Chiral splitting of Kondo peak in triangular triple quantum dot

New characteristics of the Kondo effect, arising from spin chirality induced by the Berry phase in the equilibrium state, are investigated. The analysis is based on the hierarchical equations of motion (HEOM) approach in a triangular triple quantum-dot (TTQD) structure. In the absence of magnetic field, TTQD has four-fold degenerate chiral ground states with degenerate spin chirality. When a perpendicular magnetic field is applied, the chiral interaction is induced by the magnetic flux threading through TTQD and the four-fold degenerate states split into two chiral state pairs. The chiral excited states manifest as chiral splitting of the Kondo peak in the spectral function. The theoretical analysis is confirmed by the numerical computations. Furthermore, under a Zeeman magnetic field B, the chiral Kondo peak splits into four peaks, owing to the splitting of spin freedom. The influence of spin chirality on the Kondo effect signifies an important role of the phase factor. This work provides insight into the quantum transport of strongly correlated electronic systems.     

Factorization of correlation functions and the replica limit of the Toda lattice equation

Exact microscopic spectral correlation functions are derived by means of the replica limit of the Toda lattice equation. We consider both Hermitian and non-Hermitian theories in the Wigner–Dyson universality class (class A) and in the chiral universality class (class AIII). In the Hermitian case we rederive two-point correlation functions for class A and class AIII as well as several one-point correlation functions in class AIII. In the non-Hermitian case the average spectral density of non-Hermitian complex random matrices in the weak non-Hermiticity limit is obtained directly from the replica limit of the Toda lattice equation. In the case of class A, this result describes the spectral density of a disordered system in a constant imaginary vector potential (the Hatano–Nelson model) which is known from earlier work. New results are obtained for the average spectral density in the weak non-Hermiticity limit of a quenched chiral random matrix model at non-zero chemical potential. These results apply to the ergodic or ϵ domain of the quenched QCD partition function at non-zero chemical potential. Our results have been checked against numerical results obtained from a large ensemble of random matrices. The spectral density obtained is different from the result derived by Akemann for a closely related model, which is given by the leading order asymptotic expansion of our result. In all cases, the replica limit of the Toda lattice equation explains the factorization of spectral one- and two-point functions into a product of a bosonic (non-compact integral) and a fermionic (compact integral) partition function. We conclude that the fermionic partition functions, the bosonic partition functions and the supersymmetric partition function are all part of a single integrable hierarchy. This is the reason that it is possible to obtain the supersymmetric partition function, and its derivatives, from the replica limit of the Toda lattice equation.     

Electron interactions and transport between coupled quantum Hall edge states

We examine the effects of electron-electron interactions on transport between edge states in a multilayer integer quantum Hall system. The edge states of such a system, coupled by interlayer tunneling, form a two-dimensional, chiral metal at the sample surface. We calculate the temperature-dependent conductivity and the amplitude of conductance fluctuations in this chiral metal, treating Coulomb interactions and disorder exactly in the weak-tunneling limit. We find that the conductivity increases with increasing temperature, as observed in recent experiments, and we show that the correlation length characterizing conductance fluctuations varies inversely with temperature.     

The mesoscopic chiral metal-insulator transition

Sharp localization transitions of chiral edge states in disordered quantum wires subject to a strong magnetic field are shown to be driven by crossovers from two-to one-dimensional localization of bulk states. As a result, the two-terminal conductance is found to exhibit discontinuous transitions at zero temperature between exactly integer plateau values and zero, reminiscent of first-order phase transitions. We discuss the corresponding phase diagram. The spin of the electrons is shown to result in a multitude of phases when the spin degeneracy is raised by the Zeeman energy. The width of conductance plateaus is found to depend sensitively on the spin flip rate 1/τ_s.     

Quasiparticle conductivities in disordered d-wave superconductors

We study the quasiparticle transport coefficients in disordered d-wave superconductors. We find that spin and charge excitations are generally localized unless magnetic impurities are present. If the system is close to a nesting point in the impurity-scattering unitary limit, the tendency towards localization is reduced while the quasiparticle density of states gets enhanced by disorder. We also show that the residual repulsive interaction among quasiparticles has a delocalizing effect and increases the density of states.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

The orientational relaxation of methane molecules in the solid phase II at low temperatures

A model for the dynamics of the coupling between the orientations of the ordered CH₄ molecules in phase II of solid methane at low temperatures is proposed. The model is equivalent to the dynamics of disordered solid hydrogen. The effective interaction strength is determined by the overlap of the librational ground states in the molecular field potential and vanishes in the classical limit. An approximate expression for the effective interaction strength is derived, showing an exponential dependence on the uncertainty of orientation in the librational ground states. This parameter is estimated from the experimental values of the tunnel energies. The second moments of the spectral densities of several anisotropic operators are evaluated in the infinite temperature limit. The resulting gaussian approximations for the spectra are applied in a derivation of the spin lattice relaxation time. The calculated values of the spin lattice relaxation time are compared to experiment.     

Detecting the chirality for coupled quantum dots

We propose a scheme to detect the chirality for a system consisting of three coupled quantum dots. The chirality is found to be determined by the frequency of the transition between chiral states under the chiral symmetry broken perturbation. The results are important to construct quantum gates and to demonstrate chiral entangle states in the triangle spin dots.     

