Persistent Currents In Mesoscopic Rings Research Articles

Spin states and persistent currents in mesoscopic rings: Spin-orbit interactions

We investigate theoretically electron spin states in one dimensional (1D) and two dimensional (2D) hard-wall mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI) in a perpendicular magnetic field. The Hamiltonian of the RSOI alone is mathematically equivalent to that of the DSOI alone using an SU(2) spin rotation transformation. Our theoretical results show that the interplay between the RSOI and DSOI results in an effective periodic potential, which consequently leads to gaps in the energy spectrum. This periodic potential also weakens and smoothens the oscillations of the persistent charge current (CC) and spin current (SC) and results in the localization of electrons. For a 2D ring with a finite width, higher radial modes destroy the periodic oscillations of persistent currents.

Electronic delocalization and persistent currents in nonsymmetric-dimer mesoscopic rings threaded by magnetic flux

We investigate electronic delocalization and magnetic-flux-induced persistent current in the mesoscopic ring, which is constructed according to the nonsymmetric-dimer (NSD) model. The flux-dependent energy spectra, electronic wavefunctions, and persistent currents are theoretically obtained. It is demonstrated that due to the localization-delocalization transition of electrons, the electronic state in the NSD ring can be localized, extended, and the intermediate case between extended states and localized ones. The persistent current (PC) approaches the behavior of free electrons if the Fermi level is around the near-resonant energy. Otherwise, the PC is depressed dramatically. This conclusion could be generalized to other correlated-disordered systems.

Persistent currents in the presence of nonclassical electromagnetic fields

Persistent currents in mesoscopic rings and cylinders threaded by a magnetostatic flux and also by monochromatic nonclassical electromagnetic fields are considered. The results depend on the quantum state of the nonclassical electromagnetic fields. It is shown that quantum and thermal noise in the field reduces the current and can change its character from diamagnetic to paramegnetic, and vice versa. Four different examples of nonclassical electromagnetic fields are considered (number eigenstates, coherent states with randomized phase, coherent states, and thermal states) and the corresponding currents are calculated. Two-mode entangled electromagnetic fields are also considered, and the effect of entanglement on the currents is studied.

Boson-fermion model: An exact diagonalization study

The main features of a generic boson-fermion scenario for electron pairing in a many-body correlated fermionic system are: i) a cross-over from a poor metal to an insulator and finally a superconductor as the temperature decreases, ii) the build-up of a finite amplitude of local electron pairing below a certain temperature $T^*$, followed by the onset of long-range phase correlations among electron pairs below a second characteristic temperature $T_{\phi}$, iii) the opening of a pseudogap in the DOS of the electrons below $T^*$, rendering these electrons poorer and poorer quasi-particles as the temperature decreases, with the electron transport becoming ensured by electron pairs rather than by individual electrons. A number of these features have been so far obtained on the basis of different many-body techniques, all of which have their built-in shortcomings in the intermediate coupling regime, which is of interest here. In order to substantiate these features, we investigate them on the basis of an exact diagonalization study on rings up to eight sites. Particular emphasis has been put on the possibility of having persistent currents in mesoscopic rings tracking the change-over from single- to two-particle transport as the temperature decreases and the superconducting state is approached.

Persistent currents in mesoscopic rings: A numerical and renormalization group study

The persistent current in a lattice model of a one-dimensional interacting electron system is systematically studied using a complex version of the density matrix renormalization group algorithm and the functional renormalization group method. We mainly focus on the situation where a single impurity is included in the ring penetrated by a magnetic flux. Due to the interplay of the electron-electron interaction and the impurity the persistent current in a system of N lattice sites vanishes faster then 1/N. Only for very large systems and large impurities our results are consistent with the bosonization prediction obtained for an effective field theory. The results from the density matrix renormalization group and the functional renormalization group agree well for interactions as large as the band width, even though as an approximation in the latter method the flow of the two-particle vertex is neglected. This confirms that the functional renormalization group method is a very powerful tool to investigate correlated electron systems. The method will become very useful for the theoretical description of the electronic properties of small conducting ring molecules.

