arXiv subjects

Rok Zitko

Publications and source records attributed to Rok Zitko.

At least 37 records · Page 2Linked to original sources

arXiv2015

Numerical sub-gap spectroscopy of double quantum dots coupled to superconductors

Double quantum dot nanostructures embedded between two superconducting leads or in a superconducting ring have complex excitation spectra inside the gap which reveal the competition between different many-body phenomena. We study the corresponding two-impurity Anderson model using the non-perturbative numerical renormalization group (NRG) technique and identify the characteristic features in the spectral function in various parameter regimes. At half-filling, the system always has a singlet ground state. For large hybridization, we observe an inversion of excited inter-dot triplet and singlet states due to the level-repulsion between two sub-gap singlet states. The Shiba doublet states split in two cases: a) at non-zero superconducting phase difference and b) away from half-filling. The most complex structure of sub-gap states is found when one or both dots are in the valence fluctuation regime. Doublet splitting can lead to a parity-changing quantum phase transition to a doublet ground state in some circumstances. In such cases, we observe very different spectral weights for the transitions to singlet or triplet excited Shiba states: the triplet state is best visible on the valence-fluctuating dot, while the singlets are more pronounced on the half-filled dot.

cond-mat.str-el↗

arXiv2015

Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

We determine the phase diagram of an Anderson impurity in contact with superconducting and normal-state leads for arbitrary ratio of the gap $Δ$ to the Kondo temperature $T_K$. We observe a considerable effect of even very weak coupling to the normal lead that is usually considered as a non-perturbing tunneling probe. The numerical renormalization group results are analyzed in the context of relevant experimental scenarios such as parity crossing (doublet-singlet) quantum phase transitions induced by a gap reduction as well as novel Kondo features induced by the normal lead. We point out the important role of finite temperatures and magnetic fields. Overall, we find a very rich behavior of spectral functions with zero-bias anomalies which can emerge irrespective of whether the ground state is a doublet or a singlet. Our findings are pertinent to the tunnelling-spectroscopy experiments aiming at detecting Majorana modes in nanowires.

cond-mat.mes-hall↗

arXiv2014

Fine structure of spectra in the antiferromagnetic phase of the Kondo lattice model

We study the antiferromagnetic phase of the Kondo lattice model on bipartite lattices at half-filling using the dynamical mean-field theory with numerical renormalization group as the impurity solver, focusing on the detailed structure of the spectral function, self-energy, and optical conductivity. We discuss the deviations from the simple hybridization picture, which adequately describes the overall band structure of the system (four quasiparticle branches in the reduced Brillouin zone), but neglects all effects of the inelastic-scattering processes. These lead to additional structure inside the bands, in particular asymmetric resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic Kondo insulator quantum phase transition. These features, which we name "spin resonances", appear generically in all models where the $f$-orbital electrons are itinerant (large Fermi surface) and there is Néel antiferromagnetic order (staggered magnetization), such as periodic Anderson model and Kondo lattice model with antiferromagneitc Kondo coupling, but are absent in antiferromagnetic phases with localized $f$-orbital electrons (small Fermi surface), such as the Kondo lattice model with ferromagnetic Kondo coupling. We show that with increasing temperature and external magnetic-field the spin resonances become suppressed at the same time as the staggered magnetization is reduced. Optical conductivity $σ(Ω)$ has a threshold associated with the indirect gap, followed by a plateau of low conductivity and the main peak associated with the direct gap, while the spin resonances are reflected as a secondary peak or a hump close to the main optical peak. This work demonstrates the utility of high-spectral-resolution impurity solvers to study the dynamical properties of strongly correlated fermion systems.

