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We present a self-consistent analysis of the topological superconductivity arising from the interaction between self-ordered localized magnetic moments and electrons in one-dimensional conductors in contact with a superconductor. We show that due to a gain in entropy there exists a magnetically ordered yet non-topological phase at finite temperatures that is relevant for systems of magnetic adatom chains on a superconductor. Spin-orbit interaction is taken into account, and we show that it causes a modification of the magnetic order yet without affecting the topological properties., Comment: 5 pages, 4 figures, final version

We consider a superconducting microwave cavity capacitively coupled to both a quantum conductor and its electronic reservoirs. We analyze in details how the measurements of the cavity microwave field, which are related to the electronic charge susceptibility, can be used to extract information on the transport properties of the quantum conductor. We show that the asymmetry of the capacitive couplings between the electronic reservoirs and the cavity plays a crucial role in relating optical measurements to transport properties. For asymmetric capacitive couplings, photonic measurements can be used to probe the finite low frequency admittance of the quantum conductor, the real part of which being related to the differential conductance. In particular, when the quantum dot is far from resonance, the charge susceptibility is directly proportional to the admittance for a large range of frequencies and voltages. However, when the quantum conductor is near a resonance, such a relation generally holds only at low frequency and for equal tunnel coupling or low voltage. Beyond this low-energy near equilibrium regime, the charge susceptibility and thus the optical transmission offers new insights on the quantum conductors since the optical observables are not directly connected to transport quantities. For symmetric lead capacitive couplings, we show that the optical measurements can be used to reveal the Korringa-Shiba relation, connecting the reactive to the dissipative part of the susceptibility, at low frequency and low bias., Comment: 16 pages, 6 figures, published version

One of the main goals of spintronics is to improve transport of information carriers and to achieve new functionalities with ultra-low dissipation. A most promising strategy for this holy grail is to use pure magnon currents created and transported in insulating magnets, in the complete absence of any conducting metallic elements. Here we propose a realistic solution to this fundamental challenge by analyzing magnon and heat transport in insulating ferromagnetic junctions. We calculate all transport coefficients for magnon transport and establish Onsager relations between them. We theoretically discover that magnon transport in junctions has a universal behavior, i.e. is independent of material parameters, and establish a magnon analog of the celebrated Wiedemann-Franz law which governs charge transport at low temperatures. We calculate the Seebeck and Peltier coefficients which are crucial quantities for spin caloritronics and demonstrate that they assume universal values in the low temperature limit. Finally, we show that our predictions are within experimental reach with current device and measurement technologies., Comment: 10 pages, 3 figures, updated into published version from PRB

The quantum coherent coupling of completely different degrees of freedom is a challenging path towards creating new functionalities for quantum electronics. Usually the antagonistic coupling between spins of magnetic impurities and superconductivity leads to the destruction of the superconducting order. Here we show that a localized classical spin of an iron atom immersed in a superconducting condensate can give rise to new kind of long range coherent magnetic quantum state. In addition to the well-known Shiba bound state present on top of an impurity we reveal the existence of a star shaped pattern which extends as far as 12 nm from the impurity location. This large spatial dispersion turns out to be related, in a non-trivial way, to the superconducting coherence length. Inside star branches we observed short scale interference fringes with a particle-hole asymmetry. Our theoretical approach captures these features and relates them to the electronic band structure and the Fermi wave length of the superconductor. The discovery of a directional long range effect implies that distant magnetic atoms could coherently interact leading to new topological superconducting phases with fascinating properties.

We study a voltage biased Josephson junction coupled to two resonators of incommensurate frequencies. Using a density approach to analyze the cavity fields and an input-output description to analyze the emitted photonic fluxes and their correlation functions, we have shown, both for infinite and finite bandwidth detectors, that the emitted radiation is non-classical in the sense that the correlators violates Cauchy-Schwarz inequalities. We have also studied the time dependence of the photonic correlations and showed that their line-width becomes narrower with the increase of the emission rate approaching from below the threshold limit., Comment: 9 pages, 5 figures

We study transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer $\nu=1$ or fractional $\nu=1/3$ quantum Hall bar. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the inter antidot tunnelling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the $\nu=1/3$ fractional Hall state, producing an effective inter-edge tunnelling. We relate the inter-edge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both $\nu=1$ and $\nu=1/3$.

