Andres Somoza - Academia.edu (original) (raw)

Papers by Andres Somoza

Research paper thumbnail of Slow Charge Relaxation in Highly Disordered Electronic Systems studied by Electrostatic Scanning Force Microscopy

Proceedings of the nanoGe Fall Meeting 2018

Research paper thumbnail of Construction of many-body eigenstates with displacement transformations in disordered systems

Physical Review B

Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local inte... more Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local integrals of motion (IOM), although their actual computation has been until now a daunting task. We present a new practical computation of IOMS based on displacement transformations. It represents a general and systematic way to extend Hartree-Fock and configuration interaction theories to higher order. Our method combines minimization of energy and energy variance of a reference state with exact diagonalization. We show that our implementation is able to perform ground state calculations with high precision for relatively large systems. Since it keeps track of the IMO's forming a reference state, our method is particularly efficient dealing with excited states, both in accuracy and the number of different states that can be constructed.

Research paper thumbnail of Many-body localization from the perspective of Integrals of Motion

Research paper thumbnail of Conductance fluctuations in the localized regime

We have studied numerically the fluctuations of the conductance, ggg, in two-dimensional, three-d... more We have studied numerically the fluctuations of the conductance, ggg, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of lng\ln glng varies with the lateral sample size as L2/5L^{2/5}L2/5 in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of lng\ln glng in two- and three-dimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.

Research paper thumbnail of Conductance fluctuations in the localized regime: Numerical study in disordered noninteracting systems

Physical Review B Condensed Matter and Materials Physics, May 1, 2006

We have studied numerically the fluctuations of the conductance, g, in two-dimensional, threedime... more We have studied numerically the fluctuations of the conductance, g, in two-dimensional, threedimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of ln g varies with the lateral sample size as L 2/5 in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of ln g in two-and threedimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.

Research paper thumbnail of 3-d Simulations of Phase Separation in Binary Alloy Systems with Elastic Fields

Aps March Meeting Abstracts, Mar 1, 1998

We report on large-scale three-dimensional simulations of phase separation in model binary alloy ... more We report on large-scale three-dimensional simulations of phase separation in model binary alloy systems in the presence of elastic fields. The elastic field has several important effects on the morphology of the system: the ordered domains are subject to shape transformations, and spatial ordering. In contrast to two-dimensional system, no significant slowing down in the growth is observed. There is also no evidence of any "reverse coarsening" of the domains.

Research paper thumbnail of Conducting polymers as electron glasses: surface charge domains and slow relaxation

Scientific Reports, 2016

The surface potential of conducting polymers has been studied with scanning Kelvin probe microsco... more The surface potential of conducting polymers has been studied with scanning Kelvin probe microscopy. The results show that this technique can become an excellent tool to really 'see' interesting surface charge interaction effects at the nanoscale. The electron glass model, which assumes that charges are localized by the disorder and that interactions between them are relevant, is employed to understand the complex behavior of conducting polymers. At equilibrium, we find surface potential domains with a typical lateral size of 50 nm, basically uncorrelated with the topography and strongly fluctuating in time. These fluctuations are about three times larger than thermal energy. The charge dynamics is characterized by an exponentially broad time distribution. When the conducting polymers are excited with light the surface potential relaxes logarithmically with time, as usually observed in electron glasses. In addition, the relaxation for different illumination times can be scaled within the full aging model. Conducting and semiconducting polymers have been proposed as the fourth generation of polymeric materials 1. Due to their easy processability, high tunability and low-cost production, they have a great potential for a variety of applications. Plastic electronics devices, such as organic field-effect transistors, organic light-emitting diodes, and organic solar cells, are already fabricated and commercialized 2. Apart from their technological applications, conducting polymers offer a wealth of interesting and challenging basic phenomena from the fundamental point of view. Typical conducting polymers are semi-crystalline in the sense that locally the chains align in an ordered structure forming nano-crystallites which are surrounded by amorphous regions. This nanostructure determines the intra and inter-chain interactions that govern the electronic properties of the material 3-5. It is well accepted that, due to the high degree of disorder, in polimeric materials the conduction occurs by phonon assisted hopping between localized states, involving the formation of polarons or bipolarons 6,7. Although it has been profoundly studied for the last decades, the complexity of conducting polymers prevent a full consensus about the underlying conduction mechanisms and in particular the way they relax after excitation far from equilibrium. Interactions between carriers are likely to be significant enough to affect their conduction mechanism, as evidenced by the T −1/2 dependence of the logarithm of the conductivity in the variable-range hopping regime 8 , and makes the conduccting polymers excellent candidates to be electron glasses. Electron glasses are systems with states localized by the disorder and with long-range Coulomb interactions between carriers. Disorder produces localization of the wavefunctions, which in turn results in a lack of screening and an increase in the importance of Coulomb interactions. Very slow relaxation rates are commonly observed in these systems due to the exponential dependence of the transition rates on hopping length and energy and to the many-valley structure of the phase space produced by the interactions 9. Typical glassy phenomena observed in electron glasses include a slow logarithmic decrease of the conductivity 10,11 , a memory dip 11-13 and aging 12,14,15. These phenomena have been observed in a great variety of materials, such as indium oxides 10 , granular metals 11 , thin metal films 13,16 , and recently GeSbTe films, where glassy phenomena coexist with persistent photoconductivity 17. Electron glasses have been excited with electromagnetic radiation, and for high enough frequency, slow relaxation is observed 10,17,18. These results are consistent with the following picture. At equilibrium, charges are arranged in low energy configurations that minimize the Coulomb energy and present complex correlations

