Tunneling two-level systems (TLSs), generic to amorphous solids, dictate the low-temperature properties of amorphous solids and dominate noise and decoherence in quantum nano-devices. The properties of the TLSs are generally described by the phenomenological standard tunneling model. Yet, significant deviations from the predictions of this model found experimentally suggest the need for a more precise model in describing TLSs. Here we show that the temperature dependence of the sound velocity, dielectric constant, specific heat, and thermal conductivity, can be explained using an energy-dependent TLS density of states reduced at low energies due to TLS-TLS interactions. This reduction is determined by the ratio between the strengths of the TLS-TLS interactions and the random potential, which is enhanced in systems with dominant electric dipolar interactions.
We compare the heat release data of organic glasses with that of amorphous and glass like crystalline solids. Anomalous behavior was found in all these materials, which disagrees with the standard tunneling model. We can explain the most of the experimental observations within a phenomenological model, where we assume that for a part of tunneling systems the barrier heights are strongly reduced as a consequence of the local stress produced during the cooling process.
We consider the effect of the internal nuclear quadrupole interaction on quantum tunneling in complex multi-atomic two-level systems. Two distinct regimes of strong and weak interactions are found. The regimes depend on the relationship between a characteristic energy of the nuclear quadrupole interaction $λ_{\ast}$ and a bare tunneling coupling strength $Δ_{0}$. When $Δ_{0}>λ_{\ast}$, the internal interaction is negligible and tunneling remains coherent determined by $Δ_{0}$. When $Δ_{0}<λ_{\ast}$, coherent tunneling breaks down and an effective tunneling amplitude decreases by an exponential…
We have conducted a thorough study of the acoustic properties between 10^-4 and 1 Kelvin for the amorphous metal Zr_x Cu_1-x (x=0.3 and x=0.4), by measuring the relative change of sound velocity dv/v and internal friction Q^-1 as a function of temperature and also of the applied strain, in both superconducting and normal state. We have found that when plotted versus the ratio of strain energy to thermal energy, all measurements display the same behavior: a crossover from a linear regime of ``independent'' tunneling systems at very low strains and/or high enough temperatures to a nonlinear regi…
Internal friction and speed of sound of a-SiO(2) was measured above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, non-linear effects, and clamping losses. Strain amplitudes e(A) = 10^{-8} mark the transition between the linear and non-linear regime. In the linear regime, excellent agreement with the Tunneling Model was observed for both the internal friction and speed of sound, with a cut-off energy of E(min) = 6.6 mK. In the non-linear regime, two different behaviors were observed. Above 10 mK the behavior was typical for non-linear harmonic oscillators, whi…
A generalized tunneling model of insulating glasses is formulated, considering tunneling states to be paramagnetic centers of spin 1/2. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of the expression for the nonmonotonic magnetic field dependence of dielectric constant, recently observed in several glasses in the millikelvin temperature range.
We discuss the strain dependence of the acoustic properties of amorphous metals in both normal and superconducting states, in the temperature range 0.1 mK $ \le T \le 1 $K. A crossover is found when the strain energy is of the order of the effective interaction energy between tunneling systems at the corresponding temperature. Our results provide clear evidence for the interaction between tunneling systems, whose energy is in quantitative agreement with theoretical expectations, and reveal that without the knowledge of the corresponding strain dependences, the measured temperature dependences …
Recently it has been experimentally demonstrated that certain glasses display an unexpected magnetic field dependence of the dielectric constant. In particular, the echo technique experiments have shown that the echo amplitude depends on the magnetic field. The analysis of these experiments results in the conclusion that the effect seems to be related to the nuclear degrees of freedom of tunneling systems. The interactions of a nuclear quadrupole electrical moment with the crystal field and of a nuclear magnetic moment with magnetic field transform the two-level tunneling systems inherent in a…
The accurate analytical solution for the low temperature $1/f$ noise in a microwave dielectric constant of amorphous films containing tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The results are consistent with the recent experimental investigations of $1/f$ noise in Josephson junction qubits including the power law increase of the noise amplitude with decreasing temperature at low temperatures $T<0.1$K. The long time correlations needed for $1/f$ noise are provided by the logarithmic broadening of…
The motion of the structure determining components is highly collective, both in amorphous solids and in undercooled liquids. This has been deduced from experimental low temperature data in the tunneling regime as well as from the vanishing isotope effect in diffusion in glasses and undercooled liquids. In molecular dynamics simulations of glasses one observes that both low frequency resonant vibrations and atomic jumps are centered on more than 10 atoms which, in densely packed materials, form chainlike structures. With increasing temperature the number of atoms jumping collectively increases…