Low-Temperature Dephasing and Renormalization in Model Systems

We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath. Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects. In particular in the latter case dephasing should be distinguished from renormalization effects. For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spin-boson models. Next we review Caldeira–Leggett models, with applications, e.g., to persistent currents in mesoscopic rings. Then, we analyze the more general problem of a particle which interacts with a quantum field V ( t , r ( t )), the fluctuations of which are characterized by a dielectric function e(ω, k ). Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.

Persistent currents in mesoscopic rings with a quantum dot

Using the Anderson model in the Kondo regime, we calculate the persistent current j in a ring with an embedded quantum dot (QD) as a function of the Aharonov-Bohm flux $\ensuremath{\Phi}$ for different ring length L, temperature T, and broadening of the conduction states $\ensuremath{\delta}.$ For $T=\ensuremath{\delta}=0$ and $L\ensuremath{\gg}\ensuremath{\xi},$ where $\ensuremath{\xi}$ is the Kondo screening length, $\mathrm{Lj}$ tends to the value for a noninteracting ideal ring, while it is suppressed for a side-coupled QD. For any $L/\ensuremath{\xi},$ $\mathrm{Lj}$ is also suppressed when either T or $\ensuremath{\delta}$ increase above a fraction of the level spacing, which depends on $\ensuremath{\Phi}.$

TRANSPORT IN LUTTINGER LIQUIDS

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz–Shastry exactly solvable Luttinger-like model. With a view to making this article accessible to researchers in diverse fields such as nuclear physics, particle physics, formal field theory and condensed matter physics, we begin by first giving a brief introduction. In Sec. 1, we explain the words such as "Luttinger liquid" and "transport" in the title. We also motivate the study of this subject by showing that field is very important at the current time from the applications point of view and describe why it is theoretically fascinating. We then give a quick review of some of the important results in the field in Sec. 2, before we go on to describe some work that we have recently done and are doing in this field in Sec. 3. Finally, in Sec. 4, we conclude by re-emphasizing the importance of this area and drawing attention towards future possibilities.

Persistent current in a mesoscopic ring with diffuse surface scattering

The persistent current in a clean mesoscopic ring with ballistic electron motion is calculated. The particle dynamics inside a ring is assumed to be chaotic due to scattering at the surface irregularities of atomic size. This allows one to use the so-called ``ballistic'' supersymmetric \sigma model for calculation of the two-level correlation function in the presence of a nonzero magnetic flux.

Hyperfine-driven persistent currents in mesoscopic rings based on a 2D electron gas with Rashba spin-orbit interaction

We present a detailed theory of induced persistent current (PC) produced by hyperfine interaction in mesoscopic rings based on a 2D-electron (hole) gas in the absence of external magnetic field. PC emerges due to combined action of the hyperfine interaction of charge carriers with polarized nuclei, spin-orbit interaction and Berry phase.

High-spin nuclear states and persistent currents in mesoscopic rings

An analogy is presented between periodic persistent currents in mesoscopic rings and staggerings of gamma energy transitions from some nuclear high-spin states. Various sources of damping of the expected periodic structures in both physical systems are compared. This discussion provides, in the nuclear case, a tentative explanation of the scarcity of such staggerings, their appearance near 150Gd and the existence of a spin-window for their observation.

Structures of energy spectrum and persistent currents in mesoscopic rings with radial potential barrier in magnetic field

The energy spectrum and the persistent currents are calculated for finite-width mesoscopic annular structures with radial potential barrier in the presence of a magnetic field. The introduction of the tunneling barrier leads to the creation of extra edge states around the barrier and the occurrence of oscillatory structures superimposed on the bulk Landau level plateaus in the energy spectrum. We found that the Fermi energy E-F increases with the number of electrons N emerging many kinks. The single eigenstate persistent current exhibits complicated structures with vortex-like texture, ''bifurcation'', and multiple ''furcation'' patterns as N is increased. The total currents versus N display wild fluctuations.

