Power-law Density Of States Research Articles

Power-Law Density of States in Organic Solar Cells Revealed by the Open-Circuit Voltage Dependence of the Ideality Factor.

The density of states (DOS) is fundamentally important for understanding physical processes in organic disordered semiconductors, yet hard to determine experimentally. We evaluated the DOS by considering recombination via tail states and using the temperature and open-circuit voltage (V_{oc}) dependence of the ideality factor. By performing Suns-V_{oc} measurements, we find that the energetic disorder increases deeper into the band gap, which is not expected for a Gaussian or exponential DOS. The linear dependence of the disorder on energy reveals the power-law DOS in organic solar cells.

Low-energy doublet states, quantum phase transition, and partial Kondo screening in the triple dot system

We consider a triple dot system with one of the dots coupled to a lead whose density of states varies in power-law fashion. Using the poor-man's scaling and the numerical renormalization group method, we investigate a quantum phase transition between local moment and partially Kondo-screened strong coupling phases with the variation of non-thermal control parameters. These quantum phases are closely related to low-energy doublet states formed by the triangular symmetry breaking. Since the lead has power-law density of states, the transition fixed point separating odd-parity and even-parity doublets depends on pseudo-gap exponent. The quantum phase in the even-parity doublet is determined by the magnitude of the hybridization width; the triple dot system lies in partially Kondo-screened strong coupling phase only for large enough hybridization width. Scaling result for the critical hybridization width is compared with that of numerical renormalization group method.

Disorder induced power-law gaps in an insulator–metal Mott transition

A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and a variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems. Theory predicts that disorder might play a role in driving a Mott insulator across an IMT, with the emergent metallic state hosting a power-law suppression of the density of states (with exponent close to 1; V-shaped gap) centered at the Fermi energy. Such V-shaped gaps have been observed in Mott systems, but their origins are as-yet unknown. To investigate this, we use scanning tunneling microscopy and spectroscopy to study isovalent Ru substitutions in Sr3(Ir1-xRux)2O7 (0 ≤ x ≤ 0.5) which drive the system into an antiferromagnetic, metallic state. Our experiments reveal that many core features of the IMT, such as power-law density of states, pinning of the Fermi energy with increasing disorder, and persistence of antiferromagnetism, can be understood as universal features of a disordered Mott system near an IMT and suggest that V-shaped gaps may be an inevitable consequence of disorder in doped Mott insulators.

Poor man's scaling: anisotropic Kondo and Coqblin–Schrieffer models

We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive scaling equation to the second order for such a model. We show how the scaling equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general scaling equation. We introduce the anisotropic Coqblin–Schrieffer model, apply the general method to derive scaling equation for that model for the power law DOS, and integrate the derived equation analytically.

Quantum criticality out of equilibrium in the pseudogap Kondo model

We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels {\mu}_L/R, {\rho}_c,L(R) ({\omega}) \propto |{\omega} - {\mu}_L(R) |r, and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.

Dissipative spin dynamics near a quantum critical point: Numerical renormalization group and Majorana diagrammatics

We provide an extensive study of the sub-ohmic spin-boson model with power law density of states J(\omega)=\omega^s (with 0<s<1), focusing on the equilibrium dynamics of the three possible spin components, from very weak dissipation to the quantum critical regime. Two complementary methods, the bosonic Numerical Renormalization Group (NRG) and Majorana diagrammatics, are used to explore the physical properties in a wide range of parameters. We show that the bosonic self-energy is the crucial ingredient for the description of critical fluctuations, but that many-body vertex corrections need to be incorporated as well in order to obtain quantitative agreement of the diagrammatics with the numerical simulations. Our results suggest that the out-of-equilibrium dynamics in dissipative models beyond the Bloch-Redfield regime should be reconsidered in the long-time limit. Regarding also the spin-boson Hamiltonian as a toy model of quantum criticality, some of the insights gained here may be relevant for field theories of electrons coupled to bosons in higher dimensions.

The Sinai model in the presence of dilute absorbers

We study the Sinai model for the diffusion of a particle in aone-dimensional random potential in the presence of a small concentrationρ of perfect absorbers using the asymptotically exact real space renormalization method. Wecompute the survival probability, the averaged diffusion front and return probability, thetwo-particle meeting probability, the distribution of total distance traveled beforeabsorption and the averaged Green’s function of the associated Schrödinger operator. Ourwork confirms some recent results of Texier and Hagendorf obtained by Dyson–Schmidtmethods, and extends them to other observables and the presence of a drift. Inparticular the power law density of states is found to hold in all cases. Irrespective ofthe drift, the asymptotic rescaled diffusion front of surviving particles is foundto be a symmetric step distribution, uniform for , where ξ(t) is a new length scale for survival ( in the absence of drift). Survival outside this sharp region is found to decaywith a larger exponent, continuously varying with the rescaled distancex/ξ(t). A simple physical picture based on a saddle point is given, and universality isdiscussed.

Universal crossovers and critical dynamics of quantum phase transitions: A renormalization group study of the pseudogap Kondo problem

The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment with a power-law density of states, displays continuous quantum phase transitions between free and screened moment phases. In this paper we employ renormalization group techniques to analytically calculate universal crossover functions, associated to these transitions, for various observables. Quantitative agreement with the results of Numerical Renormalization Group (NRG) simulations is obtained for temperature-dependent static and zero-temperature dynamic quantities, at and away from criticality. In the notoriously difficult realm of finite-temperature low-frequency dynamics, usually inaccessible to both NRG and perturbative methods, we show that progress can be made by a suitable renormalization procedure in the framework of the Callan-Symanzik equations. Our general strategy can be extended to other zero-temperature phase transitions, both in quantum impurity models and bulk systems.