cond-mat.str-el↗

arXiv2013

Spin thermopower in the overscreened Kondo model

We study the spin thermopower in the two-channel spin-1/2 Kondo model which exhibits the phenomenon of impurity spin overscreening and non-Fermi-liquid properties. While magnetic field lower than the Kondo temperature does not strongly polarize the impurity spin, we show that it nevertheless strongly affects the low-energy part of the spectral function. In turn, this leads to characteristic saturation of the spin Seebeck coefficient at the value of 0.388kB/|e| at T ~ T*, where T* ~ B^2/TK is the scale of the crossover between the intermediate-temperature non-Fermi-liquid regime and the low-temperature Fermi-liquid regime. We show that measuring the spin thermopower at low magnetic fields would provide a sensitive test for distinguishing regular Fermi liquid, singular Fermi liguid, and non-Fermi liquid behaviour in nanodevices.

cond-mat.str-el↗

arXiv2013

Lifshitz phase transitions in the ferromagnetic regime of the Kondo lattice model

We establish the low-temperature phase diagrams of the spin-1/2 and spin-1 Kondo lattice models as a function of the conduction-band filling n and the exchange coupling strength J in the regime of ferromagnetic effective exchange interactions (n ~< 0.5). We show that both models have several distinct ferromagnetic phases separated by continuous Lifshitz transitions of the Fermi-pocket vanishing or emergence type: one of the phases has a true gap in the minority band (half metal), the others only a pseudogap. They can be experimentally distinguished by their magnetization curves; only the gapped phase exhibits magnetization rigidity. We find that, quite generically, ferromagnetism and Kondo screening coexist rather than compete, both in spin-1/2 and spin-1 models. We compute the Curie temperatures and establish a "ferromagnetic Doniach diagram" for both models.

cond-mat.str-el↗

arXiv2013

Unconventional Superconductivity from Local Spin Fluctuations in the Kondo Lattice

The explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to non-local fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust s-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation of heavy quasiparticle bands and the presence of strong local spin fluctuations.

cond-mat.str-el↗

arXiv2013

How bad metals turn good: spectroscopic signatures of resilient quasiparticles

We investigate transport in strongly correlated metals. Within dynamical mean-field theory, we calculate the resistivity, thermopower, optical conductivity and thermodynamic properties of a hole-doped Mott insulator. Two well-separated temperature scales are identified: T_FL below which Landau Fermi liquid behavior applies, and T_MIR above which the resistivity exceeds the Mott-Ioffe-Regel value and `bad-metal' behavior is found. We show that quasiparticle excitations remain well-defined above T_FL and dominate transport throughout the intermediate regime T_FL < T_MIR. The lifetime of these `resilient quasiparticles' is longer for electron-like excitations, and this pronounced particle-hole asymmetry has important consequences for the thermopower. The crossover into the bad-metal regime corresponds to the disappearance of these excitations, and has clear signatures in optical spectroscopy.

cond-mat.str-el↗

arXiv2012

SU(3) Kondo effect in spinless triple quantum dots

We discuss a device --- a purely capacitively coupled interacting spinless triple quantum dot system --- for the observation of the SU(3) Kondo effect. Unlike more familiar SU(2) and SU(4) Kondo effects in quantum dot devices which lead to unitary linear conductance at low temperatures, the SU(3) Kondo scenario can be easily identified by the conductance pinned to a characteristic value of 3/4 of the unitary limit. This is associated with the interesting fact that the SU(3) Kondo effect does not occur at the particle-hole symmetric point, where the system is found instead in the valence-fluctuating regime with the total dot occupancy flipping between 1 and 2, but for gate voltages in the two Kondo plateaux where the dot occupancy is pinned to an integer value, either 1 or 2. From the thermodynamic analysis in the Kondo regime we find that the effective impurity orbital moment, defined through the impurity orbital susceptibility (chi_imp) multiplied by the temperature, is Tχ_imp=1 at high temperatures and then it increases to the characteristic value of Tχ_imp=4/3 corresponding to the three-fold degenerate local-moment fixed point where the impurity entropy is S_imp=ln 3. Then, at much lower temperatures, the system flows to the non-degenerate strong-coupling fixed point in which the SU(3) Kondo effect takes place. We also report results about the robustness of the SU(3) Kondo effect against various perturbations present in real experimental setups. Finally, we describe possible mechanisms to restore the SU(3) Kondo physics by properly tuning the on-site dot potentials. We briefly comment on the spinfull case which has very different behavior and shows Kondo plateaus in conductance for all integer values of the occupancy, including at the particle-hole symmetric point.