Research paper thumbnail of Kinetics of an order-disorder phase transition with topological defects

Physical Review E - PHYS REV E, 1996

We have investigated the time evolution of a vectorial model C system following a temperature que... more We have investigated the time evolution of a vectorial model C system following a temperature quench from the disordered state into the order-disorder coexistence region, with numerical Langevin simulations. The system is characterized by a vectorial, nonconserved order parameter coupled to a conserved quantity such as a concentration. Two different ordering mechanisms are observed. If the mean concentration co is co>1/2, then the minority phase is the ordered phase and growth is driven by long-range diffusion. On the other hand, if co<1/2, then it is the disordered phase that is in the minority. In this case, defects of the order parameter (vortices) are strongly coupled to that of the position of the disordered phase. Growth takes place primarily via the diffusion and coalescence of the defects, giving rise to an n=1/4 growth exponent over a significant time regime.

Research paper thumbnail of Random Walks and Anderson Localization in a Three-Dimensional Class C Network Model

Physical Review Letters, 2009

We study the disorder-induced localisation transition in a three-dimensional network model that b... more We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behaviour at an Anderson transition than has been possible previously in any context.

Research paper thumbnail of Monte Carlo method for relaxation in electron glasses

Physical Review B, 2005

We have developed a kinetic Monte Carlo algorithm to simulate nonequilibrium relaxation of Coulom... more We have developed a kinetic Monte Carlo algorithm to simulate nonequilibrium relaxation of Coulomb glasses at low temperatures. It is much faster than present procedures and can qualitatively change our scopes in the simulation of slowly relaxing systems. The algorithm chooses a transition according to its total probability, including the spatial and energy factors involved in the transition rates of hopping processes. It incorporates two important advantages. First, it can find all the relevant transitions restricting the search to only a small subset. Second, it can integrate out exactly soft, low energy transitions and other repetitive hops characteristic of metastable states. This is a general procedure that can be extended to most slow relaxation systems. We have applied the method to study energy relaxation and the distribution of the relaxation times up to 1010 Monte Carlo steps. We found that this distribution is roughly constant, in logarithmic scale, for long times.

Research paper thumbnail of Effects of many-electron jumps in the relaxation and conductivity of Coulomb glasses

Physical Review B, 2011

A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. Th... more A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. The role of many-electron transitions is studied by two complementary methods: a kinetic Monte Carlo algorithm and a master equation in configuration space method. A calculation of the transition rate for two-electron transitions is presented, and the proper extension of this to multi-electron transitions is discussed. It is shown that two-electron transitions are important in bypassing energy barriers which effectively block sequential one-electron transitions. The effect of two-electron transitions is also discussed.