We performed detailed conductivity and tunneling mesurements on the amorphous, magnetically doped material $α$-Gd$_x$Si$_{1-x}$ (GdSi), which can be driven through the metal-insulator transition by the application of an external magnetic field. Conductivity increases linearly with field near the transition and slightly slower on the metallic side. The tunneling conductance, proportional to the density of states $N(E)$, undergoes a gradual change with increasing field, from insulating, showing a soft gap at low bias, with a slightly weaker than parabolic energy dependence, i.e. $N(E) \sim E^c$,…
Amorphous solids, and many disordered lattices, exhibit a remarkable qualitative and quantitative universality in their acoustic properties at temperature $\lesssim 3$K. This phenomenon is attributed to the existence of tunneling two level systems (TTLSs), characterized by a homogenous density of states (DOS) at energies much lower than the disorder energy ($\approx 0.1$eV). Here we calculate numerically, from first principles, the DOS of KBr:CN glass, the archetypal disordered lattice showing universality. In contrast to the standard tunneling model, we find that the DOS diminishes abruptly a…
The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking $\hbar\to 0$ limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitra…
A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of the expression for the nonmonotonic magnetic field dependence of dielectric susceptibility, recently observed in amorphous BaO-Al_2O_3-SiO_2 in sub-Kelvin temperature range.
We have studied the internal friction and the relative change in the speed of sound of amorphous diamond-like carbon films prepared by pulsed-laser deposition from 0.3 K to room temperature. Like the most of amorphous solids, the internal friction below 10 K exhibits a temperature independent plateau. The values of the internal friction plateau, however, are slightly below the universal ``glassy range'' where the internal frictions of almost all amorphous solids lie. Similar observations have been made in our earlier studies in the thin films of amorphous silicon and amorphous germanium, and t…
Using empirical potential molecular dynamics we compute dynamical matrix eigenvalues and eigenvectors for a 4096 atom model of amorphous silicon and a set of models with voids of different size based on it. This information is then employed to study the localization properties of the low-energy vibrational states, calculate the specific heat C(T) and examine the low-temperature properties of our models usually attributed to the presence of tunneling states in amorphous silicon. The results of our calculations for C(T) and "excess specific heat bulge" in the C(T)/T^3 vs. T graph for voidless a-…
Boron doped amorphous conducting carbon films show MI transition induced by doping. In this paper we discuss the ac conductivity of the films, which lie on the insulating side of MI transition. The ac conductivity data is analyzed as a function of frequency as well as temperature for both real as well as imaginary part of the conductivity data. The ac conductivity of these samples shows enhanced interaction effect at low temperature. The conduction mechanism at high frequency and at low temperature is due to the tunneling mechanism. At intermediate temperatures and at moderate frequencies, the…
The novel isotope and magnetic effects on two level system echoes in glasses observed by Nagel et al.(Phys.Rev.Lett. 92, 245511 (2004)) provide unique experimental insight into the nature of tunneling systems in amorphous solids. We show their observations are consistent with tunneling systems being extended systems having of order 100 moving units, as predicted by theory (Phys.Rev.Lett. 87, 195901 (2001)). The numerous nuclear quadrupole interactions within a tunneling center explain the magnitude of the magnetic and frequency dependence observed in deuterated glycerol. The extended nature of…
We study the metal-insulator transition in two sets of amorphous Si_{1-x}Ni_x films. The sets were prepared by different, electron-beam-evaporation-based technologies: evaporation of the alloy, and gradient deposition from separate Ni and Si crucibles. The characterization included electron and scanning tunneling microscopy, glow discharge optical emission spectroscopy, and Rutherford back scattering. Investigating the logarithmic temperature derivative of the conductivity, w = d ln sigma / d ln T, we observe that, for insulating samples, w(T) shows a minimum increasing at both low and high T.…
The quantum excitations in glasses have long presented a set of puzzles for condensed matter physicists. A common view is that they are largely disordered analogs of elementary excitations in crystals, supplemented by two level systems which are chemically local entities coming from disorder. A radical revision of this picture argues that the excitations in low temperature glasses are deeply connected to the energy landscape of the glass when it vitrifies: the excitations are not low excited states built on a single ground state but locally defined resonances, high in the energy spectrum of a …