cond-mat.str-el↗

arXiv2012

Vibrational Andreev bound states in magnetic molecules

We predict the existence of vibrational Andreev bound states in deformable magnetic molecules on superconducting surfaces. We discuss the Anderson impurity model with electron-phonon coupling to a realistic anharmonic vibrational mode that modulates the tunneling barrier and show that the vibronic features are spectroscopically most visibile near the transition point between the Kondo-screened singlet and the unscreened doublet ground state. We find competing tendencies between phonon hardening due to anharmonicity and softening due to coupling to electrons, contrary to the Anderson-Holstein model and other models with harmonic local phonon mode where the vibrational mode is always softened. In addition, we find that the singlet and doublet many-body states may experience very different effective phonon potentials.

cond-mat.str-el↗

arXiv2012

Spin-thermopower in interacting quantum dots

Using analytical arguments and the numerical renormalization group method we investigate the spin-thermopower of a quantum dot in a magnetic field. In the particle-hole symmetric situation the temperature difference applied across the dot drives a pure spin current without accompanying charge current. For temperatures and fields at or above the Kondo temperature, but of the same order of magnitude, the spin-Seebeck coefficient is large, of the order of k_B/e. Via a mapping, we relate the spin-Seebeck coefficient to the charge-Seebeck coefficient of a negative-U quantum dot where the corresponding result was recently reported by Andergassen et al. in Phys. Rev. B 84, 241107 (2011). For several regimes we provide simplified analytical expressions. In the Kondo regime, the dependence of the spin-Seebeck coefficient on the temperature and the magnetic field is explained in terms of the shift of the Kondo resonance due to the field and its broadening with the temperature and the field. We also consider the influence of breaking the particle-hole symmetry and show that a pure spin current can still be realized provided a suitable electric voltage is applied across the dot. Then, except for large asymmetries, the behavior of the spin-Seebeck coefficient remains similar to that found in the particle-hole symmetric point.

cond-mat.mes-hall↗

arXiv2011

Ground state of the parallel double quantum dot system

We resolve the controversy regarding the ground state of the parallel double quantum dot system near half filling. The numerical renormalization group (NRG) predicts an underscreened Kondo state with residual spin-1/2 magnetic moment, ln 2 residual impurity entropy, and unitary conductance, while the Bethe Ansatz (BA) solution predicts a fully screened impurity, regular Fermi-liquid ground state, and zero conductance. We calculate the impurity entropy of the system as a function of the temperature using the hybridization-expansion continuous-time quantum Monte Carlo technique, which is a numerically exact stochastic method, and find excellent agreement with the NRG results. We show that the origin of the unconventional behavior in this model is the odd-symmetry "dark state" on the dots.

cond-mat.str-el↗

arXiv2011

Kondo resonance line-shape of magnetic adatoms on decoupling layers

The zero-bias resonance in the dI/dV tunneling spectrum recorded using a scanning tunneling microscope above a spin-1/2 magnetic adatom (such as Ti) adsorbed on a decoupling layer on metal surface can be accurately fitted using the universal spectral function of the Kondo impurity model both at zero field and at finite external magnetic field. Excellent agreement is found both for the asymptotic low-energy part and for the high-energy logarithmic tails of the Kondo resonance. For finite magnetic field, the nonlinear fitting procedure consists in repeatedly solving the impurity model for different Zeeman energies in order to obtain accurate spectral functions which are compared with the experimental dI/dV curves. The experimental results at zero field are sufficiently restraining to enable an unprecedented reliability in the determination of the Kondo temperature, while at finite fields the results are more ambiguous and two different interpretations are proposed.

cond-mat.mes-hall↗

arXiv2011

The Kondo effect in the presence of the Rashba spin-orbit interaction

We study the temperature scale of the Kondo screening of a magnetic impurity which hybridizes with a two-dimensional electron gas in the presence of the Rashba spin-orbit interaction. The problem is mapped to an effective single-band impurity model with a hybridization function having an inverse-square-root divergence at the bottom of the band. We study the effect of this divergence on the Kondo screening. The problem is solved numerically without further approximations using the numerical renormalization group technique. We find that the Rashba interaction leads to a small variation of the Kondo temperature (increase or decrease) which depends on the values of the impurity parameters.