Research paper thumbnail of Crossover from diffusive to strongly localized regime in two-dimensional systems

Physical Review B, 2009

We have studied the conductance distribution function of two-dimensional disordered noninteractin... more We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean conductance, g , in agreement with the strong version of the single parameter scaling hypothesis. The distribution seems to change drastically at a critical value very close to one. For conductances larger than this critical value, the distribution is roughly gaussian, while for smaller values it resembles a log normal distribution. The two distributions match at the critical point with an often appreciable change in behavior. This matching implies a jump in the first derivative of the distribution which does not seem to disappear as system size increases. We have also studied 1/ g corrections to the skewness to quantify the deviation of the distribution from a gaussian function in the diffusive regime.

Research paper thumbnail of Spin quantum Hall effect and plateau transitions in multilayer network models

Physical Review B, 2011

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensio... more We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of n weakly coupled layers. Standard scaling ideas lead one to expect n distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.

Research paper thumbnail of Conductance fluctuations and corrections to the localization length in two-dimensional localized systems

physica status solidi (b), 2006

ABSTRACT We have studied numerically the average and the fluctuations of the conductance in two-d... more ABSTRACT We have studied numerically the average and the fluctuations of the conductance in two-dimensional disordered non-interacting systems in the localized regime. We have calculated the zero temperature conductance from the Green functions, which can be efficiently obtained propagating strip by strip. We have studied the finite size corrections to the average of the logarithm of the conductance and they turn out to be crucial in the numerical calculation of the localization length. We found that the third moment of the logarithm of the conductance ln g is proportional to ln g for large systems. As the variance goes as ln g2/3, we conclude that the distribution of ln g does not tend to a log normal distribution, but to an asymmetric distribution that keeps a constant shape in the limit of large sizes.

Research paper thumbnail of Conductance fluctuations and single-parameter scaling in two-dimensional disordered systems

Physical Review B, 2005

We have studied numerically the fluctuations of the conductance, g , and the applicability of sin... more We have studied numerically the fluctuations of the conductance, g , and the applicability of single parameter scaling in two-dimensional disordered noninteracting systems. We have checked that the variance of lng varies with the lateral sample size as L2/3 . In agreement with this, we have introduced a parameter to establish the applicability of the single-parameter scaling (SPS) hypothesis. We

Research paper thumbnail of Scaling of the interfacial tension of microemulsions: A phenomenological description

Recent experiments revealed a striking scaling behavior of the low and ultralow interfacial tensi... more Recent experiments revealed a striking scaling behavior of the low and ultralow interfacial tension of microemulsions. A description of this behavior based on the Helfrich elastic free energy, which is symmetric in the principal curvatures c 1 and c 2 , appears to be inconsistent. We show that, within the phenomenological theory of membrane bending elasticity, symmetry breaking between the two principal curvatures seems to be required in order to explain the low, but nonzero, values of the interfacial tension and its temperature dependence. We propose two simple generalizations of the Helfrich free energy which describe the experimental results. The first considers a quadratic elastic free energy and anisotropy in the membrane which breaks the symmetry between the two principal curvatures. In the second, which is applicable to systems with positive saddle-splay rigidities, the symmetry between the two principal curvatures is spontaneously broken by inclusion of higher-order terms in the curvatures in order to stabilize the free energy of the system. This analysis provides a straightforward method to obtain estimates of the bending elastic constants from interfacial tension measurements. Experiments confirming the theoretical picture are presented and values for k and k ¯ , for a variety of systems, are obtained. © 1996 American Institute of Physics.

Research paper thumbnail of Study of two-electron jumps in relaxation of Coulomb glasses

Annalen der Physik, 2009

ABSTRACT A long-standing debate in the theory of hopping insulators concerns the role of multi-el... more ABSTRACT A long-standing debate in the theory of hopping insulators concerns the role of multi-electron transitions in the dynamics of the system. The natural assumption is that as temperature is lowered, two-electron transitions will play an increasingly important role since they provide a way of tunneling through additional energy barriers which would be energetically unfavorable as successive one-electron transitions. This was disputed in [1], but later it was seen in [2]. The reason for this discrepancy is not clear and deserves further attention. One point where the two approaches diverged was in the selection and weighting of the two-electron transitions relative to one-electron transitions. We present calculations of the transition rates to second order in the tunneling matrix element, which will be used in improved numerical studies. We compare results for only one-electron jumps with results including also two-electron jumps.

