Search

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 at $\approx 3$ K, and that tunneling states differ essentially by their symmetry under inversion. This structure of the TTLSs dictates the low temperature below which universality is observed, and the quantitative universality of the acoustic properties in glasses. Consequences to the properties of glasses at intermediate temperatures, as well as to the microscopic structure of amorphous solids, are discussed., Comment: 6 pages, 2 figures, published version

Many disordered lattices exhibit remarkable universality in their low temperature properties, similar to that found in amorphous solids. Recently a two-TLS (two-level system) model was derived based on the microscopic characteristics of disordered lattices. Within the two-TLS model the quantitative universality of phonon attenuation, and the energy scale of $1-3$ K below which universality is observed, are derived as a consequence of the existence of two types of TLSs, differing by their interaction with the phonon field. In this paper we calculate analytically and numerically the densities of states (DOS) of the weakly and strongly interacting TLSs. We find that the DOS of the former can be well described by a Gaussian function, whereas the DOS of the latter have a power law correlation gap at low energies, with an intriguing dependence of the power on the short distance cutoff of the interaction. Both behaviors are markedly different from the logarithmic gap exhibited by a single species of interacting TLSs. Our results support the notion that it is the weakly interacting $\tau$-TLSs that dictate the standard low temperature glassy physics. Yet, the power-law DOS we find for the $S$-TLSs enables the prediction of a number of deviations from the universal glassy behavior that can be tested experimentally. Our results carry through to the analogous system of electronic and nuclear spins, implying that electronic spin flip rate is significantly reduced at temperatures smaller than the magnitude of the hyperfine interaction., Comment: Version submitted to EPJ ST

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 our description. We find that inversion symmetric tunnelling is not dressed by phonons whereas other tunnelling pathways are dressed by phonons and, thus, are suppressed by strong defect-phonon coupling. We provide the linear acoustic and dielectric response functions for a crystalline tunnelling defect for strong defect-phonon coupling. This allows direct experimental determination of the defect-phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric two-level systems play a unique role in the low energy properties of disordered solids., Comment: 18 pages, 4 figures; minor modification, final version

Amorphous solids, as well as many disordered lattices, display remarkable universality in their low temperature acoustic properties. This universality is attributed to the attenuation of phonons by tunneling two-level systems (TLSs), facilitated by the interaction of the TLSs with the phonon field. TLS-phonon interaction also mediates effective TLS-TLS interactions, which dictates the existence of a glassy phase and its low energy properties. Here we consider KBr:CN, the archetypal disordered lattice showing universality. We calculate numerically, using conjugate gradients method, the effective TLS-TLS interactions for inversion symmetric (CN flips) and asymmetric (CN rotations) TLSs, in the absence and presence of disorder, in two and three dimensions. The observed dependence of the magnitude and spatial power law of the interaction on TLS symmetry, and its change with disorder, characterizes TLS-TLS interactions in disordered lattices in both extreme and moderate dilutions. Our results are in good agreement with the two-TLS model, recently introduced to explain long-standing questions regarding the quantitative universality of phonon attenuation and the energy scale of $\approx 1-3$ K below which universality is observed., Comment: 6 pages, 4 figures, final version

The low temperature universal properties in disordered and amorphous solids are considered. We introduce a model that includes two types of two level systems (TLSs), which, based on their local symmetry, interact weakly or strongly with the phonon field. This accounts well for the experimental results, and addresses some long-standing questions: the nature of the TLSs; the smallness and universality of the phonon attenuation, and the energy scale of $3$K below which universality is observed. Our model describes disordered lattices; we also discuss its application to amorphous solids., Comment: 12 pages, 4 figures, published version

Both orientational glasses and dipolar glasses possess an intrinsic random field, coming from the volume difference between impurity and host ions. We show this suppresses the glass transition, causing instead a crossover to the low $T$ phase. Moreover the random field is correlated with the inter-impurity interactions, and has a broad distribution. This leads to a peculiar variant of the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen pairs. These domains are small: predictions of domain size are given for specific systems, and their possible experimental verification is outlined. In magnetic glasses in zero field the glass transition survives, because the random fields are disallowed by time-reversal symmetry; applying a magnetic field then generates random fields, and suppresses the spin glass transition., Comment: minor modifications, final version

