Two-level Tunneling Systems Research Articles

Non-Fermi liquid ground state in magnetic multilayers tuned by electric and magnetic fields

We report on anomalous electron transport properties of low dimentional magnetic systems which may be tuned by electric and magnetic fields. In magnetic trilayers Co/M/Co (M – nonmagnetic spacer), which have been used to reveal the ground state of a disordered two-dimentional metal, at lower temperatures the crossover from a logarithmic to an anomalous non-Fermi liquid behaviour ( Δρ∼β T ) is observed which is interpreted as due to scattering of the electrons by symmetrical two-level tunnelling systems. We have also demonstrated that classical magnetic multilayers [Fe/Cr] 10 with enhanced spin dependent scattering effect may be used to study quantum magnetic phase transitions from ferromagnet to antiferromagnet.

The Second-Order Doppler Displacement of the M�ssbauer ?-Radiation in Amorphous Solid States

The influence of two-level tunnelling systems and bosonic peak on the second-order Doppler displacement of Mossbauer γ-radiation in disordered materials is investigated. It is shown, that the Mossbauer frequency temperature displacement at temperatures 10 -4 K < T < ω m ∞/k B is determined by bosonic peak and at T < 10 -4 K by two-level tunnelling systems.

Anomalous low-temperature resistivity of metallic trilayers: Possible evidence for electron scattering on symmetrical two-level systems

We report on a study of the ground state of $\mathrm{Co}/M/\mathrm{Co}$ $(M$ is a nonmagnetic metallic spacer) metallic trilayers where electrical resistivity increases logarithmically with decreasing temperature $(\ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\sim}A\mathrm{log}T)$ down to about 100 mK due to two-dimensional electron-electron interactions. At lower temperatures the crossover from a logarithmic to an anomalous non-Fermi-liquid behavior $(\ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\sim}\ensuremath{\beta}\sqrt{T})$ is observed, with $\ensuremath{\beta}$ independent of the magnetic field up to 13 T. The $\sqrt{T}$ dependence of the resistivity is interpreted as due to scattering of the electrons by symmetrical two-level tunneling systems.

The 2-Channel Kondo Model*1I. Review of Experimental Evidence for Its Realization in Metal Nanoconstrictions

Certain zero-bias anomalies (ZBAs) in the voltage, temperature and magnetic field dependence of the conductanceG(V, T, H) of quenched Cu point contacts have previously been interpreted to be due to non-magnetic 2-channel Kondo (2CK) scattering from near-degenerate atomic two-level tunneling systems (Ralph and Buhrman, 1992; Ralphet al., 1994) and hence to represent an experimental realization of the non-Fermi-liquid physics of theT=0 fixed point of the 2-channel Kondo model. In this, the first in a series of three papers (I, II, III) devoted to 2-channel Kondo physics, we present a comprehensive review of the quenched Cu ZBA experiments and their 2CK interpretation, including new results on ZBAs in constrictions made from Ti or from metallic glasses. We first review the evidence that the ZBAs are due to electron scattering from stuctural defects that are not static, but possess internal dynamics. In order to distinguish between several mechanisms proposed to explain the experiments, we then analyze the scaling properties of the conductance at low temperature and voltage and extract from the data a universal scaling functionΓ(v). The theoretical calculation of the corresponding scaling function within the 2CK model is the subject of papers II and III. The main conclusion of our work is that the properties of the ZBAs, and most notably their scaling behavior, are in good agreement with the 2CK model and clearly different from several other proposed mechanisms.

The 2-Channel Kondo Model: I. Review of Experimental Evidence for Its Realization in Metal Nanoconstrictions