We present a microscopic theory of magnon transport in ferromagnetic insulators (FIs). Using magnon injection through microwave pumping, we propose a way to generate magnon dc currents and show how to enhance their amplitudes in hybrid ferromagnetic insulating junctions. To this end focusing on a single FI, we first revisit microwave pumping at finite (room) temperature from the microscopic viewpoint of magnon injection. Next, we apply it to two kinds of hybrid ferromagnetic insulating junctions. The first is the junction between a quasi-equilibrium magnon condensate and magnons being pumped by microwave, while the second is the junction between such pumped magnons and noncondensed magnons. We show that quasi-equilibrium magnon condensates generate ac and dc magnon currents, while noncondensed magnons produce essentially a dc magnon current. The ferromagnetic resonance (FMR) drastically increases the density of the pumped magnons and enhances such magnon currents. Lastly, using microwave pumping in a single FI, we discuss the possibility that a magnon current through an Aharonov-Casher phase flows persistently even at finite temperature. We show that such a magnon current arises even at finite temperature in the presence of magnon-magnon interactions. Due to FMR, its amplitude becomes much larger than the condensed magnon current., Comment: 12 pages, 5 figures, accepted for publication in Phys. Rev. B

We study one-dimensional $p$-wave superconductors capacitively coupled to a microwave stripline cavity. By probing the light exiting from the cavity, one can reveal the electronic susceptibility of the $p$-wave superconductor. We analyze two superconducting systems: the prototypical Kitaev chain, and a topological semiconducting wire. For both systems, we show that the photonic measurements, via the electronic susceptibility, allows us to determine the topological phase transition point, the emergence of the Majorana fermions, and the parity of their ground state. We show that all these effects, which are absent in effective theories that take into account the coupling of light to Majorana fermions only, are due to the interplay between the Majorana fermions and the bulk states of the superconductors., Comment: 17 pages, 7 figures; New sections added, including the description of a realistic topological semiconductor wire

We study the renormalization of the gap of an s-wave superconductor in the presence of two magnetic impurities. For weakly bound Shiba states, we analytically calculate the part of the gap renormalization that is sensitive to the relative orientation of the two impurity spins. For impurities with a strong exchange coupling to the conduction electrons, we solve the gap equation self-consistently by numerics and find that the sub-gap Shiba state turns into a supra-gap Andreev state when the local gap parameter changes sign under the impurities., Comment: 6 pages, 4 figures - final version

Among the most exciting recent advances in the field of superconducting quantum circuits is the ability to coherently couple microwave photons in low-loss cavities to quantum electronic conductors (e.g.~semiconductor quantum dots or carbon nanotubes). These hybrid quantum systems hold great promise for quantum information processing applications; even more strikingly, they enable exploration of completely new physical regimes. Here we study theoretically the new physics emerging when a quantum electronic conductor is exposed to non-classical microwaves (e.g.~squeezed states, Fock states). We study this interplay in the experimentally-relevant situation where a superconducting microwave cavity is coupled to a conductor in the tunneling regime. We find the quantum conductor acts as a non-trivial probe of the microwave state; in particular, the emission and absorption of photons by the conductor is characterized by a non-positive definite quasi-probability distribution. This negativity has a direct influence on the conductance of the conductor., Comment: 8 pages, 5 figures; Supplementary Information: 12 pages 8 figures

Using the Aharonov-Casher (A-C) phase, we present a microscopic theory of the Josephson and persistent spin currents in quasi-equilibrium Bose-Einstein condensates (BECs) of magnons in ferromagnetic insulators. Starting from a microscopic spin model that we map onto a Gross-Pitaevskii Hamiltonian, we derive a two-state model for the Josephson junction between the weakly coupled magnon-BECs. We then show how to obtain the alternating-current (ac) Josephson effect with magnons as well as macroscopic quantum self-trapping in a magnon-BEC. We next propose how to control the direct-current (dc) Josephson effect electrically using the A-C phase, which is the geometric phase acquired by magnons moving in an electric field. Finally, we introduce a magnon-BEC ring and show that persistent magnon-BEC currents flow due to the A-C phase. Focusing on the feature that the persistent magnon-BEC current is a steady flow of magnetic dipoles that produces an electric field, we propose a method to directly measure it experimentally., Comment: 8 pages, 6 figures, updated into published version

