Search Results (148 total)

Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes conditions on microscopic properties, namely, curvatures at the saddle points of the potential, and links them to the macroscopic phenomenon of a phase transition. We apply our result to two exactly solvable models, corroborating that the criterion derived is not only valid, but also sharp and useful: For both models studied, the criterion excludes the occurrence of a phase transition for all values of the potential energy but the transition energy. This result adds a geometrical ingredient to an established topological condition for the occurrence of a phase transition, thereby providing an answer to the long-standing question of which topology changes in configuration space can induce a phase transition.

We report electrical transport measurements of arrays of PbSe nanocrystals forming the channels of field-effect transistors. We measure the current in these devices as a function of source-drain voltage, gate voltage, and temperature. Annealing is necessary to observe measurable current, after which a simple model of hopping between intrinsic localized states describes the transport properties of the nanocrystal solid. We find that the majority carriers are holes, which are thermally released from acceptor states. At low source-drain voltages, the activation energy for the conductivity is given by the energy required to generate holes plus the activation over barriers resulting from site disorder. At high source-drain voltages, the activation energy is given by the former only. The thermal activation energy of the zero-bias conductance indicates that the Fermi energy is close to the highest-occupied valence level, the 1S_h state, and this is confirmed by field-effect measurements, which give a density of states of approximately 8 per nanocrystal as expected from the degeneracy of the 1S_h state.

We demonstrate electrical control of the spin relaxation time T₁ between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W≡T₁^-1 by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T₁ exceeds 1 s.

Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for the presence, or the absence, of a phase transition, and an investigation of these properties may lead to a deeper understanding of the physical phenomenon. One possible way to approach this problem, reviewed and discussed in the present paper, is the study of topology changes in configuration space which are found to be related to equilibrium phase transitions in classical statistical mechanical systems. For the study of configuration space topology, one considers the subsets M_v, consisting of all points from configuration space with a potential energy per particle equal to or less than a given v. For finite systems, topology changes of M_v are intimately related to nonanalytic points of the microcanonical entropy. In the thermodynamic limit, a more complex relation between nonanalytic points of thermodynamic functions (i.e., phase transitions) and topology changes is observed. For some class of short-range systems, a topology change of the M_v at v=v_t was proven to be necessary, but not sufficient, for a phase transition to take place at a potential energy v_t. In contrast, phase transitions in systems with long-range interactions or in systems with nonconfining potentials need not be accompanied by such a topology change. Instead, for such systems the nonanalytic point in a thermodynamic function is found to have some maximization procedure at its origin. These results may foster insight into the mechanisms which lead to the occurrence of a phase transition, and thus may help to explore the origin of this physical phenomenon.

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. [Phys. Rev. Lett. 95, 145702 (2005)] on topological signatures of the spherical model are elucidated.

We present measurements of the rates for an electron to tunnel on and off a quantum dot, obtained using a quantum point contact charge sensor. The tunnel rates show exponential dependence on drain-source bias and plunger gate voltages. The tunneling process is shown to be elastic, and a model describing tunneling in terms of the dot energy relative to the height of the tunnel barrier quantitatively describes the measurements.

In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems. The relation between finite and infinite system nonanalyticities is illustrated by means of a simple classical spinlike model which is exactly solvable for both finite and infinite system sizes, showing a phase transition in the latter case. The microcanonical entropy is found to have exactly one nonanalytic point in the interior of its domain. For all finite system sizes, this point is located at the same fixed energy value ε_c^finite, jumping discontinuously to a different value ε_c^infinite in the thermodynamic limit. Remarkably, ε_c^finite equals the average potential energy of the infinite system at the phase transition point. The result indicates that care is required when trying to infer infinite system properties from finite system nonanalyticities.

We measure the conductance of close-packed films of CdTe nanocrystals in field-effect structures in the dark and in the presence of light. We find that the majority carriers are holes, that they are injected from gold electrodes into the CdTe nanocrystal films, and that the hole density can be modulated with gate voltage. Secondary photocurrents have a photoconductive gain of ∼10 at 10⁶ V∕cm showing that the hole mobility is higher than the electron mobility. A single phenomenological description of the field dependence of the hole mobility can explain the dependence of current on source-drain voltage for both dark and light currents.

A large deviation technique is applied to the mean-field φ⁴ model, providing an exact expression for the configurational entropy s(v,m) as a function of the potential energy v and the magnetization m. Although a continuous phase transition occurs at some critical energy v_c, the entropy is found to be a real analytic function in both arguments, and it is only the maximization over m which gives rise to a nonanalyticity in ŝ(v)=sup_m  s(v,m). This mechanism of nonanalyticity-generation by maximization over one variable of a real analytic entropy function is restricted to systems with long-range interactions and has—for continuous phase transitions—the generic occurrence of classical critical exponents as an immediate consequence. Furthermore, this mechanism can provide an explanation why, contradictory to the so-called topological hypothesis, the phase transition in the mean-field φ⁴ model need not be accompanied by a topology change in the family of constant-energy submanifolds.