Research paper thumbnail of Phase separation in the presence of a surface

Journal of Physics A-mathematical and General, 1993

We have studied the phase separation of a system with a conserved order parameter in the presence... more We have studied the phase separation of a system with a conserved order parameter in the presence of a flat surface via Monte Carlo simulations. For various quench parameters, we observed the domain growth in a surface layer. The kinetics of this ordering was studied, both in the presence and absence of bulk phase separation. In the absence of bulk

Research paper thumbnail of Two-and three-dimensional simulations of the phase separation of elastically coherent binary alloys subject to external stresses

Physical Review B, 2000

... 183, 169 1994 ; AB Kamora, AJ Ardell, and CN Wagner, Metall. Mater. Trans. ... The Minerals, ... more ... 183, 169 1994 ; AB Kamora, AJ Ardell, and CN Wagner, Metall. Mater. Trans. ... The Minerals, Metals, and Materials Society, Warrendale, PA, 1996 , p. 267; H. Mughrabi, W. Schneider, V. Sass, and C. Lang, in Strength of Materials, edited by Oikawa et al. Japan Inst. ...

Research paper thumbnail of Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials

We propose systems with structures defined by self-assembled triply periodic minimal surfaces (ST... more We propose systems with structures defined by self-assembled triply periodic minimal surfaces (STPMS) as candidates for photonic bandgap materials. To support our proposal we have calculated the photonic bands for different STPMS and we have found that, at least, the double diamond and gyroid structures present full photonic bandgaps. Given the great variety of systems which crystalize in these structures, the diversity of possible materials that form them and the range of lattice constants they present, the construction of photonic bandgap materials with gaps in the visible range may be presently within reach.

Research paper thumbnail of Slow Charge Relaxation in Highly Disordered Electronic Systems studied by Electrostatic Scanning Force Microscopy

Proceedings of the nanoGe Fall Meeting 2018

Research paper thumbnail of Construction of many-body eigenstates with displacement transformations in disordered systems

Physical Review B

Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local inte... more Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local integrals of motion (IOM), although their actual computation has been until now a daunting task. We present a new practical computation of IOMS based on displacement transformations. It represents a general and systematic way to extend Hartree-Fock and configuration interaction theories to higher order. Our method combines minimization of energy and energy variance of a reference state with exact diagonalization. We show that our implementation is able to perform ground state calculations with high precision for relatively large systems. Since it keeps track of the IMO's forming a reference state, our method is particularly efficient dealing with excited states, both in accuracy and the number of different states that can be constructed.

Research paper thumbnail of Many-body localization from the perspective of Integrals of Motion

Research paper thumbnail of Conductance fluctuations in the localized regime

We have studied numerically the fluctuations of the conductance, ggg, in two-dimensional, three-d... more We have studied numerically the fluctuations of the conductance, ggg, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of lng\ln glng varies with the lateral sample size as L2/5L^{2/5}L2/5 in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of lng\ln glng in two- and three-dimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.

Research paper thumbnail of Conductance fluctuations in the localized regime: Numerical study in disordered noninteracting systems

Physical Review B Condensed Matter and Materials Physics, May 1, 2006

We have studied numerically the fluctuations of the conductance, g, in two-dimensional, threedime... more We have studied numerically the fluctuations of the conductance, g, in two-dimensional, threedimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of ln g varies with the lateral sample size as L 2/5 in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of ln g in two-and threedimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.