We study the magnetization dynamics in ferromagnet$\mid$insulator$\mid$ferromagnet and ferromagnet$\mid$insulator$\mid$normal metal ultra-small tunnel junctions, and the associated voltage drop in the presence of an electromagnetic environment assisting the tunneling processes. We show that the environment strongly affects the resulting voltage, which becomes a highly non-linear function of the precession cone angle $\theta$. We find that voltages comparable to the driving frequency $\omega$ can be reached even for small precession cone angles $\theta$, in stark contrast to the case where the environment is absent. Such an effect could be useful for the detection local magnetization precessions in textured ferromagnets or, conversely, for probing the environment via the magnetization dynamics., Comment: 7 pages, 9 figures

We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong coupling regime. This method allows for a non-perturbative treatment in the disorder strength, electron- electron interactions and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase, and a glassy, non-topological localized phase, characterized by replica symmetry breaking., Comment: 9 pages, 2 figures

We propose a setup that is the spin analog of the charge-based quantum RC circuit. We define and compute the spin capacitance and the spin resistance of the circuit for both ferromagnetic (FM) and antiferromagnetic (AF) systems. We find that the antiferromagnetic setup has universal properties, but the ferromagnetic setup does not. We discuss how to use the proposed setup as a quantum source of spin excitations, and put forward a possible experimental realization using ultracold atoms in optical lattices.

We present a detailed study for the finite-frequency current noise of a Kondo quantum dot in presence of a magnetic field by using a recently developed real time functional renormalization group approach [Phys. Rev. B $\mathbf{83}$, 201303(R) (2011)]. The scaling equations are modified in an external magnetic field; the couplings and non-local current vertices become strongly anisotropic, and develop new singularities. Consequently, in addition to the natural emission threshold frequency, $\hbar\omega = |eV|$, a corresponding singular behavior is found to emerge in the noise spectrum at frequencies $\hbar \omega \approx |eV\pm B|$. The predicted singularities are measurable with present-day experimental techniques., Comment: 17 pages, 18 figures

We present a theoretical study based on the Anderson model of the transport properties of a Kondo impurity (atom or quantum dot) connected to ferromagnetic leads, which can sustain a non-equilibrium spin current. We analyze the case where the spin current is injected by an external source and when it is generated by the voltage bias. Due to the presence of ferromagnetic contacts, a static exchange field is produced that eventually destroys the Kondo correlations. We find that such a field can be compensated by an appropriated combination of the spin-dependent chemical potentials leading to the restoration of the Kondo resonance. In this respect, a Kondo impurity may be regarded as a very sensitive sensor for non-equilibrium spin phenomena., Comment: 10 pages, 5 figures, final version

We study a one-dimensional (1D) interacting electronic liquid coupled to a 1D array of classical magnetic moments and to a superconductor. We show that at low energy and temperature the magnetic moments and the electrons become strongly entangled and that a magnetic spiral structure emerges without any adjustable parameters. For strong enough coupling between the two, the 1D electronic liquid is driven into a topological superconducting phase supporting Majorana fermions without any fine-tuning of external parameters. Our analysis applies at low enough temperature to a quantum wire in proximity of a superconductor when the hyperfine interaction between electrons and nuclear spins is taken into account or to a chain of magnetic adatoms adsorbed on a superconducting surface., Comment: 7 pages, 2 figures, final version

We use a low-temperature scanning tunneling microscope to study the interplay between the Kondo effect of a single-atom contact and a spin current. To this end, a nickel tip is coated by a thick layer of copper and brought into contact with a single Co atom adsorbed on a Cu(100) surface. We show that upon contact the Kondo resonance of Co is spin split and attribute the splitting to the spin current produced by the nickel tip and flowing across the copper spacer. A quantitative line shape analysis indicates that the spin polarization of the junction amounts up to 18%, but decreases when a pristine nickel tip is directly contacted to the Co atom., Comment: This work is superseded by arXiv:1609.02363

We study superconducting-normal-superconducting (SNS) Josephson junctions in one-dimensional topological superconductors which support more than one Majorana end mode. The variation of the energy spectrum with the superconducting phase is investigated by combining numerical diagonalizations of tight-binding models describing the SNS junction together with an analysis of appropriate low-energy effective Hamiltonians. We show that the four pi-periodicity characteristic of the fractional dc Josephson effect is preserved. Additionally, the ideal conductance of a NS junction with a topological supraconductor, hosting two Majorana modes at its ends, is doubled compared to the single Majorana case. Last, we illustrate how a nonzero superconducting phase gradient can potentially destroy the phases supporting multiple Majorana end states., Comment: 9 pages, 11 figures

Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index. This tool allows in principle to conceive 2-bands Hamiltonians with arbitrary Chern numbers. We apply our methodology to gradually construct a quantum anomalous Hall insulator (Chern insulator) which can be tuned through five topological phases indexed by the Chern numbers {0,+/-1,+/-2}. On a cylindrical finite geometry, such insulator can therefore sustain up to two edge states which we characterize analytically. From this non-trivial Chern insulator and its time reversed copy, we build a quantum spin Hall insulator and show how the phases with a +/-2 Chern index yield trivial Z2 insulating phases., Comment: 10 pages, 9 figures

We study interacting 1D two-component mixtures of cold atoms in a random potential, and extend the results reported earlier [{\it Phys. Rev. Lett.} {\bf 105}, 115301 (2010)]. We construct the phase diagram of a disordered Bose-Fermi mixture as a function of the strength of the Bose-Bose and Bose-Fermi interactions, and the ratio of the bosonic sound velocity and the Fermi velocity. Performing renormalization group and variational calculations, three phases are identified: (i) a fully delocalized two-component Luttinger liquid with superfluid bosons and fermions (ii) a fully localized phase with both components pinned by disorder, and (iii) an intermediate phase where fermions are localized but bosons are superfluid. Within the variational approach, each phase corresponds to a different level of replica symmetry breaking. In the fully localized phase we find that the bosonic and fermionic localization lengths can largely differ. We also compute the momentum distribution as well as the structure factor of the atoms (both experimentally accessible), and discuss how the three phases can be experimentally distinguished., Comment: 30 pages, 17 figures. Submitted to PRA

We investigate the effects induced by spin polarization in the contacts attached to a serial double quantum dot. The polarization generates effective magnetic fields and suppresses the Kondo effect in each dot. The super-exchange interaction ($J_{\mathrm{AFM}}$), tuned by the inter-dot tunnelling rate $t$, can be used to compensate the effective fields and restore the Kondo resonance when the contact polarizations are aligned. As a consequence, the direction of the spin conductance can be controlled and even reversed using electrostatic gates alone. Furthermore, we study the associated two-impurity Kondo model and show that a ferromagnetic exchange coupling ($J_{\mathrm{FM}}$) leads to an effective spin-1 exchange-anisotropic Kondo model which exhibits a quantum phase transition in the presence of partially polarized contacts., Comment: 5 pages, 4 figures

We provide analytic expressions for the Green's functions in position-frequency space as well as for the tunneling density of states of various Luttinger liquids at zero temperature: the standard spinless and spinful Luttinger liquids, the helical Luttinger liquid at the edge of a topological insulator, and the Luttinger liquid that appears either together with an ordering transition of nuclear spins in a one-dimensional conductor, or in spin-orbit split quantum wires in an external magnetic field. The latter system is often used to mimic a helical Luttinger liquid, yet we show here that it exhibits significantly different response functions and, to discriminate, we call it the spiral Luttinger liquid. We give fully analytic results for the tunneling density of state of all the Luttinger liquids as well as for most of the Green's functions. The remaining Green's functions are expressed by simple convolution integrals between analytic results., Comment: 17 pages, 4 figures; corresponding to published version

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies $\nu$ of the order or higher than the frequency associated with the Kondo effect $k_B T_K/h$, with $T_K$ the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for $h \nu \approx k_B T_K$ a Kondo effect related singularity at a voltage bias $eV \approx h \nu $, and a strong reduction of this singularity for $h \nu \approx 3 k_B T_K$, in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the non-equilibrium dynamics of many-body phenomena in nanoscale devices., Comment: 6 pages, 4 figures

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local "Majorana polarization" is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement., Comment: 6 pages, 5 figures, RevTeX4; added analytical results section and supplementary material; new references added

We study a quantum impurity coupled to the edge states of a two-dimensional helical topological superconductor, i.e., to a pair of counterpropagating Majorana fermion edge channels with opposite spin polarizations. For an impurity described by the Anderson impurity model, we show that the problem maps onto a variant of the interacting resonant two-level model which, in turn, maps onto the ferromagnetic Kondo model. Both magnetic and non-magnetic impurities are considered. For magnetic impurities, the bosonization and numerical renormalization group analyses show that the system flows to a fixed point with residual ln 2 entropy and we find characteristically anisotropic static and dynamic impurity magnetic susceptibilities. For non-magnetic impurities, the system flows to a fixed point with no residual entropy and we find diamagnetic response at low temperatures. We comment on the Schrieffer-Wolff transformation for problems with non-standard conduction band continua and on the issues related to the differences in describing the impurities by either Anderson or Kondo impurity models., Comment: 13 pages, 10 figures