An artificial atom with four electrons is driven through a singlet-triplet transition by varying the confining potential. In the triplet, a Kondo peak with a narrow dip at drain-source voltage V_ds=0 is observed. The low energy scale V_ds^* characterizing the dip is consistent with predictions for the two-stage Kondo effect. The phenomenon is studied as a function of temperature T and magnetic field B_‖, parallel to the two-dimensional electron gas. The low energy scales T^* and B_‖^* are extracted from the behavior of the zero-bias conductance and are compared to the low energy scale V_ds^* obtained from the differential conductance. Good agreement is found between k_BT^* and ∣g∣μ_BB_‖^*, but eV_ds^* is larger, perhaps because of nonequilibrium effects.

A model of transport is proposed to explain power-law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Lévy process of transmission events and thereby requires no time dependence of system properties. The waiting time distribution with a characteristic long tail gives rise to a nonstationary response in the presence of a voltage pulse. We report on noise measurements that agree well with the predicted non-Poissonian fluctuations in current, and discuss possible mechanisms leading to this behavior.

A Kondo peak in the differential conductance of a single-electron transistor is measured as a function of both the magnetic field and the Kondo temperature. We observe that the Kondo splitting decreases logarithmically with the Kondo temperature and that there exists a critical magnetic field B_C below which the Kondo peak does not split, in qualitative agreement with theory. However, we find that the magnitude of the prefactor of the logarithm is larger than predicted and is independent of B, in contradiction with theory. Our measurements also suggest that the value of B_C is smaller than predicted.

We report the observation of a magnetic-field-induced transition between magnetically disordered and ordered phases in slightly underdoped La_2−xSr_xCuO₄ with x=0.144. Static incommensurate spin-density-wave order is induced above a critical field of about 3 T, as measured by elastic neutron scattering. Our results allow us to constrain the location of a quantum critical point on the phase diagram.

We present measurements of photoconductivity in CdSe quantum dot films treated with a variety of reagents. While the photocurrent of untreated samples is highly voltage dependent at all voltages, after treatment the photocurrent is much larger, depends strongly on voltage at low voltage, displays a linear region above a voltage threshold, and finally saturates at high voltage. All regions of the current-voltage curves after treatment can be reproduced with a model that requires noninjecting contacts and a field dependent exciton ionization efficiency that saturates to unity. This model is shown to be consistent with the trends observed with different treatments. The changes in photocurrent with treatment are shown to be largely a consequence of increased quantum dot surface passivation and decreased quantum dot spacing, regardless of whether the molecules used for treatment are conjugated or able to cross-link the quantum dots.

We measure the spin splitting in a magnetic field B of localized states in single-electron transistors using a new method, inelastic spin-flip cotunneling. Because it involves only internal excitations, this technique gives the most precise value of the Zeeman energy Δ=|g|μ_BB. In the same devices we also measure the splitting with B of the Kondo peak in differential conductance. The Kondo splitting appears only above a threshold field as predicted by theory. However, the magnitude of the Kondo splitting at high fields exceeds 2|g|μ_BB in disagreement with theory.

The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of submanifolds of configuration space is investigated, corroborating the hypothesis that, in general, a change of the topology within this family is a necessary condition in order to observe a phase transition. Considering two slightly differing versions of this solid-on-solid model, one showing a phase transition in the thermodynamic limit and the other not, we find that the difference in the quality or strength of this topology change appears to be insignificant. This example indicates the unattainability of a condition of exclusively topological nature which is sufficient to guarantee the occurrence of a phase transition in systems with nonconfining potentials.

We have measured the specific heat and magnetization versus temperature in a single crystal sample of superconducting La₂CuO_4.11 and in a sample of the same material after removing the excess oxygen, in magnetic fields up to 15 T. Using the deoxygenated sample to subtract the phonon contribution, we find a broad peak in the specific heat, centered at 50 K. This excess specific heat is attributed to fluctuations of the Cu spins possibly enhanced by an interplay with the charge degrees of freedom, and appears to be independent of magnetic field, up to 15 T. Near the superconducting transition T_c(H=0)=43 K, we find a sharp feature that is strongly suppressed when the magnetic field is applied parallel to the crystallographic c axis. A model for three-dimensional vortex fluctuations is used to scale magnetization measured at several magnetic fields. When the magnetic field is applied perpendicular to the c axis, the only observed effect is a slight shift in the superconducting transition temperature.

