arXiv subjects

J. Paaske

Publications and source records attributed to J. Paaske.

At least 19 recordsLinked to original sources

arXiv2024

Majorana modes in quantum dots coupled via a floating superconducting island

Majorana modes can be engineered in arrays where quantum dots (QDs) are coupled via grounded superconductors, effectively realizing an artificial Kitaev chain. Minimal Kitaev chains, composed by two QDs, can host fully-localized Majorana modes at discrete points in parameter space, known as Majorana sweet spots. Here, we extend previous works by theoretically investigating a setup with two QDs coupled via a floating superconducting island. We study the effects of the charging energy of the island and the properties of the resulting minimal Kitaev chain. We initially employ a minimal perturbative model, valid in the weak QD-island coupling regime, to derive analytic expressions for the Majorana sweet spots and the splitting of the ground state degeneracy as a function of tunable physical parameters. The conclusions from this perturbative approximation are then benchmarked using a microscopic model that explicitly describes the internal degrees of freedom of the island. Our work shows the existence of Majorana sweet spots, even when the island is not tuned at a charge-degeneracy point. In contrast to the Kitaev chains in grounded superconductors, these sweet spots involve a degeneracy between states with a well-defined number of particles.

cond-mat.mes-hall↗

arXiv2020

Two-Impurity Yu-Shiba-Rusinov States in Coupled Quantum Dots

Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated two-impurity Kondo model. The device shows a cusped current-voltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary ground-state indicators to demonstrate gate-tuned changes of the ground state from an inter-dot singlet to independently screened Yu-Shiba-Rusinov (YSR) singlets. In contrast to the two-impurity Kondo effect in normal-state systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened.

cond-mat.mes-hall↗

arXiv2020

Supercurrent in a double quantum dot

We demonstrate the Josephson effect in a serial double quantum dot defined in a nanowire with epitaxial superconducting leads. The supercurrent stability diagram adopts a honeycomb pattern with electron-hole and left-right reflection symmetry. We observe sharp discontinuities in the magnitude of the critical current, $I_c$, as a function of dot occupation, related to doublet to singlet ground state transitions. Detuning of the energy levels offers a tuning knob for $I_c$, which attains a maximum at zero detuning. The consistency between experiment and theory indicates that our device is a faithful realization of the two-impurity Anderson model.

cond-mat.mes-hall↗

arXiv2017

Yu-Shiba-Rusinov screening of spins in double quantum dots

A magnetic impurity coupled to a superconductor gives rise to a Yu-Shiba-Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR groundstate with bound quasiparticles screening the impurity spin by $\hbar/2$. Here we explore InAs nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zero-bias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zero-energy YSR states. These enclose regions of YSR-screened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zero-bandwidth approximation, and with numerical renormalization group calculations for the two-orbital Anderson model.

cond-mat.mes-hall↗

arXiv2017

Nematic Bond Theory of Heisenberg Helimagnets

We study classical two-dimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spin-nematic "order by disorder" transition is developed based on the self-consistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wavevector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of bicritical points.

cond-mat.str-el↗

arXiv2016

Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor

We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `self-organized' 1D topologically non-trivial superconducting phase within the set of subgap Yu-Shiba-Rusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between short-range ferromagnetic and long-range antiferromagnetic electron-induced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spin-orbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.

cond-mat.supr-con↗

arXiv2016

Self-Organized Topological Superconductivity in a Yu-Shiba-Rusinov Chain

We study a chain of magnetic moments exchange coupled to a conventional three dimensional superconductor. In the normal state the chain orders into a collinear configuration, while in the superconducting phase we find that ferromagnetism is unstable to the formation of a magnetic spiral state. Beyond weak exchange coupling the spiral wavevector greatly exceeds the inverse superconducting coherence length as a result of the strong spin-spin interaction mediated through the subgap band of Yu-Shiba-Rusinov states. Moreover, the simple spin-spin exchange description breaks down as the subgap band crosses the Fermi energy, wherein the spiral phase becomes stabilized by the spontaneous opening of a $p-$wave superconducting gap within the band. This leads to the possibility of electron-driven topological superconductivity with Majorana boundary modes using magnetic atoms on superconducting surfaces.