Two magnetic atoms, one attached to the tip of a Scanning Tunneling Microscope (STM) and one adsorbed on a metal surface, each constituting a Kondo system, have been proposed as one of the simplest conceivable systems potentially exhibiting quantum critical behaviour. We have succeeded in implementing this concept experimentally for cobalt dimers clamped between an STM tip and a gold surface. Control of the tip-sample distance with sub-picometer resolution allows us to tune the interaction between the two cobalt atoms with unprecedented precision. Electronic transport measurements on this two-impurity Kondo system reveal a rich physical scenario which is governed by a crossover from local Kondo screening to non-local singlet formation due to antiferromagnetic coupling as a function of separation of the cobalt atoms., Comment: 22 pages, 5 figures

One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depends on the so-called Jordan-Wigner string, real-space observables are similar for free-fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed, and leads to a totally different physics between free-fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but non-trivial model of hard-core bosons hopping in a two-leg ladder geometry. At half-filling, while a band insulator appears for fermions at large interchain hopping tperp >2t only, a Mott gap opens up for bosons as soon as tperp\neq0 through a Kosterlitz-Thouless transition. Away from half-filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a non-trivial filling-dependent Luttinger parameter 1/2\leq Ks \leq 1. Consequences for experiments in cold atoms, spin ladders in a magnetic field, as well as disorder effects are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a 1D superfluid and an insulating Bose glass phase., Comment: 24 pages, 23 figures

We show that one-dimensional electron systems in proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime, in which the Majorana edge states persist. We present strategies how this regime can be reached., Comment: 4.2 page, 1 figure

We propose a scheme to investigate the effect of frustration on the magnetic phase transitions of cold atoms confined in an optical lattice. We also demonstrate how to get two-leg spin ladders with frustrated spin-exchange coupling which display a phase transition from a spin liquid to a fully incompressible state. Various experimental quantities are further analyzed for describing this phase., Comment: 10 pages, 7 figures. Published in Phys. Rev. A

We analyze an interacting Bose-Fermi mixture in a 1D disordered potential using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and inter-species interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics., Comment: 4 pages, 2 figures

We theoretically investigate the transport properties of a molecule embedded in one arm of a mesoscopic Aharonov-Bohm interferometer. Due to the presence of phonons the molecule level position ($\epsilon_d$) and the electron-electron interaction ($U$) undergo a \emph{polaronic shift} which affects dramatically the electronic transport through the molecular junction. When the electron-phonon interaction is weak the linear conductance presents Fano-line shapes as long as the direct channel between the electrodes is opened. The observed Fano resonances in the linear conductance are originated from the interference between the spin Kondo state and the direct path. For strong enough electron-phonon interaction, the electron-electron interaction is renormalized towards negative values, {\it i.e.} becomes effectively attractive. This scenario favors fluctuations between the empty and doubly occupied charge states and therefore promotes a charge Kondo effect. However, the direct path between the contacts breaks the electron-hole symmetry which can efficiently suppress this charge Kondo effect. Nevertheless, we show that a proper tuning of the gate voltage is able to revive the Kondo resonance. Our results are obtained by using the Numerical Renormalization approximation to compute the electronic spectral function and the linear conductance., Comment: 17 pages, 12 figures

The interaction between localized magnetic moments and the electrons of a one-dimensional conductor can lead to an ordered phase in which the magnetic moments and the electrons are tightly bound to each other. We show here that this occurs when a lattice of nuclear spins is embedded in a Luttinger liquid. Experimentally available examples of such a system are single wall carbon nanotubes grown entirely from 13C and GaAs-based quantum wires. In these systems the hyperfine interaction between the nuclear spin and the conduction electron spin is very weak, yet it triggers a strong feedback reaction that results in an ordered phase consisting of a nuclear helimagnet that is inseparably bound to an electronic density wave combining charge and spin degrees of freedom. This effect can be interpreted as a strong renormalization of the nuclear Overhauser field and is a unique signature of Luttinger liquid physics. Through the feedback the order persists up into the millikelvin range. A particular signature is the reduction of the electric conductance by the universal factor 2., Comment: 30 pages, 10 figures; Sec. II contains a 2+ pages summary giving a complete overview to the main conditions and results; v3: updated references, typos corrected

