We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U > Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.     

Spin transport in antiferromagnetic insulators

Electrical spin, which is the key element of spintronics, has been regarded as a powerful substitute for the electrical charge in the next generation of information technology, in which spin plays the role of the carrier of information and/or energy in a similar way to the electrical charge in electronics. Spin-transport phenomena in different materials are central topics of spintronics. Unlike electrical charge, spin transport does not depend on electron motion, particularly spin can be transported in insulators without accompanying Joule heating. Therefore, insulators are considered to be ideal materials for spin conductors, in which magnetic insulators are the most compelling systems. Recently, we experimentally studied and theoretically discussed spin transport in various antiferromagnetic systems and identified spin susceptibility and the Néel vector as the most important factors for spin transport in antiferromagnetic systems. Herein, we summarize our experimental results, physical nature, and puzzles unknown. Further challenges and potential applications are also discussed.     

Low frequency hopping conductivity in disordered one-dimensional lattice

We investigate classical hopping on a one-dimensional chain with random nearest-neighbour transfer rates. It is found, by studying corrections, that an Effective-Medium approach gives the exact asymptotic hopping conductivity at low frequencies for certain distributions of the transfer rates.     

On thermopower in hopping transport

Certain general aspects of hopping transport in the context of thermopower are reinvestigated. Onsager symmetry of the macroscopic kinetic coefficients is derived from detailed balance of the microscopic coefficients of the kinetic equation by an expansion of the kinetic equation around local equilibrium in an external potential and temperature gradient. The resulting expression for the thermopower differs from expressions proposed in the literature. The difference however, seems to be small.     

Diffusion and hopping conductivity in disordered one-dimensional lattice systems

We investigate one-dimensional lattice systems with (symmetric) nearest neighbor transfer ratesW _{n, n+1} which are independently distributed according to a probability density(w). For two general classes of(w), we rigorously determine the asymptotic behavior of the relevant single site Green function ₀() near=0, and obtain exact results for the long time decay of the initial probability amplitude and for the low energy density of states. A scaling hypothesis, accurately confirmed by computer simulations, is used to relate the low frequency hopping conductivity() uniquely to ₀(–i), and we conjecture that the resulting asymptotic behavior for() is also exact. The critical exponents associated with the various asymptotic laws depend on(w) and show a crossover from universal to non-universal behavior. Comparison is made with the results of several approximate treatments.