Research paper thumbnail of 3-d Simulations of Phase Separation in Binary Alloy Systems with Elastic Fields

Aps March Meeting Abstracts, Mar 1, 1998

We report on large-scale three-dimensional simulations of phase separation in model binary alloy ... more We report on large-scale three-dimensional simulations of phase separation in model binary alloy systems in the presence of elastic fields. The elastic field has several important effects on the morphology of the system: the ordered domains are subject to shape transformations, and spatial ordering. In contrast to two-dimensional system, no significant slowing down in the growth is observed. There is also no evidence of any "reverse coarsening" of the domains.

Research paper thumbnail of Conducting polymers as electron glasses: surface charge domains and slow relaxation

Scientific Reports, 2016

The surface potential of conducting polymers has been studied with scanning Kelvin probe microsco... more The surface potential of conducting polymers has been studied with scanning Kelvin probe microscopy. The results show that this technique can become an excellent tool to really 'see' interesting surface charge interaction effects at the nanoscale. The electron glass model, which assumes that charges are localized by the disorder and that interactions between them are relevant, is employed to understand the complex behavior of conducting polymers. At equilibrium, we find surface potential domains with a typical lateral size of 50 nm, basically uncorrelated with the topography and strongly fluctuating in time. These fluctuations are about three times larger than thermal energy. The charge dynamics is characterized by an exponentially broad time distribution. When the conducting polymers are excited with light the surface potential relaxes logarithmically with time, as usually observed in electron glasses. In addition, the relaxation for different illumination times can be scaled within the full aging model. Conducting and semiconducting polymers have been proposed as the fourth generation of polymeric materials 1. Due to their easy processability, high tunability and low-cost production, they have a great potential for a variety of applications. Plastic electronics devices, such as organic field-effect transistors, organic light-emitting diodes, and organic solar cells, are already fabricated and commercialized 2. Apart from their technological applications, conducting polymers offer a wealth of interesting and challenging basic phenomena from the fundamental point of view. Typical conducting polymers are semi-crystalline in the sense that locally the chains align in an ordered structure forming nano-crystallites which are surrounded by amorphous regions. This nanostructure determines the intra and inter-chain interactions that govern the electronic properties of the material 3-5. It is well accepted that, due to the high degree of disorder, in polimeric materials the conduction occurs by phonon assisted hopping between localized states, involving the formation of polarons or bipolarons 6,7. Although it has been profoundly studied for the last decades, the complexity of conducting polymers prevent a full consensus about the underlying conduction mechanisms and in particular the way they relax after excitation far from equilibrium. Interactions between carriers are likely to be significant enough to affect their conduction mechanism, as evidenced by the T −1/2 dependence of the logarithm of the conductivity in the variable-range hopping regime 8 , and makes the conduccting polymers excellent candidates to be electron glasses. Electron glasses are systems with states localized by the disorder and with long-range Coulomb interactions between carriers. Disorder produces localization of the wavefunctions, which in turn results in a lack of screening and an increase in the importance of Coulomb interactions. Very slow relaxation rates are commonly observed in these systems due to the exponential dependence of the transition rates on hopping length and energy and to the many-valley structure of the phase space produced by the interactions 9. Typical glassy phenomena observed in electron glasses include a slow logarithmic decrease of the conductivity 10,11 , a memory dip 11-13 and aging 12,14,15. These phenomena have been observed in a great variety of materials, such as indium oxides 10 , granular metals 11 , thin metal films 13,16 , and recently GeSbTe films, where glassy phenomena coexist with persistent photoconductivity 17. Electron glasses have been excited with electromagnetic radiation, and for high enough frequency, slow relaxation is observed 10,17,18. These results are consistent with the following picture. At equilibrium, charges are arranged in low energy configurations that minimize the Coulomb energy and present complex correlations

Research paper thumbnail of Kinetics of an order-disorder phase transition with topological defects

Physical Review E - PHYS REV E, 1996

We have investigated the time evolution of a vectorial model C system following a temperature que... more We have investigated the time evolution of a vectorial model C system following a temperature quench from the disordered state into the order-disorder coexistence region, with numerical Langevin simulations. The system is characterized by a vectorial, nonconserved order parameter coupled to a conserved quantity such as a concentration. Two different ordering mechanisms are observed. If the mean concentration co is co>1/2, then the minority phase is the ordered phase and growth is driven by long-range diffusion. On the other hand, if co<1/2, then it is the disordered phase that is in the minority. In this case, defects of the order parameter (vortices) are strongly coupled to that of the position of the disordered phase. Growth takes place primarily via the diffusion and coalescence of the defects, giving rise to an n=1/4 growth exponent over a significant time regime.