We investigate theoretically spin relaxation in heavy hole quantum dots in low external magnetic fields. We demonstrate that two-phonon processes and spin-orbit interaction are experimentally relevant and provide an explanation for the recently observed saturation of the spin relaxation rate in heavy hole quantum dots with vanishing magnetic fields. We propose further experiments to identify the relevant spin relaxation mechanisms in low magnetic fields., Comment: 5 pages, 2 figures

We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states (ABS) in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic (or molecular) levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to recent Numerical Renormalization Group calculations. This simple formulation may have bearings for interpreting Andreev spectroscopic experiments in superconducting devices, such as STM measurements on carbon nanotubes, or radiative emission in optical quantum dots., Comment: 12 pages, 11 figures. Last version: we added several extra references, modified two figures, and discussed recent proposals for Andreev spectroscopy

We study two quantum dots embedded in the arms of an Aharonov-Bohm ring threaded by a magnetic flux. The system can be described by an effective one-impurity Anderson model with an energy- and flux-dependent density of states. For specific values of the flux, this density of states vanishes at the Fermi energy, yielding a controlled realization of the pseudogap Kondo effect. The conductance and transmission phase shifts reflect a nontrivial interplay between wave interference and interactions, providing clear signatures of quantum phase transitions between Kondo and non-Kondo ground states., Comment: Published version

We consider the effect of rescattering of pairs of quasiparticles in the Cooper channel resulting in the strong renormalization of second-order corrections to the spin susceptibility in a two-dimensional electron system. We use the Fourier expansion of the scattering potential in the vicinity of the Fermi surface to find that each harmonic becomes renormalized independently. Since some of those harmonics are negative, the first derivative of the spin susceptibility is bound to be negative at small momenta, in contrast to the lowest order perturbation theory result, which predicts a positive slope. We present in detail an effective method to calculate diagrammatically corrections to the spin susceptibility to infinite order.

The hyperfine interaction between the electron spin and the nuclear spins is one of the main sources of decoherence for spin qubits when the nuclear spins are disordered. An ordering of the latter largely suppresses this source of decoherence. Here we show that such an ordering can occur through a thermodynamic phase transition in two-dimensional (2D) Kondo-lattice type systems. We specifically focus on nuclear spins embedded in a 2D electron gas. The nuclear spins interact with each other through the RKKY interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behavior of the 2D static electron spin susceptibility due to electron-electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron-electron interactions and may reach up into the millikelvin regime. The further reduction of dimensionality to one dimension is shortly discussed., Comment: Proceedings for 2nd International Workshop on Solid-State Quantum Computing (Taipei, Taiwan, June 2008); 6 pages, 2 figures

Despite the experimental successes of Scanning Tunneling Microscopy (STM) and the interest in more complex magnetic nanostructures, our present understanding and theoretical description of STM spectra of magnetic adatoms is mainly phenomenological and most often ignores many-body effects. Here, we propose a theory which includes a microscopic description of the wave functions of the substrate and magnetic adatoms together with quantum many-body effects. To test our theory, we have computed the STM spectra of magnetic Cobalt monomers and dimers adsorbed on metallic Copper surfaces and succesfully compared our results to recent available experimental data., Comment: 4 pages, 2 figures, discussion of calculation of RKKY interaction and connection to NRG included. Extended discussion on calculations of the one-electron parameters of Anderson model. Typos corrected

Single wall carbon nanotubes grown entirely from 13-C form an ideal system to study the effect of electron interaction on nuclear magnetism in one dimension. If the electrons are in the metallic, Luttinger liquid regime, we show that even a very weak hyperfine coupling to the 13-C nuclear spins has a striking effect: The system is driven into an ordered phase, which combines electron and nuclear degrees of freedom, and which persists up into the millikelvin range. In this phase the conductance is reduced by a universal factor of 2, allowing for detection by standard transport experiments., Comment: 7 pages, 3 figures; final version