cond-mat.supr-con↗

arXiv2015

Probing Transverse Magnetic Anisotropy by Electronic Transport through a Single-Molecule Magnet

By means of electronic transport, we study the transverse magnetic anisotropy of an individual Fe$_4$ single-molecule magnet (SMM) embedded in a three-terminal junction. In particular, we determine in situ the transverse anisotropy of the molecule from the pronounced intensity modulations of the linear conductance, which are observed as a function of applied magnetic field. The proposed technique works at temperatures exceeding the energy scale of the tunnel splittings of the SMM. We deduce that the transverse anisotropy for a single Fe$_4$ molecule captured in a junction is substantially larger than the bulk value.

cond-mat.mes-hall↗

arXiv2012

Manipulation of organic polyradicals in a single-molecule transistor

Inspired by cotunneling spectroscopy of spin-states in a single OPE5-based molecule, we investigate the prospects for electric control of magnetism in purely organic molecules contacted in a three-terminal geometry. Using the gate electrode, the molecule is reversibly switched between three different redox states, with magnetic spectra revealing both ferromagnetic and antiferromagnetic exchange couplings on the molecule. These observations are shown to be captured by an effective low-energy Heisenberg model, which we substantiate microscopically by a simple valence bond description of the molecule. These preliminary findings suggest an interesting route towards functionalized all-organic molecular magnetism.

cond-mat.mes-hall↗

arXiv2012

Magnetic-Field Dependence of Tunnel Couplings in Carbon Nanotube Quantum Dots

By means of sequential and cotunneling spectroscopy, we study the tunnel couplings between metallic leads and individual levels in a carbon nanotube quantum dot. The levels are ordered in shells consisting of two doublets with strong- and weak-tunnel couplings, leading to gate-dependent level renormalization. By comparison to a one- and two-shell model, this is shown to be a consequence of disorder-induced valley mixing in the nanotube. Moreover, a parallel magnetic field is shown to reduce this mixing and thus suppress the effects of tunnel renormalization.

cond-mat.str-el↗

arXiv2011

Sources of negative tunneling magneto-resistance in multilevel quantum dots with ferromagnetic contacts

We analyze distinct sources of spin-dependent energy level shifts and their impact on the tunneling magnetoresistance (TMR) of interacting quantum dots coupled to collinearly polarized ferromagnetic leads. Level shifts due to virtual charge fluctuations can be quantitatively evaluated within a diagrammatic representation of our transport theory. The theory is valid for multilevel quantum dot systems and we exemplarily apply it to carbon nanotube quantum dots, where we show that the presence of many levels can qualitatively influence the TMR effect.

cond-mat.mes-hall↗

arXiv2011

Nonequilibrium transport through a spinful quantum dot with superconducting leads

We study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV-characteristics with varying asymmetry in the tunnel coupling to source and drain electrodes. The current is found to be carried respectively by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Russinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IV-characteristics in the cross-over regime of intermediate symmetry, consistent with recent experimental observations of negative differential conductance and re-positioned conductance peaks in sub-gap cotunneling spectroscopy.

cond-mat.mes-hall↗

arXiv2011

Spin-orbit interaction and asymmetry effects on Kondo ridges at finite magnetic field

We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude B in presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage Vg equally shifting the levels on both dots shows two B=0 Kondo ridges which are robust against SOI as time-reversal symmetry is preserved. Resulting from the crossing of a spin-up and a spin-down level at vanishing SOI two additional Kondo plateaus appear at finite B. They are not protected by symmetry and rapidly vanish if the SOI is turned on. Left-right asymmetric level-lead couplings and detuned on-site energies lead to a simultaneous breaking of left-right and bonding-anti-bonding state symmetry. In this case the finite-B Kondo ridges in the Vg-B plane are bent with respect to the Vg-axis. For the Kondo ridge to develop different level renormalizations must be compensated by adjusting B.

