arXiv subjects

Pascal Simon

Publications and source records attributed to Pascal Simon.

At least 91 records · Page 5Linked to original sources

arXiv2013

Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase

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.

cond-mat.mes-hall↗

arXiv2013

Josephson effect in superconducting wires supporting multiple Majorana edge states

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.

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arXiv2012

Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index

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.

cond-mat.mes-hall↗

arXiv2012

Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids

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.

cond-mat.mes-hall↗

arXiv2012

Quantum Noise Measurement of a Carbon Nanotube Quantum Dot in the Kondo Regime

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies $ν$ 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 $h ν\approx k_B T_K$ a Kondo effect related singularity at a voltage bias $eV \approx h ν$, and a strong reduction of this singularity for $h ν\approx 3 k_B T_K$, 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.

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arXiv2011

Spin and Majorana polarization in topological superconducting wires

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.

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arXiv2011

Mixtures of ultra-cold atoms in 1D disordered potentials

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.

cond-mat.quant-gas↗

arXiv2011

Tunable Kondo effect in double quantum dots coupled to ferromagnetic contacts

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.

cond-mat.mes-hall↗

arXiv2011

Quantum impurity coupled to Majorana edge fermions

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.

cond-mat.str-el↗

arXiv2011

A Tunable Two-impurity Kondo system in an atomic point contact

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.

cond-mat.str-el↗

arXiv2011

Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator - Luttinger liquid - Bose glass

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.

cond-mat.str-el↗

arXiv2010

Majorana edge states in interacting one-dimensional systems

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.

cond-mat.str-el↗

arXiv2010

Disordered one-dimensional Bose-Fermi mixtures: The Bose-Fermi glass

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.

cond-mat.quant-gas↗

arXiv2010

Incompressible states of a two-component Fermi gas in a double-well optical lattice

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.

cond-mat.quant-gas↗

arXiv2010

Transport properties of a molecule embedded in an Aharonov-Bohm interferometer

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 ($ε_d$) 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.

cond-mat.mes-hall↗

arXiv2009

Nuclear magnetism and electron order in interacting one-dimensional conductors

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.

cond-mat.mes-hall↗

arXiv2009

Tunable pseudogap Kondo effect and quantum phase transitions in Aharonov-Bohm interferometers

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.

cond-mat.mes-hall↗

arXiv2009

Momentum dependence of the spin susceptibility in two dimensions: nonanalytic corrections in the Cooper channel

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.

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