Electronic transport through a quantum ring coupled to ferromagnetic leads

We study the spin-dependent transport through a one-dimensional quantum ring with taking both the Rashba spin--orbit coupling (RSOC) and ferromagnetic leads into consideration. The linear conductance is obtained by the Green's function method. We find that due to the quantum interference effect arising from the RSOC-induced spin precession phase and the difference in travelling phase between the two arms of the ring, the conductance becomes spin-polarized even in the antiparallel magnetic configuration of the two leads, which is different from the case in single conduction channel system. The linear conductance, the spin polarization and the tunnel magnetoresistance are periodic functions of the two phases, and can be efficiently tuned by the structure parameters.     

Magnetopumping current in graphene Corbino pump

We study conductance and adiabatic pumped charge and spin currents in a graphene quantum pump with Corbino geometry in the presence of an applied perpendicular magnetic field. Pump is driven by the periodic and out of phase modulations of the magnetic field and an electrostatic potential applied to the ring area of the pump. We show that Zeeman splitting, despite its smallness, suppresses conductance and pumped current oscillations at zero doping. Moreover, quite considerable spin conductance and pumped spin current are generated at low dopings due to Zeeman splitting. We find that pumped charge and spin currents increase by increasing the magnetic field, with small oscillations, until they are suppressed due to the effect of nonzero doping and Zeeman splitting.     

Magnetic field symmetry and phase rigidity of the nonlinear conductance in a ring

We have performed nonlinear transport measurements as a function of a perpendicular magnetic field in a semiconductor Aharonov-Bohm ring connected to two leads. While the voltage-symmetric part of the conductance is symmetric in the magnetic field, the voltage-antisymmetric part of the conductance is not symmetric. These symmetry relations are compatible with the scattering theory for nonlinear mesoscopic transport. The observed asymmetry can be tuned continuously by changing the gate voltages near the arms of the ring, showing that the phase of the nonlinear conductance in a two-terminal interferometer is not rigid, in contrast with the case for the linear conductance.     

Wave attenuation model for dephasing and measurement of conditional times

Inelastic scattering induces dephasing in mesoscopic systems. An analysis of previous models to simulate inelastic scattering in such systems is presented and a relatively new model based on wave attenuation is introduced. The problem of Aharonov-Bohm (AB) oscillations in conductance of a mesoscopic ring is studied. We show that the conductance is symmetric under flux reversal and the visibility of AB oscillations decays to zero as a function of the incoherence parameter, signaling dephasing. Further the wave attenuation model is applied to a fundamental problem in quantum mechanics, that of the conditional (reflection/transmission) times spent in a given region of space by a quantum particle before scattering off from that region.     

Aharonov-Bohm oscillations in the presence of strong spin-orbit interactions

We have measured highly visible Aharonov-Bohm (AB) oscillations in a ring structure defined by local anodic oxidation on a p-type GaAs heterostructure with strong spin-orbit interactions. Clear beating patterns observed in the raw data can be interpreted in terms of a spin geometric phase. Besides h/e oscillations, we resolve the contributions from the second harmonic of AB oscillations and also find a beating in these h/2e oscillations. A resistance minimum at B=0 T, present in all gate configurations, is the signature of destructive interference of the spins propagating along time-reversed paths.     

Aharonov-Bohm effect as a probe of interaction between magnetic impurities

We study the effects of the RKKY interaction between magnetic impurities on the mesoscopic conductance fluctuations of a metal ring with dilute magnetic impurities. At sufficiently low temperatures and strong magnetic fields, the loss of electron coherence occurs mainly due to the scattering off rare pairs of strongly coupled magnetic impurities. We establish a relation between the dephasing rate and the distribution function of the exchange interaction within such pairs. In the case of the RKKY exchange interaction, this rate exhibits 1/B(2) behavior in strong magnetic fields. We demonstrate that the Aharonov-Bohm conductance oscillations may be used as a probe of the distribution function of the exchange interaction between magnetic impurities in metals.     