Quantum dot in the pseudogap Kondo state

We investigate the transport properties of a (small) quantum dot connected to Fermi liquid leads with a power-law density of states (DOS). Such a system, if experimentally realizable, will have interesting physical properties including: (i) non-saturating Coulomb blockade peak widths; (ii) a non-unitary Kondo peak symmetrically placed between the Coulomb blockade peaks; (iii) an absence of conductance away from particle-hole symmetry at sufficiently low temperatures; and (iv) evidence of a quantum critical point as a function of dot-lead hopping. These properties are compared and contrasted with one dimensional Luttinger systems exhibiting a power-law "tunneling-DOS".

Critical theories for the pseudogap Kondo problem

We discuss quantum phase transitions in the pseudogap Kondo problem, which describes a magnetic moment coupled to conduction electrons with a power-law density of states, ρ ( ω ) ∝ | ω | r . We show that different perturbative expansions, together with renormalization group techniques, provide effective low-energy field theories for the relevant critical fixed points. In particular, we review expansions near the lower- and upper-critical dimensions of the problem, being r = 0 and r = 1 , respectively.

A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, rho(epsilon) ~ |epsilon|^r, with exponent r<0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by second-order transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin.

Particle-hole symmetric localization in two dimensions

We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states $\ensuremath{\rho}(E)$ at the band center $E=0.$ The most general system of this kind [R. Gade, Nucl. Phys. B 398, 499 (1993)] exhibits critical behavior and has $\ensuremath{\rho}(E)$ that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. [Phys. Rev. B 50, 7526 (1994)] has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder---this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ``surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is $\ensuremath{\rho}(E)\ensuremath{\sim}{E}^{\ensuremath{-}1}{e}^{\ensuremath{-}c|\mathrm{ln}E{|}^{2/3}},$ different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ``string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.

Kondo effect of impurity moments ind-wave superconductors: Quantum phase transition and spectral properties

We discuss the dynamics of magnetic moments in d-wave superconductors. In particular, we focus on moments induced by doping nonmagnetic impurities into cuprates. The interaction of such moments with the Bogoliubov quasiparticles of the superconductors can be described by variants of the pseudogap Kondo model, characterized by a power-law density of states at the Fermi level. The numerical renormalization-group technique is employed to investigate this Kondo problem for realistic band structures and particle-hole asymmetries, both at zero and finite temperatures. In particular, we study the boundary quantum phase transition between the local-moment and asymmetric strong-coupling phases, and argue that this transition has been observed in recent nuclear magnetic resonance experiments. We determine the spectral properties of both phases and the location of the critical point as a function of Kondo coupling and doping, and discuss quantum-critical crossovers near this phase transition. In addition, changes in the local density of states around the impurity are calculated as functions of temperature, being relevant to scanning tunneling microscopy experiments.

Resonant tunneling into a biased fractional quantum Hall edge.

We observe resonant tunneling into a voltage biased fractional quantum Hall effect (FQHE) edge, using atomically sharp tunnel barriers unique to cleaved-edge overgrown devices. The resonances demonstrate different tunnel couplings to the metallic lead and the FQHE edge. Weak coupling to the FQHE edge produces clear non-Fermi liquid behavior with a sixfold increase in resonance area under bias arising from the power law density of states at the FQHE edge. A simple device model uses the resonant tunneling formalism for chiral Luttinger liquids to successfully describe the data.

On Magnetic Impurities in Gapless Fermi Systems

In ordinary metals, antiferromagnetic exchange between conduction electrons and a magnetic impurity leads to screening of the impurity spin below the Kondo temperature, TK. In systems such as semimetals, small-gap semiconductors and unconventional superconductors, a reduction in available conduction states near the chemical potential can greatly depress Tx. The behavior of an Anderson impurity in a model with a power-law density of states, p(e) c|c|r, > 0, for |e| 0, as T -> 0, indicating a complete screening of the impurity spin.

Entropy ambiguity in a system in equilibrium with a finite heat bath

Plastino and Plastino [Phys. Lett. A 193 (1994) 140] have recently shown that the probability distribution for a system in equilibrium with a finite heat bath having a power-law density of states is given by the generalized canonical distribution of Tsallis [J. Stat. Phys. 52 (1988) 479]. Here we show that the entropy S of such a system is however ambiguous, and is not uniquely given by the Tsallis entropy (or its additive equivalent the Rényi entropy). The ambiguity is due to the fact that the extension of the Boltzmann formula S = ln W to nonuniform probability distributions requires an additional postulate, which in the present context may be taken to be the definition of the entropy of the finite heat bath. Two reasonable alternative definitions D1 and D2 lead to the conventional Boltzmann-Gibbs-Shannon entropy and the Rényi entropy, respectively. Since the Tsallis distribution maximizes the Rényi entropy, definition D2 preserves the entropy maximum principle, whereas D1 does not. The distinction between D1 and D2 vanishes for large heat baths, while small baths exhibit thermodynamic peculiarities such as unequal system and bath temperatures.