Certain zero-bias anomalies (ZBAs) in the voltage, temperature and magnetic field dependence of the conductanceG(V, T, H) of quenched Cu point contacts have previously been interpreted to be due to non-magnetic 2-channel Kondo (2CK) scattering from near-degenerate atomic two-level tunneling systems (Ralph and Buhrman, 1992; Ralphet al., 1994) and hence to represent an experimental realization of the non-Fermi-liquid physics of theT=0 fixed point of the 2-channel Kondo model. In this, the first in a series of three papers (I, II, III) devoted to 2-channel Kondo physics, we present a comprehensive review of the quenched Cu ZBA experiments and their 2CK interpretation, including new results on ZBAs in constrictions made from Ti or from metallic glasses. We first review the evidence that the ZBAs are due to electron scattering from stuctural defects that are not static, but possess internal dynamics. In order to distinguish between several mechanisms proposed to explain the experiments, we then analyze the scaling properties of the conductance at low temperature and voltage and extract from the data a universal scaling functionΓ(v). The theoretical calculation of the corresponding scaling function within the 2CK model is the subject of papers II and III. The main conclusion of our work is that the properties of the ZBAs, and most notably their scaling behavior, are in good agreement with the 2CK model and clearly different from several other proposed mechanisms.

Second-order nuclear magnetic relaxation in samples with two-level tunneling systems

Second-order nuclear magnetic relaxation associated with electric quadrupole interaction between paramagnetic centers and two-level systems is studied. First- and second-order relaxation times are compared. It is shown that second-order relaxation prevails in relatively low magnetic fields.

Strong-coupling theory for the spin-phonon model

We present a strong-coupling approach to the spin-phonon model with a cubic spectral density, which relies on a matrix representation for the reduced time evolution operator on the four-dimensional space of pseudospins. The $4\ifmmode\times\else\texttimes\fi{}4$ self-energy matrix $\ensuremath{\Sigma}$ is written as an infinite series in powers of bath fluctuation operators, and the lowest-order approximation is evaluated explicitly. The diagonal element ${\ensuremath{\Sigma}}_{\mathrm{zz}}$ corresponds to the result of the noninteracting blip approximation (NIBA); retaining the full matrix is equivalent to taking into account certain blip-blip interactions. Contrary to NIBA, this approach agrees with a rigorous result for the quadratic term of the rate. As a main result, we find a crossover to incoherent motion at a temperature ${T}^{*}$, which is compared to previous theoretical work and discussed in view of experimental data for various two-level tunneling systems.

Nonlinear acoustic and microwave absorption in glasses

A theory of weakly-nonlinear low-temperature relaxational absorption of acoustic and electromagnetic waves in dielectric and metallic glasses is developed. Basing upon the model of two-level tunneling systems we show that the nonlinear contribution to the absorption can be anomalously large. This is the case at low enough frequencies, where freqeuency times the minimal relaxation time for the two-level system are much less than one. In dielectric glasses, the lowest-order nonlinear contribution is proportional to the wave's intensity. It is negative and exhibits anomalous frequency and temperature dependencies. In metallic glasses, the nonlinear contribution is also negative, and it is proportional to the square root of the wave's intensity and to the frequency. Numerical estimates show that the predicted nonlinear contribution can be measured experimentally.

Similarities and differences between the low-temperature acoustic properties of crystalline materials and glasses

We report on measurements of the acoustic properties of single crystals of alkali halides and aluminum, and polycrystalline copper at kHz frequencies and temperatures down to 8 mK. The goal of this study was to examine in several crystals with a small number of defects the presence and influence of two-level tunneling systems which commonly govern the low-temperature behavior of amorphous solids. The samples were investigated using vibrating reed and torsional oscillator techniques. In contrast to recent reports on glasslike behavior for a large variety of pure polycrystalline metals, our results confirm the ``traditional'' point of view that the low-temperature acoustic properties of pure monatomic crystals can be well distinguished from those of amorphous solids.

Theory of Single-Molecule Optical Line-Shape Distributions in Low-Temperature Glasses

We present a theoretical framework for analyzing the distribution of optical line shapes in low-temperature glasses, as measured by single-molecule spectroscopy. The theory is based on the standard tunneling two-level system model of low-temperature glasses and on the stochastic sudden jump model for the two-level system dynamics. Within this framework we present an explicit formula for the line shape of a single molecule and employ Monte Carlo simulation techniques to calculate the distribution of single-molecule line shapes. We compare our calculated line-width distributions to those measured experimentally. We find that the two-level system model captures the features of the experimental line-width distributions very well, although there are discrepancies for small line widths. We also discuss the relation of single-molecule line-shape distributions to more traditional “line shapes”, as measured by hole-burning and photon echo spectroscopies. Using the results from our analysis of the single-molecule line-width distributions, with no adjustable parameters we can compare theoretical predictions with experiment for photon echo decay times and hole widths. In general, the agreement is good, providing further evidence that the standard tunneling model in glasses is basically correct. For two systems, however, theory and experiment do not agree quantitatively.

