Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b ≈ 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length L(?) ? b in the range of sheet resistances considered, so that the effective dimension is d = 3. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation (localization) length critical exponent ν- ≈ 1.4 (ν+ ≈ 0.8) on the metallic (insulating) side.     

Effects of a parallel magnetic field on the metal-insulator transition in a dilute two-dimensional electron system

The temperature dependence of conductivity sigma(T) of a two-dimensional electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a metal-insulator transition at a critical electron density n(c)(0), and dsigma/dT>0 in the metallic phase. At low fields ( B < or approximately equal to 2 T), n(c) increases as n(c)(B)-n(c)(0) proportional, variant Bbeta ( beta approximately 1), and the zero-temperature conductivity scales as sigma(n(s),B,T = 0)/sigma(n(s),0,0) = f(B(beta)/delta(n)), where delta(n) = [n(s)-n(c)(0)]/n(c)(0) and n(s) is electron density, as expected for a quantum phase transition. The metallic phase persists in fields of up to 18 T, consistent with the saturation of n(c) at high fields.     

Bose-Einstein condensation of magnons in Cs2CuCl4

We report on results of specific heat measurements on single crystals of the frustrated quasi-2D spin-1/2 antiferromagnet Cs2CuCl4 (T(N)=0.595 K) in external magnetic fields B<12 T and for temperatures T>30 mK. Decreasing B from high fields leads to the closure of the field-induced gap in the magnon spectrum at a critical field Bc approximately = 8.51 T and a magnetic phase transition is clearly seen below Bc. In the vicinity of Bc, the phase transition boundary is well described by the power law Tc(B) proportional, variant (Bc-B)(1/phi), with the measured critical exponent phi approximately =1.5. These findings are interpreted as a Bose-Einstein condensation of magnons.     

Random walks on a ( 2+1)-dimensional deformable medium

A model of random walks on a deformable medium is proposed in 2+1 dimensions. The behavior of the walk is characterized by the stability parameter beta and the stiffness exponent alpha. The average square end-to-end distance l approximately equals (2nu) and the average number of visited sites approximately equals (k) are calculated. As beta increases, for each alpha there exists a critical transition point beta(c) from purely random walks ( nu = 1/2 and k approximate to 1) to compact growth ( nu = 1/3 and k = 2/3). The relationship between beta(c) and alpha can be expressed as beta(c) = e(alpha). The landscape generated by a walk is also investigated by means of the visit-number distribution N(n)(beta). There exists a scaling relationship of the form N(n)(beta)approximately n(-2)f(n/beta(z)).     

Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system

By carefully analyzing the low temperature density dependence of 2D conductivity in undoped high-mobility n-GaAs heterostructures, we conclude that the 2D metal-insulator transition in this 2D electron system is a density inhomogeneity driven percolation transition due to the breakdown of screening in the random charged impurity disorder background. In particular, our measured conductivity exponent of approximately 1.4 approaches the 2D percolation exponent value of 4/3 at low temperatures and our experimental data are inconsistent with there being a zero-temperature quantum critical point in our system.     

Fluctuation conductivity in layered d-wave superconductors near critical disorder

We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the systems conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.Received: 10 October 2003, Published online: 23 December 2003PACS: 74.40. + k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 73.43.Nq Quantum phase transitions     

Critical Behavior of Nonlinear Properties in Percolating Superconductor/Nonlinear-Normal Conductor Networks

The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)-voltage (ν) response of the form ν = ri + bi^α (bi^α-1《t and α > 1). Both the crossover current density and the crossover electric field are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies ～(f_c - f)^H and ～(f_c - f)^M as the percolation threshold f_c of the superconductor is approached from below, where H = ν_d - s_d > 0, M = ν_d > 0, ν_d and s_d are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear ν-i response, i.e., i = X^να The effective nonlinear response X_e, behaves as X_e ～(f_c - f)^-W(α), where W ( α ) is the critical exponent of the nonlinear response x_e(α) and is α-dependent in general. The results are compared with recently published data, reasonable agreement is found.     

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

We study the superconductor to insulator transition at zero temperature in aJosephson-junction array model on a honeycomb lattice with f flux quantum perplaquette. The path integral representation of the model corresponds to a (2 + 1)-dimensional classical model, which isused to investigate the critical behavior by extensive Monte Carlo simulations on largesystem sizes. In contrast to the model on a square lattice, the transition is found to befirst order for f = 1 /3 and continuous for f = 1 / 2 but in a different universality class.The correlation-length critical exponent is estimated from finite-size scaling of vortexcorrelations. The estimated universal conductivity at the transition is approximately fourtimes its value for f =0. The results are compared with experimental observations on ultrathinsuperconducting films with a triangular lattice of nanoholes in a transverse magneticfield.     

Scaling of the magnetoconductivity of silicon MOSFETs: evidence for a quantum phase transition in two dimensions

For a broad range of electron densities n and temperatures T, the in-plane magnetoconductivity of the two-dimensional system of electrons in silicon MOSFETs can be scaled onto a universal curve with a single parameter H(sigma)(n,T), where H(sigma) obeys the empirical relation H(sigma) = A(n) [Delta(n)(2)+T2](1/2). The characteristic energy k(B)Delta associated with the magnetic field dependence of the conductivity decreases with decreasing density, and extrapolates to 0 at a critical density n(0), signaling the approach to a zero-temperature quantum phase transition. We show that H(sigma) = AT for densities near n(0).     

Crossover from Mott to Efros-Shklovskii variable range-hopping in Si:P

The low-temperature conductivity of uncompensated insulating Si:P with P concentration just below the metal-insulator (MI) transition shows with decreasingN a crossover from Mott variable range hopping (VRH) to Efros-Shklovskii VRH. From the concentration dependence of the Mott temperatureT _M a correlation-length exponent ν=1.1 is obtained which is compatible with the conductivity exponent μ=1.3 for metallic samples.     