We investigate the ac transport of magnetization in non-itinerant quantum systems such as spin chains described by the XXZ Hamiltonian. Using linear response theory, we calculate the ac magnetization current and the power absorption of such magnetic systems. Remarkably, the difference in the exchange interaction of the spin chain itself and the bulk magnets (i.e. the magnetization reservoirs), to which the spin chain is coupled, strongly influences the absorbed power of the system. This feature can be used in future spintronic devices to control power dissipation. Our analysis allows to make quantitative predictions about the power absorption and we show that magnetic systems are superior to their electronic counter parts., Comment: 4+ pages, 2 figures

We investigate the magnetic behavior of nuclear spins embedded in a 2D interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins which is of the RKKY type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility, and thus provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. Using various perturbative and non-perturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as function of its wave vector, we show that the nuclear spins locally order ferromagnetically, and that this ordering can become global in certain regimes of interest. We demonstrate that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range., Comment: 18 pages, 2 figures, final version

Strong correlation effects in a capacitively coupled double quantum-dot setup were previously shown to provide the possibility of both entangling spin-charge degrees of freedom and realizing efficient spin-filtering operations by static gate-voltage manipulations. Motivated by the use of such a device for quantum computing, we study the influence of electromagnetic noise on a general spin-orbital Kondo model, and investigate the conditions for observing coherent, unitary transport, crucial to warrant efficient spin manipulations. We find a rich phase diagram, where low-energy properties sensitively depend on the impedance of the external environment and geometric parameters of the system. Relevant energy scales related to the Kondo temperature are also computed in a renormalization-group treatment, allowing to assess the robustness of the device against environmental effects., Comment: 13 pages, 13 figures. Minor modifications in V2

We consider a simple setup in which a small quantum dot is strongly connected to a finite size box. This box can be either a metallic box or a finite size quantum wire.The formation of the Kondo screening cloud in the box strongly depends on the ratio between the Kondo temperature and the box level spacing. By weakly connecting two metallic reservoirs to the quantum dot, a detailed spectroscopic analysis can be performed. Since the transport channels and the screening channels are almost decoupled, such a setup allows an easier access to the measure of finite-size effects associated with the finite extension of the Kondo cloud., Comment: contribution to Les Houches proceeding, ``Quantum magnetism'' 2006

We investigate the influence of an electromagnetic environment, characterized by a finite impedance $Z(\omega)$, on the Kondo effect in quantum dots. The circuit voltage fluctuations couple to charge fluctuations in the dot and influence the spin exchange processes transferring charge between the electrodes. We discuss how the low-energy properties of a Kondo quantum dot subject to dynamical Coulomb blockade resemble those of Kondo impurities in Luttinger liquids. Using previous knowledge based on the bosonization of quantum impurity models, we show that low-voltage conductance anomalies appear at zero temperature. The conductance can vanish at low temperatures even in presence of a screened impurity spin. Moreover, the quantitative determination of the corresponding Kondo temperature depends on the full frequency-dependent impedance of the circuit. This is demonstrated by a weak-coupling calculation in the Kondo interaction, taking into account the full distribution $P(E)$ of excited environmental modes., Comment: 10 pages, 4 figures, revised version, new title

Electrons in a two-dimensional semiconducting heterostructure interact with nuclear spins via the hyperfine interaction. Using a a Kondo lattice formulation of the electron-nuclear spin interaction, we show that the nuclear spin system within an interacting two-dimensional electron gas undergoes a ferromagnetic phase transition at finite temperatures. We find that electron-electron interactions and non-Fermi liquid behavior substantially enhance the nuclear spin Curie temperature into the $mK$ range with decreasing electron density., Comment: 4.1 pages

We discuss the realization of the quantum-critical non-Fermi liquid state, originally discovered within the two-impurity Kondo model, in double quantum-dot systems. Contrary to the common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries, and is only unstable to charge transfer between the two dots. We propose an experimental set-up where such charge transfer processes are suppressed, allowing a controlled approach to the quantum critical state. We also discuss transport and scaling properties in the vicinity of the critical point., Comment: 4 pages, 3 figs; (v2) final version as published

We study the problem of underscreened Kondo physics in an interacting electronic system modeled by a Luttiger Liquid (LL). We find that the leading temperature dependence of thermodynamical quantities like the specific heat, spin susceptibility are Fermi Liquid like in nature. However, anomalous power law exponents are seen in the subleading terms. We also discuss possible realizations through single and double quantum dot configurations coupled to LL leads and its consequences for electronic transport. The leading low temperature transport behavior is seen to exhibit in general, non Fermi liquid LL behavior unlike the thermodynamical quantities., Comment: 8 pages, 1 figure, final version