cond-mat.str-el↗

arXiv2010

Nonequilibrium transport via spin-induced sub-gap states in superconductor/quantum dot/normal metal cotunnel junctions

We study low-temperature transport through a Coulomb blockaded quantum dot (QD) contacted by a normal (N), and a superconducting (S) electrode. Within an effective cotunneling model the conduction electron self energy is calculated to leading order in the cotunneling amplitudes and subsequently resummed to obtain the nonequilibrium T-matrix, from which we obtain the nonlinear cotunneling conductance. For even occupied dots the system can be conceived as an effective S/N-cotunnel junction with subgap transport mediated by Andreev reflections. The net spin of an odd occupied dot, however, leads to the formation of sub-gap resonances inside the superconducting gap which gives rise to a characteristic peak-dip structure in the differential conductance, as observed in recent experiments.

cond-mat.supr-con↗

arXiv2010

Exchange cotunneling through quantum dots with spin-orbit coupling

We investigate the effects of spin-orbit interaction (SOI) on the exchange cotunneling through a spinful Coulomb blockaded quantum dot. In the case of zero magnetic field, Kondo effect is shown to take place via a Kramers doublet and the SOI will merely affect the Kondo temperature. In contrast, we find that the breaking of time-reversal symmetry in a finite field has a marked influence on the effective Anderson, and Kondo models for a single level. The nonlinear conductance can now be asymmetric in bias voltage and may depend strongly on direction of the magnetic field. A measurement of the angle dependence of finite-field cotunneling spectroscopy thus provides valuable information about orbital, and spin degrees of freedom and their mutual coupling.

cond-mat.mes-hall↗

arXiv2009

Superconductivity-enhanced bias spectroscopy in carbon nanotube quantum dots

We study low-temperature transport through carbon nanotube quantum dots in the Coulomb blockade regime coupled to niobium-based superconducting leads. We observe pronounced conductance peaks at finite source-drain bias, which we ascribe to elastic and inelastic cotunneling processes enhanced by the coherence peaks in the density of states of the superconducting leads. The inelastic cotunneling lines display a marked dependence on the applied gate voltage which we relate to different tunneling-renormalizations of the two subbands in the nanotube. Finally, we discuss the origin of an especially pronounced sub-gap structure observed in every fourth Coulomb diamond.

cond-mat.mes-hall↗

arXiv2009

Nonequilibrium Cotunneling through a Three-Level Quantum Dot

We calculate the nonlinear cotunneling conductance through a quantum dot with 3 electrons occupying the three highest lying energy levels. Starting from a 3-orbital Anderson model, we apply a generalized Schrieffer-Wolff transformation to derive an effective Kondo model for the system. Within this model we calculate the nonequilibrium occupation numbers and the corresponding cotunneling current to leading order in the exchange couplings. We identify the inelastic cotunneling thresholds and their splittings with applied magnetic field, and make a qualitative comparison to recent experimental data on carbon nanotube and InAs quantum-wire quantum dots. Further predictions of the model like cascade resonances and a magnetic-field dependence of the orbital level splitting are not yet observed but within reach of recent experimental work on carbon nanotube and InAs nanowire quantum dots.

cond-mat.str-el↗

arXiv2008

Gate-dependent tunneling-induced level shifts observed in carbon nanotube quantum dots

We have studied electron transport in clean single-walled carbon nanotube quantum dots. Because of the large number of Coulomb blockade diamonds simultaneously showing both shell structure and Kondo effect, we are able to perform a detailed analysis of tunneling renormalization effects. Thus determining the environment induced level shifts of this artificial atom. In shells where only one of the two orbitals is coupled strongly, we observe a marked asymmetric gate-dependence of the inelastic cotunneling lines together with a systematic gate dependence of the size (and shape) of the Coulomb diamonds. These effects are all given a simple explanation in terms of second-order perturbation theory in the tunnel coupling.

cond-mat.mes-hall↗