Scalings of domain wall energies in two dimensional Ising spin glasses

We study domain wall energies of two dimensional spin glasses. The scaling of these energies depends on the model's distribution of quenched random couplings, falling into three different classes. The first class is associated with the exponent theta approximately -0.28; the other two classes have theta=0, as can be justified theoretically. In contrast to previous claims, we find that theta=0 does not indicate d=d(c)(l) but rather d< or =d(c)(l), where d(c)(l) is the lower critical dimension.     

Conductivity of heavily doped Si:P under uniaxial stress

Barely insulating, uncompensated Si:P samples have been tuned through the metal‐insulator transition applying uniaxial stress along the [100] direction. We find a critical exponent μ ≈︂ 1 of the electrical conductivity extrapolated to temperature T = 0, i.e. σ(T → 0,S) ∼ |S — S_c|^μ, in disagreement with earlier stress tuning studies along [123‐] where μ ≈︂ 0.5 was reported. Varying the stress or the concentration leads to a different T dependence of σ(T). Our stress‐tuning measurements obey finite‐T scaling with a dynamic exponent z = 3.     

Viscosity of a liquid crystal near the nematic-smectic A phase transition

We report the results of an x-ray scattering study where both the dynamic and the static properties of a liquid crystal (8OCB) near the nematic-smectic A phase transition were probed. The static, time-averaged data show the gradual formation of smectic layers in the nematic phase, and we find that the smectic order correlation length parallel to the molecular axis diverges with the critical exponent nu( parallel )=0.70(4) at the transition. The literature value is nu( perpendicular )=0.58 for the perpendicular direction. By x-ray photon correlation spectroscopy, we find that the viscosity coefficient eta(3) shows critical, diverging behavior at the phase transition with a critical exponent x=0.95(5). This contradicts previous light scattering work (x=0.50), but is in good agreement with the theoretical prediction x=3nu( parallel )-2nu( perpendicular ) by Hossain et al.     

A schematic model discussion of the conductor to insulator transition for particle motion in a random potential

A schematic model for the dynamics of a particle moving in a random environment is discussed where the latter is assumed to cause normal scattering and also scattering with time inversion symmetry breaking. The second mechanism changes the exponent unity to one half for the vanishing of the conductivity near the percolation threshold. It alters also the exponent of the critical conductivity spectrum from 1/2 to 1/3. The dynamics near the transition including all cross over phenomena to the usual effective medium theory results are described by a two parameter scaling law.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Subcritical crack growth: the microscopic origin of Paris' law

We investigate the origin of Paris' law, which states that the velocity of a crack at subcritical load grows like a power law, da/dt ~ (DeltaK)(m), where DeltaK is the stress-intensity-factor amplitude. Starting from a damage-accumulation function proportional to (Deltasigma)(gamma), Deltasigma being the stress amplitude, we show analytically that the asymptotic exponent m can be expressed as a piecewise-linear function of the exponent gamma, namely, m=6-2gamma for gamma or =gamma(c), reflecting the existence of a critical value gamma(c)=2. We perform numerical simulations to confirm this result for finite sizes. Finally, we introduce bounded disorder in the breaking thresholds and find that below gamma(c) disorder is relevant, i.e., the exponent m is changed, while above gamma(c) disorder is irrelevant.     

Anomalous lattice response at the Mott transition in a quasi-2D organic conductor

Discontinuous changes of the lattice parameters at the Mott metal-insulator transition are detected by high-resolution dilatometry on deuterated crystals of the layered organic conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Br. The uniaxial expansivities uncover a striking and unexpected anisotropy, notably a zero effect along the in-plane c axis along which the electronic interactions are relatively strong. A huge thermal expansion anomaly is observed near the end point of the first-order transition line enabling us to explore the critical behavior with very high sensitivity. The analysis yields critical fluctuations with an exponent alpha approximately 0.8+/-0.15 at odds with the novel criticality recently proposed for these materials [Kagawa et al., Nature (London) 436, 534 (2005)]. Our data suggest an intricate role of the lattice degrees of freedom in the Mott transition for the present materials.     

A neutron scattering investigation of the order of the magnetic transition in NiO

The measured sublattice magnetization of NiO indicates, in contradiction to theoretical expectations, a continuous second-order phase transition with a critical exponent β=0.38.     

Electric-field-effect modulation of the transition temperature, mobile carrier density, and in-plane penetration depth of NdBa2Cu3O7-delta thin films

We explore the relationship between the critical temperature T(c), the mobile areal carrier density n(2D), and the zero-temperature magnetic in-plane penetration depth lambda(ab)(0) in very thin underdoped NdBa(2)Cu(3)O(7-delta) films near the superconductor to insulator transition using the electric-field-effect technique. Having established consistency with a Kosterlitz-Thouless transition, we observe that T(KT) depends linearly on n(2D), the signature of a quantum superconductor to insulator transition in two dimensions with znu(over)=1, where z is the dynamic and nu is the critical exponent of the in-plane correlation length.     

Mott transition and transport crossovers in the organic compound kappa-(BEDT-TTF)2Cu[N(CN)2]Cl

We have performed in-plane transport measurements on the two-dimensional organic salt kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. A variable (gas) pressure technique allows for a detailed study of the changes in conductivity through the insulator-to-metal transition. We identify four different transport regimes as a function of pressure and temperature (corresponding to insulating, semiconducting, "bad metal," and strongly correlated Fermi-liquid behaviors). Marked hysteresis is found in the transition region, which displays complex physics that we attribute to strong spatial inhomogeneities. Away from the critical region, good agreement is found with a dynamical mean-field calculation of transport properties using the numerical renormalization group technique.