Nuclear relaxations due to paramagnetic impurities in two-level systems

The rates of two types of nuclear spin-lattice relaxation are compared. Transverse relaxation of nuclear spins interacting with paramagnetic centers is also examined under the assumption that the paramagnetic centers form two-level tunneling systems. The transverse relaxation rate is calculated and it is shown that at certain temperatures the transverse relaxation rate is governed by the two-level systems.

Generalized Bloch equations for a strongly driven tunneling system

Using the Robertson projection operator formalism, we derive generalized Bloch equations which describe the dynamics of a biased two-level tunneling system strongly driven by an external field and weakly coupled to a super-Ohmic heat bath. The generalized Bloch equations constitute a set of coupled nonlinear integro-differential equations. With their help we investigate the influence of phonons on the phenomenon of dynamical localization.

Tunneling in a cavity.

The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is studied from the viewpoint of quantum optics by considering the photon statistics of a single mode cavity field which is strongly coupled to a two-level tunneling system (TS). As a function of the interaction time between TS and cavity the photon statistics displays the tunneling dynamics. In the semiclassical limit of high photon occupation number n, coherent destruction of tunneling is exhibited in a slowing down of an amplitude modulation for certain parameter ratios of the field. The phenomenon is explained as arising from interference between displaced number states in phase space which survives the large n limit due to identical ${\mathit{n}}^{\mathrm{\ensuremath{-}}1/2}$ scaling between orbit width and displacement. \textcopyright{} 1996 The American Physical Society.

Anomalous dielectric properties of amorphous solids at low temperatures

The dielectric response, ɛ′ (ω) +iɛ″ (ω), of amorphous and glassy systems at low temperatures has been explained with considerable success by relaxation and resonant tunneling of independent tunneling two level systems (TLS) in response to an AC electric field. However, recent measurements have shown an AC response to the application of large DC electric fields which does not appear explicable in terms of independent TLS, but instead may result from the formation of a hole in the density of states of the TLS at zero effective local electric field, similar to that postulated to exist in spin glasses. This paper reports new studies of this response at very low temperatures which further support this interpretation, again suggesting that interactions are important in understanding the dynamics of such systems at low temperatures.

Nonlinear response of two-level tunneling systems in the RDP-ADP proton glass

The nonlinear dielectric constant of the RDP(RbH2PO4)-ADP(NH4H2PO4)proton glass has been measured down to 0.03 K. For the ADP concentration x. 0.22<x<0.80, the RDP-ADP mixed crystals take up a frozen random configuration of electric dipoles and the temperature dependence and the frequency dependence of the linear dielectric constant show the presence of two-level systems. The nonlinear dielectric constant has been measured for the first time and the temperature dependence has been explained in terms of the interaction between a two-level system

The low-temperature dynamics of rhodamine 640 in polyvinylalcohol

The low temperature (1.2–2.1 K) dynamics of rhodamine 640 in polyvinyl alcohol have been investigated by 2-pulse photon echo measurements. The low temperature dephasing results of this study cannot be fit utilizing only the tunneling two-level-system (TLS) model used to describe the higher temperature (10–30 K) data of Nakanishi et al. [J. Chem. Phys. 100, 3442 (1994)] on the same system. In the present study, both the low temperature (1.2–2.1 K) data and the high temperature (10–30 K) data of Nakanishi et al. are fit by a model which includes both a TLS and an electron–phonon contribution to the optical dephasing, yielding a homogeneous dephasing rate (T2*)−1=aTα+b(exp(ΔE/kT)−1)−1, where α=4/3, a=(2915 ps)−1, b=(2.9 ps)−1 and ΔE=16.7 cm−1. The present results indicate that TLS models alone are not sufficient to describe the optical dynamics of Rh640 in PVA at temperatures above 5 K. This is particularly important for studies which attempt to use chemical or physical modification of the matrix to investigate the nature of TLS.

