Tomonaga-Luttinger liquid correlations and Fabry-Perot interference in conductance and finite-frequency shot noise in a single-walled carbon nanotube

We present a detailed theoretical investigation of transport through a single-walled carbon nanotube (SWNT) in good contact to metal leads where weak backscattering at the interfaces between SWNT and source and drain reservoirs gives rise to electronic Fabry-Perot (FP) oscillations in conductance and shot noise. We include the electron-electron interaction and the finite length of the SWNT within the inhomogeneous Tomonaga-Luttinger liquid (TLL) model and treat the non-equilibrium effects due to an applied bias voltage within the Keldysh approach. In low-frequency transport properties, the TLL effect is apparent mainly via power-law characteristics as a function of bias voltage or temperature at energy scales above the finite level spacing of the SWNT. The FP-frequency is dominated by the non-interacting spin mode velocity due to two degenerate subbands rather than the interacting charge velocity. At higher frequencies, the excess noise is shown to be capable of resolving the splintering of the transported electrons arising from the mismatch of the TLL-parameter at the interface between metal reservoirs and SWNT. This dynamics leads to a periodic shot noise suppression as a function of frequency and with a period that is determined solely by the charge velocity. At large bias voltages, these oscillations are dominant over the ordinary FP-oscillations caused by two weak backscatterers. This makes shot noise an invaluable tool to distinguish the two mode velocities in the SWNT.Comment: 20 pages, 9 figure

Helical edge states in multiple topological mass domains

The two-dimensional topological insulating phase has been experimentally discovered in HgTe quantum wells (QWs). The low-energy physics of two-dimensional topological insulators (TIs) is described by the Bernevig-Hughes-Zhang (BHZ) model, where the realization of a topological or a normal insulating phase depends on the Dirac mass being negative or positive, respectively. We solve the BHZ model for a mass domain configuration, analyzing the effects on the edge modes of a finite Dirac mass in the normal insulating region (soft-wall boundary condition). We show that at a boundary between a TI and a normal insulator (NI), the Dirac point of the edge states appearing at the interface strongly depends on the ratio between the Dirac masses in the two regions. We also consider the case of multiple boundaries such as NI/TI/NI, TI/NI/TI and NI/TI/NI/TI.Comment: 11 pages, 15 figure

Enhanced quasiparticle dynamics of quantum well states: the giant Rashba system BiTeI and topological insulators

In the giant Rashba semiconductor BiTeI electronic surface scattering with Lorentzian linewidth is observed that shows a strong dependence on surface termination and surface potential shifts. A comparison with the topological insulator Bi2Se3 evidences that surface confined quantum well states are the origin of these processes. We notice an enhanced quasiparticle dynamics of these states with scattering rates that are comparable to polaronic systems in the collision dominated regime. The Eg symmetry of the Lorentzian scattering contribution is different from the chiral (RL) symmetry of the corresponding signal in the topological insulator although both systems have spin-split surface states.Comment: 6 pages, 5 figure

Helical edge states in multiple topological mass domains

The two-dimensional topological insulating phase has been experimentally discovered in HgTe quantum wells (QWs). The low-energy physics of two-dimensional topological insulators (TIs) is described by the Bernevig-Hughes-Zhang (BHZ) model, where the realization of a topological or a normal insulating phase depends on the Dirac mass being negative or positive, respectively. We solve the BHZ model for a mass domain configuration, analyzing the effects on the edge modes of a finite Dirac mass in the normal insulating region (soft-wall boundary condition). We show that at a boundary between a TI and a normal insulator (NI), the Dirac point of the edge states appearing at the interface strongly depends on the ratio between the Dirac masses in the two regions. We also consider the case of multiple boundaries such as NI/TI/NI, TI/NI/TI and NI/TI/NI/TI.Comment: 11 pages, 15 figure

Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons

We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots each of which is tunnel-coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin-singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance which allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.Comment: 11 double-column pages, 2 figures, REVTeX, minor revision

Superconductor coupled to two Luttinger liquids as an entangler for electron spins

We consider an s-wave superconductor (SC) which is tunnel-coupled to two spatially separated Luttinger liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e. it creates spin-singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin density fluctuations produced by the injected spin-entangled electrons.Comment: 15 pages, 2 figure

Decoherence of Einstein-Podolsky-Rosen pairs in a noisy Andreev entangler

We investigate quantum noise effect on the transportation of nonlocal Cooper pairs accross the realistic Andreev entangler which consists of an s-wave superconductor coupled to two small quantum dots at resonance which themselves are coupled to normal leads. The noise emerges due to voltage fluctuations felt by the electrons residing on the two dots as a result of the finite resistances in the gate leads or of any resistive lead capacitively coupled to the dots. In the ideal noiseless case, the setup provides a trustable source of mobile and nonlocal spin-entangled electrons and the transport is dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at the same energy [P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001)]. We seek to revisit the transport of those nonlocal Cooper pairs as well as the efficiency of such an Andreev entangler when including the quantum noise (decoherence).Comment: 15 pages and 6 figures; final version to appear in Physical Review

Fidelity and level correlations in the transition from regularity to chaos

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identical. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur

Two electron entanglement enhancement by an inelastic scattering process

In order to assess inelastic effects on two fermion entanglement production, we address an exactly solvable two-particle scattering problem where the target is an excitable scatterer. Useful entanglement, as measured by the two particle concurrence, is obtained from post-selection of oppositely scattered particle states. The $S$ matrix formalism is generalized in order to address non-unitary evolution in the propagating channels. We find the striking result that inelasticity can actually increase concurrence as compared to the elastic case by increasing the uncertainty of the single particle subspace. Concurrence zeros are controlled by either single particle resonance energies or total reflection conditions that ascertain precisely one of the electron states. Concurrence minima also occur and are controlled by entangled resonance situations were the electron becomes entangled with the scatterer, and thus does not give up full information of its state. In this model, exciting the scatterer can never fully destroy phase coherence due to an intrinsic limit to the probability of inelastic events.Comment: 8 pages, to appear in Phys. Rev

Mesoscopic Tunneling Magnetoresistance

We study spin-dependent transport through ferromagnet/normal-metal/ferromagnet double tunnel junctions in the mesoscopic Coulomb blockade regime. A general transport equation allows us to calculate the conductance in the absence or presence of spin-orbit interaction and for arbitrary orientation of the lead magnetizations. The tunneling magnetoresistance (TMR), defined at the Coulomb blockade conductance peaks, is calculated and its probability distribution presented. We show that mesoscopic fluctuations can lead to the optimal value of the TMR.Comment: 5 pages, 3 eps figures included using epsf.sty. Revised text and improved notation, fig. 2 removed, explicit equations for the GSE case adde