Ten-fold degenerate d-electron correlation and the metal-nonmetal transition in a disordered binary system: Inclusion of Hund's rule coupling

The Yonezawa-Watabe (YW) study of the metal-nonmetal transitions in nondegenerate, s-electron disordered binary systems: doped semiconductors, metal-ammonia solutions, liquid metals and mixed crystals (alloys), is generalized to include ten-fold d-electron (hole) degeneracy. Such degeneracy automatically includes Hund's rule d-electron coupling and intra-site enhanced Coulomb and exchange interactions. Such a calculation is specifically relevant only to transition metal alloys, transition metal oxides and mixed transition metal oxides. It is seen that potential fluctuations exist in these systems and the possibility of Anderson localization in these disordered degenerate binary transition metal systems is explored. The YW CPA treatment of the effect of substitutional disorder (alloying) upon the mobility gap and quasiparticle states of the density of states at the extreme band edges and localization due to random spin configuration are generalized to these degenerate d-electron systems and it is shown that the disappearance of the mobility gap, not the density of states gap, causes the metal-nonmetal transition for degenerate d-electrons.     

Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.     

Universal behaviors of magnon-mediated spin transport in disordered nonmagnetic metal-ferromagnetic insulator heterostructures

We numerically investigate magnon-mediated spin transport through nonmagnetic metal/ferromagnetic insulator (NM/FI) heterostructures in the presence of Anderson disorder, and discover universal behaviors of the spin conductance in both one-dimensional (1D) and 2D systems. In the localized regime, the variance of logarithmic spin conductance σ²(lnG_T) shows a universal linear scaling with its average ⟨lnG_T⟩, independent of Fermi energy, temperature, and system size in both 1D and 2D cases. In 2D, the competition between disorder-enhanced density of states at the NM/FI interface and disorder-suppressed spin transport leads to a non-monotonic dependence of average spin conductance on the disorder strength. As a result, in the metallic regime, average spin conductance is enhanced by disorder, and a new linear scaling between spin conductance fluctuation rms(G_T) and average spin conductance G_T is revealed which is universal at large system width. These universal scaling behaviors suggest that spin transport mediated by magnon in disordered 2D NM/FI systems belongs to a new universality class, different from that of charge conductance in 2D normal metal systems.     

Anyonic loops in three-dimensional spin liquid and chiral spin liquid

We established a large class of exactly soluble spin liquids and chiral spin liquids on three-dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-Abelian statistics. We characterize this kind of statistics by non-Abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.     

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H², the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.Dedicated to Freeman Dyson on the Occasion of his eightieth birthdayAcknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.     

Chiral anomalies in supersymmetric theories

The supersymmetric non-abelian chiral anomaly is computed in a theory of chiral scalar superfields coupled to external gauge superfields, both in a vector-current conserving scheme and in a left-right symmetric scheme. The corresponding supersymmetric Wess-Zumino term is discussed; in particular we give an explicit expression for the anomalous bosonic term.     

A high-efficiency spin polarizer based on edge and surface disordered silicene nanoribbons

Using the tight-binding formalism, we explore the effect of weak disorder upon the conductance of zigzag edge silicene nanoribbons (SiNRs), in the limit of phase-coherent transport. We find that the fashion of the conductance varies with disorder, and depends strongly on the type of disorder. Conductance dips are observed at the Van Hove singularities, owing to quasilocalized states existing in surface disordered SiNRs. A conductance gap is observed around the Fermi energy for both edge and surface disordered SiNRs, because edge states are localized. The average conductance of the disordered SiNRs decreases exponentially with the increase of disorder, and finally tends to disappear. The near-perfect spin polarization can be realized in SiNRs with a weak edge or surface disorder, and also can be attained by both the local electric field and the exchange field.     

Supersymmetric chiral normal coordinates

The (anti-) chiral Killing vectors of the supersymmetric Kähler manifold associated with the nonlinear realization of a global symmetry are used to define (anti-) chiral normal coordinates. This in turn leads to a background superfield expansion of the super-Kähler potential that is manifestly gauge invariant and supersymmetric. The chiral normal coordinates are further employed to construct a background superfield expansion for a locally gauge invariant supersymmetric action.     

Electron spin precession in semiconductor quantum wires with Rashba spin-orbit coupling

The influence of the Rashba spin-orbit coupling on the electron spin dynamics is investigated for a ballistic semiconductor quantum wire with a finite width. We monitor the spin evolution using the time-dependent Schrödinger equation. The pure spin precession characteristic of the 1D limit is lost in a 2D wire with a finite lateral width. In general, the time evolution in the latter case is characterized by several frequencies and a nonrigid spin motion.Received: 16 April 2003, Published online: 11 August 2003PACS: 73.21.Hb Quantum wires - 73.22.Dj Single particle states     

Identification of transverse spin currents in noncollinear magnetic structures

In this Letter we construct a spinor transport theory and derive the equations of motion for the distribution functions for currents in noncollinear magnetic multilayers. We find the length scale which characterizes the transverse spin current is of the order of 3 nm for a ferromagnetic 3d transition metal such as Co; this alters one's prediction of the spin torque generated for free magnetic layers less than 3 nm. In the limit of large exchange splitting we reproduce the results previously found for spin currents across noncollinear multilayers inasmuch as there are no transverse spin currents in the layers themselves in this limit.