cond-mat.str-el↗

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

Quantitative determination of the discretization and truncation errors in the numerical renormalization-group calculations of spectral functions

In the numerical renormalization group (NRG) calculations of the spectral functions of quantum impurity models, the results are affected by discretization and truncation errors. The discretization errors can be alleviated by averaging over different discretization meshes (z-averaging), but since each partial calculation is still performed for a finite discrete system, there are always some residual discretization and finite-size errors. The truncation errors affect the energies of the states and result in the displacement of the delta peak spectral contributions from their correct positions. The two types of errors are interrelated: for coarser discretization, the discretization errors increase, but the truncation errors decrease since the separation of energy scales in enhanced. In this work, it is shown that by calculating a series of spectral functions for a range of the total number of states kept in the NRG truncation, it is possible to estimate the errors and determine the error-bars for spectral functions, which is important when making accurate comparison to the results obtained by other methods and for determining the errors in the extracted quantities (such as peak positions, heights, and widths). The related spectral broadening issues are also discussed: it is shown that the overbroadening contorts the results without, surprisingly, reducing the variance of the curves. The method is applied to determine the error bounds in the Kondo peak splitting in the external magnetic field.

cond-mat.str-el↗

arXiv2011

SNEG - Mathematica package for symbolic calculations with second-quantization-operator expressions

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears advantageous to write numerical computer codes which allow the user to define the problem and the quantities of interest directly in terms of operator strings, rather than in some low-level programming language. Here I describe a Mathematica package which provides a flexible framework for performing the required translations between several different representations of operator expressions: condensed notation using pure ASCII character strings, traditional notation ("pretty printing"), internal Mathematica representation using nested lists (used for automatic symbolic manipulations), and various higher-level ("macro") expressions. The package consists of a collection of transformation rules that define the algebra of operators and a comprehensive library of utility functions. While the emphasis is given on the problems from solid-state and atomic physics, the package can be easily adapted to any given problem involving non-commuting operators. It can be used for educational and demonstration purposes, but also for direct calculations of problems of moderate size.

quant-ph↗

arXiv2011

Detection of Majorana edge states in topological superconductors through the non-Fermi-liquid effects induced in an interacting quantum dot

It is shown that the presence of the Majorana fermion edge states along the perimeter of a topological superconductor can be probed using an interacting quantum dot coupled to three terminals: two spin-polarized (ferromagnetic) leads and one lead supporting the Majorana edge states. The hybridization with the Majorana states induces a particular type of the Kondo effect with non-Fermi-liquid properties which can be detected by performing linear conductance measurements between the source and drain normal leads: the temperature dependence of the conductance is characteristically different from that in the conventional Kondo effect.

cond-mat.str-el↗

arXiv2011

Magnetic anisotropy effects on quantum impurities in superconducting host

We study the magnetic anisotropy effects on the localized sub-gap excitations induced by quantum impurities coupled to a superconducting host. We establish the ground-state phase diagrams for single-channel and two-channel high-spin Kondo impurities; they unveil surprising complexity that results from the (multi-stage) Kondo screening in competition with the superconducting correlations and the magnetic anisotropy splitting of the spin multiplets. We discuss the possibility of detecting the Zeeman splitting of the sub-gap states, which would provide an interesting spectroscopic tool for studying the magnetism on the single-atom level. We also study the problem of two impurities coupled by the Heisenberg exchange interaction, and we follow the evolution of the sub-gap states for both antiferromagnetic and ferromagnetic coupling. For sufficiently strong antiferromagnetic coupling, the impurities bind into a singlet state that is non-magnetic, thus the sub-gap states move to the edge of the gap and can no longer be discerned. For ferromagnetic coupling, some excited states remain present inside the gap.

cond-mat.supr-con↗