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. An important issue, not only from a theoretical point of view but also for their experimental detection, is their energy properties. We considerably enlarge the scenario of possible energy properties presented by Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]. Breather energies have a positive lower bound if the lattice dimension is greater than or equal to a certain critical value d_c. We show that d_c can generically be greater than 2 for a large class of Hamiltonian systems. Furthermore, examples are provided for systems where discrete breathers exist but do not emerge from the bifurcation of a band edge plane wave. Some of these systems support breathers of arbitrarily low energy in any spatial dimension.

We report neutron scattering measurements of the structure and magnetism of stage-4 La₂CuO_4+y with T_c≃42 K. Our diffraction results on a single crystal sample demonstrate that the excess oxygen dopants form a three-dimensional ordered superlattice within the interstitial regions of the crystal. The oxygen superlattice becomes disordered above T≃330 K, and a fast rate of cooling can freeze in the disordered-oxygen state. Hence, by controlling the cooling rate, the degree of dopant disorder in our La₂CuO_4+y crystal can be varied. We find that a higher degree of quenched disorder reduces T_c by ∼5 K relative to the ordered-oxygen state. At the same time, the quenched disorder enhances the spin-density wave order in a manner analogous to the effects of an applied magnetic field.

The ferromagnetic phase transition in a MnAs film on GaAs(111), where the MnAs unit cell is epitaxially fixed in its hexagonal plane, proceeds under conditions qualitatively different from the transition in bulk MnAs crystals or in MnAs films on GaAs(001). We present experimental evidence for the coexistence between ferromagnetic and paramagnetic phases in a temperature interval of 10 °C. Temperature dependencies of the phase fractions and the in-plane lattice parameters obtained by grazing incidence x-ray diffraction are compared with magnetization measurements.

We report sharp peaks in the differential conductance of a single-electron transistor (SET) at low temperature for gate voltages at which charge fluctuations are suppressed. For odd numbers of electrons we observe the expected Kondo peak at zero bias. For even numbers of electrons we generally observe Kondo-like features corresponding to excited states. For the latter, the excitation energy often decreases with gate voltage until a new zero-bias Kondo peak results. We ascribe this behavior to a singlet-triplet transition in zero magnetic field driven by the change of shape of the potential that confines the electrons in the SET.

We study the low-temperature magnetoresistance in thin, high-quality MnAs layers on GaAs. The ordinary Hall effect depends sensitively on the epitaxial orientation of the MnAs layer. We use a simplified model to interpret the sign reversal of the Hall resistivity as a function of the magnetic field together with the large positive magnetoresistivity. For A₀-oriented MnAs films with the c axis oriented in the plane, we conclude that the low-temperature carrier transport is dominantly holelike at zero magnetic fields, which then undergoes a transition to mixed holelike and electronlike conductivity at high magnetic fields. MnAs films with an out-of-plane oriented c axis show a mixed carrier conductivity already at zero magnetic fields. The possible influence of interface/surface scattering in high-quality MnAs layers on the transfer of holelike to electronlike conductivity is discussed.

We have measured the enhancement of the static incommensurate spin-density wave (SDW) order by an applied magnetic field in stage-4 and stage-6 samples of superconducting La₂CuO_4+y. We show that the stage-6 La₂CuO_4+y (T_c=32 K) forms static long-range SDW order with the same wave vector as that in the previously studied stage-4 material. We have measured the field dependence of the SDW magnetic Bragg peaks in both stage-4 and stage-6 materials at fields up to 14.5 T. A recent model of competing SDW order and superconductivity describes these data well.

We present results for electronic transport measurements on large three-dimensional arrays of CdSe nanocrystals. In response to a step in the applied voltage, we observe a power-law decay of the current over five orders of magnitude in time. Furthermore, we observe no steady-state dark current for fields up to 10⁶ V/cm and times as long as 2×10⁴ s. Although the power-law form of the decay is quite general, there are quantitative variations with temperature, applied field, sample history, and the material parameters of the array. Despite evidence that the charge injected into the film during the measurement causes the decay of current, we find field scaling of the current at all times. The observation of extremely long-lived current transients suggests the importance of long-range Coulomb interactions between charges on different nanocrystals.

The spin injection into GaAs has been studied for the ferromagnetic metal MnAs. Evidence for preferential minority-spin injection is obtained from the circular polarization of the electroluminescence in GaAs/(In,Ga)As light-emitting diodes (LED). The spin-injection efficiency of 6% at the MnAs/GaAs interface is estimated on the basis of spin-relaxation times extracted from time-resolved photoluminescence measurements. This efficiency, as well as the preferential spin orientation, resembles very much the injection behavior found for epitaxial Fe layers. The results do not depend on the azimuthal orientation of the epitaxial MnAs injection layer.