Recent experimental results showing untypical nonlinear absorption and marked deviations from well known universality in the low temperature acoustic and dielectric losses in amorphous solids prove the need for improving the understanding of the nature of two-level systems (TLSs) in these materials. Here we suggest the study of TLSs focused on their properties which are nonuniversal. Our theoretical analysis shows that the standard tunneling model and the recently suggested Two-TLS model provide markedly different predictions for the experimental outcome of these studies. Our results may be di…
Numerous experimental indications suggest that the Hume-Rothery mechanism plays an important role in stabilizing quasicrystalline and amorphous phases. However, the exponential damping of the conventional Friedel oscillations at the relevant, elevated temperatures $T$ poses a severe challenge to the HR stabilization. In order to resolve this problem it is shown using a Feynman diagram technique that quantum correlations in the electron sea, arising from the interplay of Coulomb interaction and impurity scattering, can strongly enhance the Friedel oscillations in these systems even at elevated …
The standard tunneling model describes quite satisfactorily the thermal properties of amorphous solids at temperatures $T<1K$ in terms of an ensemble of two-level systems possessing logarithmically uniform distribution over their tunneling amplitudes and uniform distribution over their asymmetry energies. In particular, this distribution explains the observable logarithmic temperature dependence of the dielectric constant. Yet, experiments have shown that at ultralow temperatures $T<5mK$ such a temperature behavior breaks down and the dielectric constant becomes temperature independent (platea…
Following a brief review of the "two-level (tunneling) systems" model of the low-temperature properties of amorphous solids ("glasses"), we ask whether it is in fact the unique explanation of these properties as is usually assumed, concluding that this is not necessarily the case. We point out that (a) one specific form of the model is already experimentally refuted, and (b) that a definitive test of the model in its most general form, while not yet carried out, would appear to be now experimentally feasible.
We review a model--based rather than phenomenological approach to low--temperature anomalies in glasses. Specifically, we present a solvable model inspired by spin--glass theory that exhibits both, a glassy low--temperature phase, and a collection of double-- and single--well configurations in its potential energy landscape. The distribution of parameters characterizing the local potential energy configurations can be computed, and is found to differ from those assumed in the standard tunneling model and its variants. Still, low temperature anomalies characteristic of amorphous materials are r…
Tunneling two-level systems are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect-phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a crystalline tunnelling defect strongly coupled to phonons incorporating the full 3D geometry …
In a tight binding framework, we analyze the characteristics of electronic states in strongly disordered materials (hopping sites are placed randomly with no local order) with tunneling matrix elements decaying exponentially in the atomic separation with various decay ranges l examined. We calculate the density of states (DOS) and the Inverse Participation Ratio (IPR) for amorphous atomic configurations in one, two, and three dimensions. With a finite size scaling analysis of the IPR statistical distributions, it is shown that states are either extended or localized for a particular energy, an…
The dielectric constant of amorphous solids at low temperatures is governed by the dynamics of tunneling systems, small groups of atoms which tunnel between quasi equivalent potential minima. Recent experiments showed that at temperatures below 20 mK various glasses exhibit memory for a previously applied electric bias field. A first sweep of an electric bias field may prepare resonant pairs of tunneling systems, which are temporarily formed during the sweep, in metastable states. In subsequent sweeps the same resonant pairs thus significantly contribute to the dielectric constant, leading to …
Charge Transport and Multiplication in Lateral Amorphous Selenium Devices Under Cryogenic Conditions
University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of Manchester（曼彻斯特大学）；Florida State University（佛罗里达州立大学）
Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create {\it in silico} glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than $k_{B}T_Q$, with $T_Q$ the temperature below which quantum effects are relevant ($T_Q \approx 1 \,$K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it i…
The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landsca…
Amorphous solids, confined on the nano-scale, exhibit a wealth of novel phenomena yet to be explored. In particular, the response of such solids to a mechanical load is not well understood and, as has been demonstrated experimentally, it differs strongly from bulk samples made of the same materials. Failure patterns and mechanisms are strongly affected by the geometry of the confinement and the interplay between interfacial effects in the sample and the time scale, imposed by an external mechanical field. Here, we present the mechanism of cavity formation in a confined model glass, subjected t…
