Papers by Stefan Kettemann
Taking into account the temperature gradients in solar cells, it is shown that their eeciency can... more Taking into account the temperature gradients in solar cells, it is shown that their eeciency can be increased beyond the Shockley–Queisser limit (J. Appl. Phys. 32 (1961) 510). The driving force for this gain is the temperature gradient between this region and its surroundings. A quantitative theory is given. Though the effect is found to be weak in conventional solar cells, it is argued that it can be substantially increased by proper choice of materials and design of the device. In particular, it is shown that the insertion of a quantum well can enhance the efficiency beyond one of the single gap cell, due to the presence of temperature jumps at the heterojunctions. ?
Sudden failure of a single transmission element in a power grid can induce a domino effect of cas... more Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present results of the the simulation of cascading failures in power grids, using a dynamic alternating current (AC) model. We first apply this model to regular square grid topologies. We find that for a random distribution of consumers and generators, the probability to disconnect more than Nc consumers decays as a power law, ∼ N −q c , and obeys a scaling law with respect to the linear system size L. Varying the transmitted power threshold F th above which a transmission line fails hardly changes q ≈ 1.6. We thus find clear evidence that the random distribution of consumers results in critical behavior in square grids. Furthermore, we study the influence of the distribution of generators and consumers on the number of affected consumers Nc and demonstrate that large clusters of generators and consumers are especially vulnerable to cascading failures. As a real-world topology we consider the German high-voltage transmission grid. Applying the dynamic AC model and considering a random distribution of consumers, we find that the probability to disconnect more than Nc consumers depends strongly on the threshold F th. For large F th the decay is clearly exponential, while for small F th the decay is slow, indicating a power law decay.
Local changes in the topology of electricity grids can cause overloads far away from the disturba... more Local changes in the topology of electricity grids can cause overloads far away from the disturbance [1], making the prediction of the robustness against changes in the topology – for example caused by power outages or grid extensions – a challenging task. The impact of single-line additions on the long-range response of DC electricity grids has recently been studied [2]. By solving the real part of the static AC load flow equations, we conduct a similar investigation for AC grids. In a regular 2D grid graph with cyclic boundary conditions, we find a power law decay for the change of power flow as a function of distance to the disturbance over a wide range of distances. The power exponent increases and saturates for large system sizes. By applying the same analysis to the German transmission grid topology, we show that also in real-world topologies a long-ranged response can be found.
We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator... more We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator transition. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude W c with increasing exchange coupling strength J. The resulting scaling with J is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent ν and enhances the multifractality parameter α 0. The new value of ν improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.
Nature Nanotechnology, 2008
Electrons and other fundamental particles have an intrinsic angular momentum called spin. A chang... more Electrons and other fundamental particles have an intrinsic angular momentum called spin. A change in the spin state of such a particle is therefore equivalent to a mechanical torque. This spin-induced torque is central to our understanding of experiments 1,2 ranging from the measurement of the angular momentum of photons 3 and the g-factor of metals 4-7 to magnetic resonance 8 and magnetization reversal in magnetic multilayers . When a spin-polarized current passes through a metallic nanowire in which one half is ferromagnetic and the other half is nonmagnetic, the spins of the itinerant electrons are 'flipped' at the interface between the two regions to produces a torque. Here, we report direct measurement of this mechanical torque in an integrated nanoscale torsion oscillator, and measurements of the itinerant electron spin polarization that could yield new information on the itinerancy of the d-band electrons. The unprecedented torque sensitivity of 1 3 10 222 N-m Hz 21/2 may have applications in spintronics and precision measurements of charge-parityviolating forces , and might also enable experiments on the untwisting of DNA 18 and torque-generating molecules .