Research paper thumbnail of Random Walks and Anderson Localization in a Three-Dimensional Class C Network Model

Physical Review Letters, 2009

We study the disorder-induced localisation transition in a three-dimensional network model that b... more We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behaviour at an Anderson transition than has been possible previously in any context.

Research paper thumbnail of Monte Carlo method for relaxation in electron glasses

Physical Review B, 2005

We have developed a kinetic Monte Carlo algorithm to simulate nonequilibrium relaxation of Coulom... more We have developed a kinetic Monte Carlo algorithm to simulate nonequilibrium relaxation of Coulomb glasses at low temperatures. It is much faster than present procedures and can qualitatively change our scopes in the simulation of slowly relaxing systems. The algorithm chooses a transition according to its total probability, including the spatial and energy factors involved in the transition rates of hopping processes. It incorporates two important advantages. First, it can find all the relevant transitions restricting the search to only a small subset. Second, it can integrate out exactly soft, low energy transitions and other repetitive hops characteristic of metastable states. This is a general procedure that can be extended to most slow relaxation systems. We have applied the method to study energy relaxation and the distribution of the relaxation times up to 1010 Monte Carlo steps. We found that this distribution is roughly constant, in logarithmic scale, for long times.

Research paper thumbnail of Effects of many-electron jumps in the relaxation and conductivity of Coulomb glasses

Physical Review B, 2011

A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. Th... more A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. The role of many-electron transitions is studied by two complementary methods: a kinetic Monte Carlo algorithm and a master equation in configuration space method. A calculation of the transition rate for two-electron transitions is presented, and the proper extension of this to multi-electron transitions is discussed. It is shown that two-electron transitions are important in bypassing energy barriers which effectively block sequential one-electron transitions. The effect of two-electron transitions is also discussed.

Research paper thumbnail of Crossover from diffusive to strongly localized regime in two-dimensional systems

Physical Review B, 2009

We have studied the conductance distribution function of two-dimensional disordered noninteractin... more We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean conductance, g , in agreement with the strong version of the single parameter scaling hypothesis. The distribution seems to change drastically at a critical value very close to one. For conductances larger than this critical value, the distribution is roughly gaussian, while for smaller values it resembles a log normal distribution. The two distributions match at the critical point with an often appreciable change in behavior. This matching implies a jump in the first derivative of the distribution which does not seem to disappear as system size increases. We have also studied 1/ g corrections to the skewness to quantify the deviation of the distribution from a gaussian function in the diffusive regime.

Research paper thumbnail of Spin quantum Hall effect and plateau transitions in multilayer network models

Physical Review B, 2011

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensio... more We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of n weakly coupled layers. Standard scaling ideas lead one to expect n distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.

Research paper thumbnail of Conductance fluctuations and corrections to the localization length in two-dimensional localized systems

physica status solidi (b), 2006

ABSTRACT We have studied numerically the average and the fluctuations of the conductance in two-d... more ABSTRACT We have studied numerically the average and the fluctuations of the conductance in two-dimensional disordered non-interacting systems in the localized regime. We have calculated the zero temperature conductance from the Green functions, which can be efficiently obtained propagating strip by strip. We have studied the finite size corrections to the average of the logarithm of the conductance and they turn out to be crucial in the numerical calculation of the localization length. We found that the third moment of the logarithm of the conductance ln g is proportional to ln g for large systems. As the variance goes as ln g2/3, we conclude that the distribution of ln g does not tend to a log normal distribution, but to an asymmetric distribution that keeps a constant shape in the limit of large sizes.