Kondo scattering from atomic two-level tunneling systems in metals: Enhanced conductance, critical-bias transitions, and the non-Fermi-liquid electronic state.

We describe a state of enhanced dc conductance, terminated by an abrupt transition as a function of bias current, that exists at low temperature in metal point contacts that also display a signal near zero bias attributable to Kondo scattering from a class of fast-tunneling atomic two-level systems. We argue that the regime of enhanced conductance is a consequence of the presence of a highly correlated non-Fermi-liquid electronic screening state about these two-level tunneling systems. The critical-current transition marks a sudden change in the electronic state during which this non-Fermi-liquid state is disrupted, and replaced by a lower-conductance normal state at high bias. We describe in detail the temperature and magnetic-field dependence of the critical-current transitions, as well as their hysteresis as a function of bias.

Dynamics of a coupled pair of two-level tunnelling systems

An exact solution for the dynamics of a coupled pair of symmetric two-level-systems is given by calculating the resolvent of the Liouvillian and the statistical operator of the problem. At low temperatures interference effects between the two systems turn out to be of major importance. Depending on the value and the sign of the interaction parameter the susceptibility of the pair increases or decreases compared to the situation of isolated systems. For high temperatures the interference contributions disappear.

Optical dephasing of organic dye molecules doped in cross-linked polyvinyl alcohol derivatives: Incoherent photon echo and hole-burning studies

Optical dephasing of the zero-phonon line (ZPL) of organic dye molecules doped in polyvinyl alcohol (PVA) and several cross-linked PVA derivatives was studied by using the incoherent photon echoes and the photophysical persistent hole-burning. It was found in the incoherent photon echo measurements that optical dephasing time of the ZPL increases with increasing the length of a cross-linker introduced to the PVA backbone. The difference in the temperature dependence of the dephasing time was also observed between a dye doped in PVA with and without the cross-link. When a longer cross-linker was introduced, the phonon sideband component in the incoherent photon echo signal became dominant in contrast to that in PVA with a relatively short cross-linker, while the dephasing time of the ZPL was still longer than that in PVA without the cross-link. Hole-burning studies showed that the phonon sideband spectrum of a dye doped in the cross-linked PVAs is essentially similar to that in PVA. However, the depth of the zero-phonon hole burnt with the same burning power was found to depend on the PVA hosts with the cross-linkers. These our findings suggest that the introduced cross-link does not alter the electron–phonon coupling modes or pseudo-local mode, but it drastically reduces the effect of the two-level tunneling systems in PVA on the optical dephasing of a doped dye. As a result, the dephasing time of the dye in the cross-linked PVAs becomes longer than that in PVA without the cross-link. The decrease of the optical dephasing by introducing the cross-link can be interpreted by assuming a void space in PVA, which is created near to the cross-linker. In addition, absorption and fluorescence spectra in these systems were measured, which imply the occurrence of weak dye–dye interaction when the dye is doped in PVA with a much longer cross-linker.

Low- and high-frequency conductivities of RbAg 4I 5 and Ag β″-alumina at low temperatures

The specific ionic conductivities, σ, of polycrystalline RbAg 4I 5 and Ag β″-alumina superionic conductors were determined by two- and four-probe impedance measurements at low frequencies (10 −3Hz≤ƒ≤10 2Hz) and waveguide measurements at high frequencies (18×10 9Hz≤ƒ≤26.5×10 9Hz≡:k-band) in the temperature range 15K≤ T≤298K. Above a transition temperature T t=(90±20)K, the conductivity data represent clearly a silver ion transport process with thermal activation. The activation energies of the α, β, and γ phases of RbAg 4I 5 were determined for the low- and high-frequency ranges. Below T t a nearly temperature-independent conductivity was observed in accordance with previous results. Around T t a long-time relaxation effect is observed in low-frequency EIS measurements, changing α and the dielectric constant ε. The low-temperature conductivity data can be explained neither in terms of the jump-relaxation nor in terms of the two-level tunneling system (TLS) model. A different mechanism which takes into account the influence of inhomogeneities on the ionic conductivity is proposed. This mechanism is obviously valid in a restricted temperature range located between the ion TLS-tunneling and the jump-relaxation regimes.