Doniach Diagram in Disordered Electrons System
Aps Meeting Abstracts, Mar 1, 2013
ABSTRACT We have derived the quantum phase diagram of disordered electron systems with magnetic i... more ABSTRACT We have derived the quantum phase diagram of disordered electron systems with magnetic impurities. The competition between RKKY interaction, JRKKY, and Kondo effect gives rise to a rich quantum phase diagram, or Doniach diagram. We present numerical results for disordered 2D electron systems which show that both Kondo temperature, TK and JRKKY are widely distributed and quantum critical point is extended to a critical region. We find a sharp cutoff in the distribution of their ratio, JRKKY/TK, and from that critical density of magnetic impurity below which Kondo always wins. We find that the spin coupled phase grows at the expense of Kondo phase as increasing disorder.The spin coupled phase shows a succession of 3 phases: 1. a Griffiths phase with anomalous power laws determined by distribution of JRKKY, 2. spin glass phase, 3. long range magnetic ordered phase. We report the results on graphene where we find that spin coupled phase is more stable against Kondo screening, but is more easily destroyed by disorder into a paramagnetic phase [1].[4pt] [1] H. Lee, S. Kettemann, arXiv:1211.1734(2012)
ANALYSIS OF QUANTUM CORRECTIONS TO CONDUCTIVITY AND THERMOPOWER IN GRAPHENE — NUMERICAL AND ANALYTICAL APPROACHES
Localisation 2011, 2012
ABSTRACT We present numerical and analytical studies of the crossover between weak antilocalizati... more ABSTRACT We present numerical and analytical studies of the crossover between weak antilocalization and weak localization in monolayer graphene and their influence on thermopower. By the use of the recursive Green's function method, we find that these quantum corrections result in an enhancement of thermopower, which can be observed in the resulting magnetic field dependence. This magneto thermopower strongly depends on the size and strength of the impurities as well as on the back gate voltage of the system and the impurity concentration. We show in detail the crossover of these localization effects with these parameters. Using the disorder parameters of the numerical calculation, we find quantitative agreement with the analytical calculations.
Anderson Localization and Its Ramifications: Disorder, Phase Coherence, and Electron Correlations
LOCAL PSEUDOGAPS AND FREE MAGNETIC MOMENTS AT THE ANDERSON METAL-INSULATOR TRANSITION: NUMERICAL SIMULATION USING POWER-LAW BAND RANDOM MATRICES
Localisation 2011, 2012
ABSTRACT At the Anderson metal-insulator transition the eigenstates develop multifractal fluctuat... more ABSTRACT At the Anderson metal-insulator transition the eigenstates develop multifractal fluctuations. Therefore their properties are intermediate between being extended and localized. As a result these wave functions are power-law correlated, which causes a substantial suppression of the local density of states at some random positions, resembling random local pseudogaps at the Fermi energy. Consequently the Kondo screening of magnetic moments is suppressed when a magnetic impurity happens to be at such a position. Due to these unscreened magnetic moments the critical exponents and multifractal dimensions at the metal-insulator transition take their smaller, unitary ensemble values for exchange couplings not exceeding a certain critical value J* ≈ .3D, where D is the band width. Here we present numerical calculations of the distribution of Kondo temperatures for the critical Power-law Band Random Matrix (PBRM) ensemble, whose properties are similar to that of the Anderson transition with the advantage of using a continuous parameter for tuning the generalized multifractal dimensions of the eigenstates.
INDIRECT EXCHANGE INTERACTIONS IN GRAPHENE
ABSTRACT We study the Ruderman-Kittel-Katsuya-Yoshida (RKKY) interactions in graphene controlling... more ABSTRACT We study the Ruderman-Kittel-Katsuya-Yoshida (RKKY) interactions in graphene controlling the gate voltage and applying nonmagnetic disorder. It is found that oscillations of the RKKY interactions in undoped graphene are characterized by the interference of two neighbor Dirac nodes K and K‧ in the first Brillouin zone and decays with R-3 distance dependence. In the slightly doped graphene, a beating pattern, which consists of two characteristic wavevectors (K - K and kF), starts to appear. The distance dependence in this regime shows a crossover from the R-3 to R-2. We present the effect of weak disorder on the RKKY interactions in diffusive regime. The arithmetic averaged interaction over disorder configurations decreases exponentially at distances exceeding the elastic mean free path, while the geometrical average(typical) value has the same power-law as the clean limit.