Research paper thumbnail of Conductance fluctuations and single-parameter scaling in two-dimensional disordered systems

Physical Review B, 2005

We have studied numerically the fluctuations of the conductance, g , and the applicability of sin... more We have studied numerically the fluctuations of the conductance, g , and the applicability of single parameter scaling in two-dimensional disordered noninteracting systems. We have checked that the variance of lng varies with the lateral sample size as L2/3 . In agreement with this, we have introduced a parameter to establish the applicability of the single-parameter scaling (SPS) hypothesis. We

Research paper thumbnail of Scaling of the interfacial tension of microemulsions: A phenomenological description

Recent experiments revealed a striking scaling behavior of the low and ultralow interfacial tensi... more Recent experiments revealed a striking scaling behavior of the low and ultralow interfacial tension of microemulsions. A description of this behavior based on the Helfrich elastic free energy, which is symmetric in the principal curvatures c 1 and c 2 , appears to be inconsistent. We show that, within the phenomenological theory of membrane bending elasticity, symmetry breaking between the two principal curvatures seems to be required in order to explain the low, but nonzero, values of the interfacial tension and its temperature dependence. We propose two simple generalizations of the Helfrich free energy which describe the experimental results. The first considers a quadratic elastic free energy and anisotropy in the membrane which breaks the symmetry between the two principal curvatures. In the second, which is applicable to systems with positive saddle-splay rigidities, the symmetry between the two principal curvatures is spontaneously broken by inclusion of higher-order terms in the curvatures in order to stabilize the free energy of the system. This analysis provides a straightforward method to obtain estimates of the bending elastic constants from interfacial tension measurements. Experiments confirming the theoretical picture are presented and values for k and k ¯ , for a variety of systems, are obtained. © 1996 American Institute of Physics.

Research paper thumbnail of Study of two-electron jumps in relaxation of Coulomb glasses

Annalen der Physik, 2009

ABSTRACT A long-standing debate in the theory of hopping insulators concerns the role of multi-el... more ABSTRACT A long-standing debate in the theory of hopping insulators concerns the role of multi-electron transitions in the dynamics of the system. The natural assumption is that as temperature is lowered, two-electron transitions will play an increasingly important role since they provide a way of tunneling through additional energy barriers which would be energetically unfavorable as successive one-electron transitions. This was disputed in [1], but later it was seen in [2]. The reason for this discrepancy is not clear and deserves further attention. One point where the two approaches diverged was in the selection and weighting of the two-electron transitions relative to one-electron transitions. We present calculations of the transition rates to second order in the tunneling matrix element, which will be used in improved numerical studies. We compare results for only one-electron jumps with results including also two-electron jumps.

Research paper thumbnail of Phase separation in the presence of a surface

Journal of Physics A-mathematical and General, 1993

We have studied the phase separation of a system with a conserved order parameter in the presence... more We have studied the phase separation of a system with a conserved order parameter in the presence of a flat surface via Monte Carlo simulations. For various quench parameters, we observed the domain growth in a surface layer. The kinetics of this ordering was studied, both in the presence and absence of bulk phase separation. In the absence of bulk

Research paper thumbnail of Two-and three-dimensional simulations of the phase separation of elastically coherent binary alloys subject to external stresses

Physical Review B, 2000

... 183, 169 1994 ; AB Kamora, AJ Ardell, and CN Wagner, Metall. Mater. Trans. ... The Minerals, ... more ... 183, 169 1994 ; AB Kamora, AJ Ardell, and CN Wagner, Metall. Mater. Trans. ... The Minerals, Metals, and Materials Society, Warrendale, PA, 1996 , p. 267; H. Mughrabi, W. Schneider, V. Sass, and C. Lang, in Strength of Materials, edited by Oikawa et al. Japan Inst. ...

Research paper thumbnail of Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials

We propose systems with structures defined by self-assembled triply periodic minimal surfaces (ST... more We propose systems with structures defined by self-assembled triply periodic minimal surfaces (STPMS) as candidates for photonic bandgap materials. To support our proposal we have calculated the photonic bands for different STPMS and we have found that, at least, the double diamond and gyroid structures present full photonic bandgaps. Given the great variety of systems which crystalize in these structures, the diversity of possible materials that form them and the range of lattice constants they present, the construction of photonic bandgap materials with gaps in the visible range may be presently within reach.