arXiv subjects

Leonid I. Glazman

Publications and source records attributed to Leonid I. Glazman.

At least 91 records · Page 5Linked to original sources

arXiv2013

Topological superconducting phase in helical Shiba chains

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless p-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase.

cond-mat.mes-hall↗

arXiv2013

Enhanced anti-ferromagnetic exchange between magnetic impurities in a superconducting host

It is generally believed that superconductivity only weakly affects the indirect exchange between magnetic impurities. If the distance r between impurities is smaller than than the superconducting coherence length (r < ξ), this exchange is thought to be dominated by RKKY interactions, identical to the those in a normal metallic host. This perception is based upon a perturbative treatment of the exchange interaction. Here, we provide a non-perturbative analysis and demonstrate that the presence of Yu-Shiba-Rusinov bound states induces a strong 1/r^2 anti-ferromagnetic interaction that can dominate over conventional RKKY even at distances significantly smaller than the coherence length. Experimental signatures, implications and applications are discussed.

cond-mat.mes-hall↗

arXiv2013

Dynamics of Majorana States in a Topological Josephson Junction

Topological Josephson junctions carry 4pi-periodic bound states. A finite bias applied to the junction limits the lifetime of the bound state by dynamically coupling it to the continuum. Another characteristic time scale, the phase adjustment time, is determined by the resistance of the circuit "seen" by the junction. We show that the 4pi periodicity manifests itself by an even-odd effect in Shapiro steps only if the phase adjustment time is shorter than the lifetime of the bound state. The presence of a peak in the current noise spectrum at half the Josephson frequency is a more robust manifestation of the 4pi periodicity, as it persists for an arbitrarily long phase adjustment time. We specify, in terms of the circuit parameters, the conditions necessary for observing the manifestations of 4pi periodicity in the noise spectrum and Shapiro step measurements.

cond-mat.supr-con↗

arXiv2013

Helical edge resistance introduced by charge puddles

We study the influence of electron puddles created by doping of a 2D topological insulator on its helical edge conductance. A single puddle is modeled by a quantum dot tunnel-coupled to the helical edge. It may lead to significant inelastic backscattering within the edge because of the long electron dwelling time in the dot. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on temperature and doping level, and compare it with recent experimental data.

cond-mat.mes-hall↗

arXiv2013

Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array

Quantum fluctuations in an anharmonic superconducting circuit enable frequency conversion of individual incoming photons. This effect, linear in the photon beam intensity, leads to ramifications for the standard input-output circuit theory. We consider an extreme case of anharmonicity in which photons scatter off a small set of weak links within a Josephson junction array. We show that this quantum impurity displays Kondo physics and evaluate the elastic and inelastic photon scattering cross sections. These cross sections reveal many-body properties of the Kondo problem that are hard to access in its traditional fermionic version.

cond-mat.mes-hall↗

arXiv2012

One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined to a 1D trap. We review existing results for various dynamic correlation functions, in particular the density structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and discuss its impact on the transport properties of 1D systems at finite temperatures. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.

cond-mat.str-el↗

arXiv2012

Composite fermion state of spin-orbit coupled bosons

We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in 2D. We argue that at low density its groundstate is a composite fermion state with a Chern-Simons gauge field and filling factor one. The chemical potential of such a state scales with the density as μ\propto n^{3/2}. This is a lower energy per particle than μ\propto n for the earlier suggested groundstate candidates: a condensate with broken time-reversal symmetry and a spin density wave state.

cond-mat.quant-gas↗

arXiv2012

Relaxation and edge reconstruction in integer quantum Hall systems

The interplay between the confinement potential and electron-electron interactions causes reconstructions of Quantum Hall edges. We study the consequences of this edge reconstruction for the relaxation of hot electrons injected into integer quantum Hall edge states. In translationally invariant edges, the relaxation of hot electrons is governed by three-body collisions which are sensitive to the electron dispersion and thus to reconstruction effects. We show that the relaxation rates are significantly altered in different reconstruction scenarios.

cond-mat.mes-hall↗

arXiv2012

Inelastic electron backscattering in a generic helical edge channel

We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward-scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, $δG \propto T^4$. In addition, $δG$ is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2012

Interplay of magneto-elastic and polaronic effects in electronic transport through suspended carbon-nanotube quantum dots

We investigate the electronic transport through a suspended carbon-nanotube quantum dot. In the presence of a magnetic field perpendicular to the nanotube and a nearby metallic gate, two forces act on the electrons: the Laplace and the electrostatic force. They both induce coupling between the electrons and the mechanical transverse oscillation modes. We find that the difference between the two mechanisms appears in the cotunneling current.