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyse the case where the defects can be modelled either as simple 2-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to 2nd order in the displacement field. It is shown that the linear coupling generates not only the usual $1/r^3$ Ising-like interaction between the rotational tunneling defect modes, which cause them to freeze around a temperature $T_G$, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however the coupling of these to the frozen rotational modes, now via the 2nd-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range $1/r^5$ interactions between them). Detailed expressions for all these couplings are given., Comment: 12 pages, 2 figures. Minor modifications, published version

The ${\rm LiHo_xY_{1-x}F_4}$ compound is widely considered to be the archetypal dipolar Quantum Ising system, with longitudinal dipolar interactions $V_{ij}^{zz}$ between ${\rm Ho}$ spins $\{i,j \}$ competing with transverse field-induced tunneling, to give a T=0 quantum phase transition. By varying the ${\rm Ho}$ concentration x, the typical strength $V_0$ of $V_{ij}^{zz}$ can be varied over many orders of magnitude; and so can the transverse field $H_{\perp}$. A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, and valid at low and intermediate temperatures. For any such dipolar Quantum Ising system, the hyperfine interaction will dominate the physics at low temperatures, even if its strength $A_0 < V_0$: one must therefore go beyond an electronic transverse field Quantum Ising model. We derive the full phase diagram of this system, including all nuclear levels, as a function of transverse field $H_{\perp}$, temperature $T$, and dipole concentration x. For ${\rm LiHo_xY_{1-x}F_4}$ we predict a re-entrant critical field as a function of x. We also predict the phase diagram for x$=0.045$, and the behavior of the system in magnetic resonance and $\mu$SR experiments., Comment: 19 pages, 10 figures, predictions regarding magnetic resonance experiments are added, presentation improved

This paper has been withdrawn., Comment: paper withdrawn

The spin-glass phase in the $\LHx$ compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J=8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality., Comment: 6 pages, 2 figures, to appear in J. Phys. Condens. Matter (proceedings of the HFM2006 conference)

We consider the quantum magnet $\rm LiHo_xY_{1-x}F_4$ at $x = 0.167$. Experimentally the spin glass to paramagnet transition in this system was studied as a function of the transverse magnetic field and temperature, showing peculiar features: for example (i) the spin glass order is destroyed much faster by thermal fluctuations than by the transverse field; and (ii) the cusp in the nonlinear susceptibility signaling the glass state {\it decreases} in size at lower temperature. Here we show that the hyperfine interactions of the Ho atom must dominate in this system, and that along with the transverse inter-Ho dipolar interactions they dictate the structure of the phase diagram. The experimental observations are shown to be natural consequences of this., Comment: minor modifications, published version

Small metallic grains which satisfy the conditions of the universal Hamiltonian are considered. It is shown that for such grains the effects of the interactions in the spin channel and in the Cooper channel on their spin magnetization are well separated, thus allowing the determination of the interaction parameters within this model. In particular, the existence of pairing correlations in small grains and the sign of the interaction in the Cooper channel can be uniquely determined., Comment: minor corrections, published version

We calculate the orbital magnetic response to Aharonov Bohm flux of disordered metallic rings with attractive pairing interaction. We consider the reduced BCS model, and obtain the result as an expansion of its exact solution to first order in the interaction. We emphasize the connection between the large magnetic response and the finite occupation of high energy levels in the many-body ground state of the ring., Comment: 10 pages, contribution to MS+S2002

The magnetization of an ensemble of isolated lead grains of sizes ranging from below 6 nm to 1000 nm is measured. A sharp disappearance of Meissner effect with lowering of the grain size is observed for the smaller grains. This is a direct observation by magnetization measurement of the occurrence of a critical particle size for superconductivity, which is consistent with Anderson's criterion., Comment: 7 pages, 5 figures, Submitted to PRL