Conductance oscillations and transport spectroscopy of a quantum dot

Results are reported for low temperature measurements of the conductance through small regions of a two-dimensional electron gas (2 DEG). An unconventional GaAs heterostructure is used to form a 2 DEG whose density can be tuned by the gate voltage applied to its conductive substrate. Electron beam lithography is used to pattern a narrow channel in the 2 DEG interrupted by two constrictions, defining a small 2 DEG island between them. The conductance is found to oscillate periodically with the gate voltage, namely with electron density. Calculations of the capacitance between the substrate and the island show that the period of oscillation corresponds to adding one electron to the island. The oscillatory behavior results primarily from the discreteness of charge and the Coulomb interaction between electrons. However, the observed temperature dependence of these oscillations requires a more sophisticated treatment which includes the quantized electron energy levels as well. The magnetic field dependence of the oscillations allows us to extract the discrete energy spectrum of the quantum dot in the quantum-Hall regime.     

Direct observation of the Aharonov-Casher phase

Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.     

Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states

We study Aharonov-Bohm (AB) conductance oscillations arising from the surface states of a topological insulator nanowire, when a magnetic field is applied along its length. With strong surface disorder, these oscillations are predicted to have a component with anomalous period Φ(0)=hc/e, twice the conventional period. The conductance maxima are achieved at odd multiples of 1/2Φ(0), implying that a π AB phase for electrons strengthens the metallic nature of surface states. This effect is special to topological insulators, and serves as a defining transport property. A key ingredient, the surface curvature induced Berry phase, is emphasized here. We discuss similarities and differences from recent experiments on Bi2Se3 nanoribbons, and optimal conditions for observing this effect.     

Experimental demonstration of spin geometric phase: radius dependence of time-reversal Aharonov-Casher oscillations

A geometric phase of electron spin is studied in arrays of InAlAs/InGaAs two-dimensional electron gas rings. By increasing the radius of the rings, the time-reversal symmetric Aharonov-Casher oscillations of the electrical resistance are shifted towards weaker spin-orbit interaction regions with their shortened period. We conclude that the shift is due to a modulation of the spin geometric phase, the maximum modulation of which is approximately 1.5 rad. We further show that the Aharonov-Casher oscillations in various radius arrays collapse onto a universal curve if the radius and the strength of Rashba spin-orbit interaction are taken into account. The result is interpreted as the observation of the effective spin-dependent flux through a ring.     

Phase drift and temperature-induced ordering of h/e oscillations in a small ring interferometer

Continuous phase drift and thermal ordering of the Aharonov-Bohm oscillations in a small ring interferometer have been revealed by numerical calculation of the conductance. It has been found that the sign and rate of change in the oscillation amplitude with increasing temperature depend on the Fermi energy. The calculation results have been compared with the experimental data for the same sample.     

Andreev reflection in a quantum dot coupled to ferromagnetic and superconductor leads under magnetic fields

By employing the nonequilibrium Green's function, we investigate the spin-dependent linear Andreev reflection (AR) resonant tunneling through a quantum dot connected to a ferromagnetic lead and a superconducting lead, where the magnetization direction in the ferromagnetic lead can be tuned by one. We focus our attention on the effects of the magnetic fields on the AR conductance. One high conductance peak and one low conductance peak are developed in the linear AR conductance when a stronger magnetic field is considered. The interplay between the spin-flip scattering and the magnetic fields on the AR conductance are also studied.     

Coherent nonlinear transport in quantum rings

While equilibrium properties of mesoscopic systems are well understood, many questions are still debated concerning the non-equilibrium properties, which govern nonlinear transport. Nonlinear transport measurements have been performed on two-terminal semiconductor quantum rings in the open regime, where the rings are used as electron interferometers and show the Aharonov–Bohm effect. We observe a magnetic field asymmetry of the nonlinear conductance, compatible with the non-validity of the Onsager–Casimir relations out-of-equilibrium. In particular, the voltage-antisymmetric part of the nonlinear conductance of these two-terminal devices is not phase rigid, as it is the case for the linear conductance. We show that this asymmetry is directly related to the electronic phase accumulated by the electrons along the arms of the ring and can be tuned using an electrostatic gate.     

Transmission of electron through an Aharonov－Bohm interferometer with a quantum dot in Coulomb blockade regime

We calculate conductance of an Aharonov－Bohm (AB) interferometer for which a single-level quantum dot in the Coulomb blockade regime is embedded in one of its arms. Using the Schr?dinger equations and taking into account the Coulomb interaction on the dot, we calculate conductance G as a function of flux φ threaded through the ring and as a function of gate voltage V applied to the dot. It is found that the AB oscillations of G(φ) depend on the particle occupation on the dot, controlled by V. If the system is closed, there is no loss of particles, G(φ) is periodic and G(φ)=G(-φ), satisfying the Onsager relation. In this case G(φ) can reach its maximum value, 2e^2/h, at the resonance. When the system is open, one has G(φ)≠G(-φ), G(φ) yields a phase shift which depends on the loss rate of electrons in this open system.     