cond-mat.mes-hall↗

arXiv2012

Evidence for coherent quantum phase-slips across a Josephson junction array

Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2π$ slips of the phase of the order parameter. However, in a finite-length wire coherent quantum phase-slips would manifest themselves simply as shifts of energy levels in the excitations spectrum of an electrical circuit incorporating this wire. The higher the phase-slips probability amplitude, the larger are the shifts. Phase-slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase-slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slips amplitudes random functions of time, and therefore turn energy levels shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a "slippery" wire. The slip-induced linewidths, despite being only of order 100 kHz, were resolved from the flux-dependent dephasing of the fluxonium qubit.

cond-mat.supr-con↗

arXiv2011

Nonuniversal prefactors in correlation functions of 1D quantum liquids

We develop a general approach to calculating "nonuniversal" prefactors in static and dynamic correlation functions of 1D quantum liquids at zero temperature, by relating them to the finite size scaling of certain matrix elements (form factors). This represents a new, powerful tool for extracting data valid in the thermodynamic limit from finite-size effects. As the main application, we consider weakly interacting spinless fermions with an arbitrary pair interaction potential, for which we perturbatively calculate certain prefactors in static and dynamic correlation functions. We also non-perturbatively evaluate prefactors of the long-distance behavior of correlation functions for the exactly solvable Lieb-Liniger model of 1D bosons.

cond-mat.stat-mech↗

arXiv2011

Energy Partitioning of Tunneling Currents into Luttinger Liquids

Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger liquid parameter $κ$), while the partitioning of charge is fully determined by $κ$. Moreover, unlike for charge currents, the partitioning of energy current should manifest itself in $dc$ experiments on wires contacted by conventional (Fermi-liquid) leads.

cond-mat.mes-hall↗

arXiv2010

Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory

We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take into account the nonlinearity of the fermion dispersion exactly. We calculate the power-law singularities of the spectral function and the charge and spin density structure factors for arbitrary momenta and interaction strengths. The exponents characterizing the singularities are functions of momenta and differ significantly from the predictions of the linear Luttinger liquid theory. We generalize the notion of the spin-charge separation to the nonlinear spectrum. This generalization leads to phenomenological relations between threshold exponents and the threshold energy.

cond-mat.str-el↗

arXiv2010

Relaxation of a high-energy quasiparticle in a one-dimensional Bose gas

We evaluate the relaxation rate of high-energy quasiparticles in a weakly interacting one-dimensional Bose gas. Unlike in higher dimensions, the rate is a nonmonotonic function of temperature, with a maximum at the crossover to the state of suppressed density fluctuations. At the maximum, the relaxation rate may significantly exceed its zero-temperature value. We also find the dependence of the differential inelastic scattering rate on the transferred energy. This rate yields information about temperature dependence of local pair correlations.

cond-mat.quant-gas↗

arXiv2010

Energy relaxation and thermalization of hot electrons in quantum wires

We develop a theory of energy relaxation and thermalization of hot carriers in real quantum wires. Our theory is based on a controlled perturbative approach for large excitation energies and emphasizes the important roles of the electron spin and finite temperature. Unlike in higher dimensions, relaxation in one-dimensional electron liquids requires three-body collisions and is much faster for particles than holes which relax at nonzero temperatures only. Moreover, co-moving carriers thermalize more rapidly than counterpropagating carriers. Our results are quantitatively consistent with a recent experiment.

cond-mat.mes-hall↗

arXiv2010

The fate of 1D spin-charge separation away from Fermi points

We consider the dynamic response functions of interacting one dimensional spin-1/2 fermions at arbitrary momenta. We build a non-perturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.

cond-mat.str-el↗

arXiv2010

Mesoscopic persistent currents in a strong magnetic field

Recent precision measurements of mesoscopic persistent currents in normal-metal rings rely on the interaction between the magnetic moment generated by the current and a large applied magnetic field. Motivated by this technique, we extend the theory of mesoscopic persistent currents to include the effect of the finite thickness of the ring and the resulting penetration of the large magnetic field. We discuss both the sample-specific typical current and the ensemble-averaged current which is dominated by the effects of electron-electron interactions. We find that the magnetic field strongly suppresses the interaction-induced persistent current and so provides direct access to the independent-electron contribution. Moreover, the technique allows for measurements of the entire distribution function of the persistent current. We also discuss the consequences of the Zeeman splitting and spin-orbit scattering, and include a detailed and quantitative comparison of our theoretical results to experimental data.

cond-mat.mes-hall↗