Unlike bulk superconductivity, where one energy scale, the energy gap, characterizes pairing correlations, we show that in small superconducting grains there exist two different such quantities. The first characterizes cumulative properties of the grain, such as the condensation energy, and the second single-particle properties. To describe these two energy scales, we define two corresponding pairing parameters, and show that although both reduce to the bulk gap for large grains, this occurs at different size scales., Comment: 6 pages, 1 figure, submitted to Phys. Rev. B

We calculate the orbital linear magnetic response of disordered metallic rings to an Aharonov-Bohm flux using the BCS model for attractive electron-electron interaction. The contribution of all levels including those up to a high energy cutoff results in a much larger value than previously obtained using the local interaction model. The possible relevance of our results to the resolution of the discrepancy between the experimental and theoretical values for the ensemble-averaged persistent currents in these systems is discussed., Comment: Submitted to PRL

We investigate the phenomenon of reflectionless tunneling in ballistic normal-metal--superconductor (NS) structures, using a semiclassical formalism. It is shown that applied magnetic field and superconducting phase difference both impair the constructive interference leading to this effect, but in a qualitatively different way. This is manifested both in the conductance and in the shot noise properties of the system considered. Unlike diffusive systems, the features of the conductance are sharp, and enable fine spatial control of the current, as well as single channel manipulations. We discuss the possibility of conducting experiments in ballistic semiconductor-superconductor structures with smooth interfaces and some of the phenomena, specific to such structures, that could be measured. A general criterion for the barrier at NS interfaces, though large, to be effectively transparent to pair current is obtained., Comment: published version

The dc Josephson effect is considered from the thermodynamic point of view. Universal thermodynamic equations, relating both bound and continuum contributions to the Josephson current with the normal electron scattering amplitudes are derived for the single mode case. To derive these equations we use and further develop the method of spatial separation between the superconducting and normal parts of the junction. We also use this method to find the Andreev bound states in structures containing superconducting components. The general thermodynamic formulas are applied to the calculation of the current in various Josephson-type structures. In particular, the crucial role of the continuum contribution is demonstrated, even for short junctions (where it is usually neglected). We also find structures where the bound states supporting the giant currents are well separated; thus they can, hopefully, be populated nonuniformly and such current can be measured., Comment: 11 pages, 9 figures

The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered. The crossover between the ultrasmall regime, in which the level spacing, $d$, is larger than the bulk superconducting gap, $\Delta$, and the small regime, where $\Delta \gtrsim d$, is investigated analytically and numerically. The condensation energy, spin magnetization and tunneling peak spectrum are calculated analytically in the ultrasmall regime, using an approximation controlled by $1/\ln N$ as small parameter, where $N$ is the number of interacting electron pairs. The condensation energy in this regime is perturbative in the coupling constant $\lambda$, and is proportional to $d N \lambda^2 = \lambda^2 \omega_D$. We find that also in a large regime with $\Delta>d$, in which pairing correlations are already rather well developed, the perturbative part of the condensation energy is larger than the singular, BCS, part. The condition for the condensation energy to be well approximated by the BCS result is found to be roughly $\Delta > \sqrt{d \omega_D}$. We show how the condensation energy can, in principle, be extracted from a measurement of the spin magnetization curve, and find a re-entrant susceptibility at zero temperature as a function of magnetic field, which can serve as a sensitive probe for the existence of superconducting correlations in ultrasmall grains. Numerical results are presented which suggest that in the large $N$ limit the 1/N correction to the BCS result for the condensation energy is larger than $\Delta$., Comment: 17 pages, 7 figures, Submitted to Phys. Rev. B

The effect of the barrier on the proximity effect in normal-superconductor junction is analyzed. A general criterion for the barrier, though large, to be effectively transparent, is given. This criterion is applied to both the conductance of a disordered NS junction (reflectionless tunneling) and the density of states across it, showing that both phenomena stem from the same physical effect., Comment: RevTeX, 4 pages, 2 figures. References added, introduction revised