Ballistic Quantum Transport: Effect of Geometrical Phases

We study the influence of nonuniform magnetic fields on the magneto conductance of mesoscopic microstructures. We show that the coupling of the electron spin to the inhomogenous field gives rise to effects of the Berry phase on ballistic quantum transport and discuss adiabaticity conditions required to observe such effects. We present numerical results for different ring geometries showing a splitting of Aharonov–Bohm conductance peaks for single rings and corresponding signatures of the geometrical phase in weak localization. The latter features can be qualitatively explained in a semiclassical approach to quantum transport.     

Quantized conductance at the Majorana phase transition in a disordered superconducting wire

Superconducting wires without time-reversal and spin-rotation symmetries can be driven into a topological phase that supports Majorana bound states. Direct detection of these zero-energy states is complicated by the proliferation of low-lying excitations in a disordered multimode wire. We show that the phase transition itself is signaled by a quantized thermal conductance and electrical shot noise power, irrespective of the degree of disorder. In a ring geometry, the phase transition is signaled by a period doubling of the magnetoconductance oscillations. These signatures directly follow from the identification of the sign of the determinant of the reflection matrix as a topological quantum number.     

Kondo effect in a few-electron quantum ring

A small quantum ring with less than ten electrons was studied by transport spectroscopy. For strong coupling to the leads a Kondo effect is observed and used to characterize the spin structure of the system in a wide range of magnetic fields. At small magnetic fields Aharonov-Bohm oscillations influenced by Coulomb interaction appear. They exhibit phase jumps by pi at the Coulomb-blockade resonances. Inside Coulomb-blockade valleys the Aharonov-Bohm oscillations can also be studied due to the finite conductance caused by the Kondo effect. Astonishingly, the maxima of the oscillations show linear shifts with increasing magnetic field and gate voltage.     

Coulomb oscillations of conductance in an open ring interferometer in a strong magnetic field

Under the conditions corresponding to tunnel-coupled edge current states in an open ring interferometer, oscillations of conductance as a function of gate voltage with two noticeably different periods are observed. The large-period oscillations are attributed to the electron tunneling between the source and drain regions via a closed edge state of the ring, when an integral number of magnetic flux quanta passes through its contour at the Fermi level. The small-period oscillations are explained by the effect of single-electron variations of the ring potential on the transparency of the barriers between the localized and delocalized edge states of the interfer-ometer.     

Conductance oscillations of a spin-orbit stripe with polarized contacts

We investigate the linear conductance of a stripe of spin-orbit interaction in a 2D electron gas; that is, a 2D region of length l\ell along the transport direction and infinite in the transverse one in which a spin-orbit interaction of Rashba type is present. Polarization in the contacts is described by means of Zeeman fields. Our model predicts two types of conductance oscillations: Ramsauer oscillations in the minority spin transmission, when both spins can propagate, and Fano oscillations when only one spin propagates. The latter are due to the spin-orbit coupling with quasibound states of the non propagating spin. In the case of polarized contacts in antiparallel configuration Fano-like oscillations of the conductance are still made possible by the spin orbit coupling, even though no spin component is bound by the contacts. To describe these behaviors we propose a simplified model based on an ansatz wave function. In general, we find that the contribution for vanishing transverse momentum dominates and defines the conductance oscillations. Regarding the oscillations with Rashba coupling intensity, our model confirms the spin transistor behavior, but only for high degrees of polarization. Including a position dependent effective mass yields additional oscillations due to the mass jumps at the interfaces.     

Interference and interactions in mesoscopic rings

We consider a mesoscopic ring connected to external reservoirs by tunnel junctions. The ring is capacitively coupled to an external gate electrode and may be pierced by a magnetic field. Due to strong electron–electron interactions within the ring the conductance shows Coulomb blockade oscillations as a function of the gate voltage, while Aharonov–Bohm interference effects lead to a dependence on the magnetic flux. The Hamiltonian of the ring is given by a Luttinger model that allows for an exact treatment of both interaction and interference effects. We conclude that the positions of conductance maxima as a function the external parameters can be used to determine the interaction parameter , and the shapes of conductance peaks are strongly affected by electron correlations within the ring.