Physical Review Letters, 2009
It is well-known that magnetic impurities can change the symmetry class of disordered metallic sy... more It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. We find that when the exchange coupling J is smaller than a certain value J * , the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states. The width of this critical region increases with a power of the concentration of magnetic impurities.
Physical Review Letters, 2007
The crossover between a free magnetic moment phase and a Kondo phase in low dimensional disordere... more The crossover between a free magnetic moment phase and a Kondo phase in low dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite size scaling analysis of the distribution of the Kondo temperature as obtained from a numerical renormalization group calculation of the local magnetic susceptibility and from the solution of the self-consistent Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic moments when the exchange coupling falls below a disorder-dependent critical value Jc. Our numerical results show that between the free moment phase due to Anderson localization and the Kondo screened phase there is a phase where free moments occur due to the appearance of random local pseudogaps at the Fermi energy whose width and power scale with the elastic scattering rate 1/τ .
Physical Review B, 2012
Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson meta... more Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical power-law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero-temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time-reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature T K is derived at the AMIT, in the metallic phase, and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field B and at finite temperature T . We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as a function of temperature. We find a phase diagram with finite-temperature transitions among insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions.
Physical Review B, 2012
We report, how the indirect exchange interaction J RKKY (R) between magnetic moments at a distanc... more We report, how the indirect exchange interaction J RKKY (R) between magnetic moments at a distance R in graphene depends on nonmagmetic disorder strength W and gate voltage. First, a semiclassical method is used to rederive J RKKY in clean graphene, yielding the asymptotic decay 1/R 2+α , where α = 1 is the power of the pseudogap at the Dirac point. Next, we perform numerical calculations with the Anderson tight-binding model on a honeycomb lattice. We observe that along the armchair direction J RKKY is more robust to nonmagnetic disorder than in other directions. This is explained semiclassically by the presence of more than one shortest path between two lattice sites in armchair directions, which is shown to reduce the disorder sensitivity compared to other directions. The distribution of J RKKY is calculated. We identify three different distribution shapes, repeated periodically along the zigzag direction, while only one kind, more narrow distribution, is observed along the armchair direction. We explain this by the different sensitivity to scattering phases. When increasing W , we find that the distribution crosses over to a logarithm-normal distribution. Its width is found to increase linearly with W . Moving away from the Dirac point, Friedel oscillations appear in addition to the one caused by the interference between two Dirac points. This results in a beating pattern. We study how this is effected by nonmagnetic disorder.
Physical Review B, 2007
Nonmagnetic disorder is shown to quench the screening of magnetic moments in metals, the Kondo ef... more Nonmagnetic disorder is shown to quench the screening of magnetic moments in metals, the Kondo effect. The probability that a magnetic moment remains free down to zero temperature is found to increase with disorder strength. Experimental consequences for disordered metals are studied. In particular, it is shown that the presence of magnetic impurities with a small Kondo temperature enhances the electron's dephasing rate at low temperatures in comparison to the clean metal case. It is furthermore proven that the width of the distribution of Kondo temperatures remains finite in the thermodynamic (infinite volume) limit due to wave function correlations within an energy interval of order 1/τ , where τ is the elastic scattering time. When time-reversal symmetry is broken either by applying a magnetic field or by increasing the concentration of magnetic impurities, the distribution of Kondo temperatures becomes narrower.