Bistability of persistent currents in mesoscopic rings

We study the persistent currents flowing in a mesoscopic ring threaded by a magnetic flux and connected to a stub of finite length. Multistability processes and Coulomb blockade are demonstrated to be present in this system. These properties are functions of the magnetic flux crossing the ring which plays the role that the external applied potential fulfills in the multistability behaviour of the standard mesoscopic heterostructures.

Functional Integration Method for 1 D Localization, Multipoint Correlators and Persistent Current in Mesoscopic Ring at Arbitrary Magnetic Fields

Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential problem I find closed functional representations for various physical quantities. These functional integrals are calculated exactly without the use of any perturbative expansions. The expressions for the multipoint densities correlators are obtained. Then I evaluate the mean square dispersion of the size of localized wave functions. As a physical application of the method, I find the expectation value of the persistent current in mesoscopic ring with arbitrary magnetic flux Φ. (For small φ this problem has been solved by O. Dorokhov.) The case when the random potential has finite correlation length is considered too.

Classical analogs of mesoscopic quantum phenomena

An important aspect of mesoscopic electronic systems is that the electrons maintain their phase coherence and propagate as waves. The resulting behavior is complicated by disorder, time-dependent scattering sites and many-electron effects (possibly modeled with a nonlinear wave equation). Studying the latter effects theoretically or experimentally in mesoscopic electronic systems is difficult. However, it is possible to contrive classical wave systems which precisely duplicate the salient features of the quantum electron problem, and which may be readily studied experimentally. This paper will describe the use of such systems to study phonon assisted hopping, the effects of nonlinearity on Anderson localization, the effects of Penrose tile symmetry, noise in mesoscopic electronics, ‘superdiffusion’, and to study an aspect of the discrepancy between theory and experiment for normal electron persistent currents in mesoscopic rings.

SIZE EFFECTS IN ORBITAL MAGNETISM

Size effects in orbital magnetism are briefly reviewed. We attempt to put recent developments focused on the persistent currents in mesoscopic rings into the context of earlier developments in ballistic finite systems. The relevant experimental evidence is discussed, when available.

Persistent currents in mesoscopic rings: A stochastic model

A stochastic model, proposed first by Landauer and Buttiker to explain the phenomenon of persistent currents in submicrometer normal metal rings, is developed quantitatively by determining the relevant relaxation time scales. The current excited by a periodically modulated magnetic field threading the ring is computed as the sum of two clear-cut components: a persistent current and a driven current. The latter component provides a notable example of astochastic resonance mechanism in solid-state physics.

Stochastic fluctuations of persistent currents in mesoscopic rings

AbstractWe investigate systematically the effect of the electronic Coulomb interaction on the stochastic fluctuations (from sample to sample) in the persistent currents I(Φ) of mesoscopic rings threaded by a magnetic flux Φ. In contrast to our recent publication [Europhys. Lett. 18 (1992) 457], we avoid separation of impurity and interaction scattering events and we present here a comprehensive view. By this alternative procedure, we are able to confirm our earlier result, namely that 〈I2〉1/2 ∼ evF/L, which is a much larger quantity than the average current 〈I〉 ∼ evFl/L2.

Effects of spin-orbit scattering in mesoscopic rings: Canonical- versus grand-canonical-ensemble averaging.

Motivated by recent experiments on persistent currents in mesoscopic rings, the effect of spin-orbit scattering on closed electron trajectories is studied. It is shown that for one-dimensional systems within either the grand-canonical ensemble or the canonical ensemble consisting exclusively of even numbers (at zero temperature), there exist universal reduction factors due to spin-orbit scattering. No such universal factors occur in the canonical ensemble for an odd number of electrons. In higher dimensions, it is argued that strong spin-orbit scattering reduces the weak-localization contribution to the paramagnetic persistent current by a factor of 1/4. Enhancement of the paramagnetic behavior due to an additional mechanism is suggested. The relevance of these results to experiments is discussed.

Comment on "Persistent currents in mesoscopic rings by suppression of charge fluctuations"

Comment on "Persistent currents in mesoscopic rings by suppression of charge fluctuations"