Physical Review B, 2012
We investigate the effects of nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yoshida (RKKY) i... more We investigate the effects of nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in graphene by studying numerically the Anderson model with on-site and hopping disorder on a honeycomb lattice at half filling. We evaluate the strength of the interaction as a function of the distance R between two magnetic ions, as well as their lattice positions and orientations. In the clean limit, we find that the strength of the interaction decays as 1/R 3 , with its sign and oscillation amplitude showing strong anisotropy. With increasing on-site disorder, the mean amplitude decreases exponentially at distances exceeding the elastic mean free path. At smaller distances, however, the oscillation amplitude increases strongly and its sign changes on the same sublattice for all directions but the armchair direction. For random hopping disorder, no sign change is observed. No significant changes to the geometrical average values of the RKKY interaction are found at small distances, while exponential suppression is observed at distances exceeding the localization length.
Physical Review B, 2014
The quantum corrections to the conductivity and the thermopower in monolayer graphene are studied... more The quantum corrections to the conductivity and the thermopower in monolayer graphene are studied. We use the recursive Green's function method to calculate numerically the conductivity and the thermopower of graphene. We then analyze these weak localization corrections by fitting with the analytical theory as function of the impurity parameters and the gate potential. As a result of the quantum corrections to the thermopower, we find large magnetothermopower which is shown to provide a very sensitive measure of the size and strength of the impurities. We compare these analytical and numerical results with existing experimental measurements of magnetoconductance of single layer graphene and find that the average size and strength of the impurities in these samples can thereby be determined accurately. We suggest favorable parameter ranges for future measurements of the magnetothermopower.
Journal of Experimental and Theoretical Physics Letters, 2006
The screening of magnetic moments in metals, the Kondo effect, is found to be quenched with a fin... more The screening of magnetic moments in metals, the Kondo effect, is found to be quenched with a finite probability in the presence of nonmagnetic disorder. Numerical results for a disordered electron system show that the distribution of Kondo temperatures deviates strongly from the result expected from random matrix theory. A pronounced second peak emerges for small Kondo temperatures, showing that the probability that magnetic moments remain unscreened at low temperatures increases with disorder. Analytical calculations, taking into account correlations between eigenfunction intensities yield a finite width for the distribution in the thermodynamic limit. Experimental consequences for disordered mesoscopic metals are discussed. PACS: 72.10.Fk, 72.15.Qm, 75.20.Hr, 72.15.Rn In a metal with antiferromagnetic exchange interaction between a local magnetic moment and the conduction electrons, correlations cause a change in the Fermi liquid ground state. The screening of the localized spin by the formation of a Kondo singlet below the Kondo temperature, T K , is affected by disorder in various ways. Fluctuations in the exchange coupling due to random positioning of magnetic moments results in a dispersion of T K [1]. Since T K is defined by an integral equation similar to the BCS equation for the critical temperature of a superconductor, one could expect, by analogy, the Anderson theorem [2] to be valid. In that case, the leading correction to T K would be of order T
Nonperturbative Scaling of the Disorder Quenched Kondo Effect
Bulletin of the American …, 2007
The quenching of the Kondo effect in weakly disordered metals with dilute magnetic impurities is ... more The quenching of the Kondo effect in weakly disordered metals with dilute magnetic impurities is studied by means of the numerical renormalisation group method. Using the one particle basis of a disordered tight binding model on a square latttice of size L, we calculate the ...
FINITE SIZE SCALING OF THE TYPICAL DENSITY OF STATES OF DISORDERED SYSTEMS WITHIN THE KERNEL POLYNOMIAL METHOD
Localisation 2011, 2012
ABSTRACT We study the (Anderson) metal-insulator transition (MIT) in tight binding models (TBM) o... more ABSTRACT We study the (Anderson) metal-insulator transition (MIT) in tight binding models (TBM) of disordered systems using the scaling behavior of the typical density of states (GDOS) as localization criterion. The GDOS is obtained as the geometrical mean value of the local density of states (LDOS) averaged over many different lattice sites and disorder realizations. The LDOS can efficiently be obtained within the kernel polynomial method (KPM). To check the validity and accuracy of the method, we apply it here to the standard Anderson model of disordered systems, for which the results (for instance for the critical disorder strength of the Anderson transition) are well known from other methods.
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Papers by Stefan Kettemann