Center for Quantum Devices > Research > Publications > Jens Paaske
Publications by Jens Paaske
 2017

Nematic Bond Theory of Heisenberg Helimagnets 
Abstract
 We study classical twodimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spinnematic "order by disorder" transition is developed based on the selfconsistent 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.
Michael Schecter, Olav. F. Syljuåsen, J. Paaske 1705.08917v1 [pdf]

Kondo blockade due to quantum interference in singlemolecule junctions 
Abstract
 Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in singlemolecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spindegenerate molecule can be either enhanced or blocked by Kondo correlations, depending on molecular structure, contacting geometry and applied gate voltages. An exact framework is developed, in terms of which the quantum interference properties of interacting molecular junctions can be systematically studied and understood. We prove that an exact Kondomediated conductance node results from destructive interference in exchangecotunneling. Nonstandard temperature dependences and gatetunable conductance peaks/nodes are demonstrated for prototypical molecular junctions, illustrating the intricate interplay of quantum effects beyond the singleorbital paradigm.
Andrew K. Mitchell, Kim G. L. Pedersen, Per Hedegaard, Jens Paaske Journal reference: Nature Communications, 8, 15210 (2017) [ 1612.04852v2 ] DOI: 10.1038/ncomms15210

Symmetry analysis of strain, electric and magnetic fields in the
$\text{Bi}_2\text{Se}_3$class of topological insulators 
Abstract
 Based on group theoretical arguments we derive the most general Hamiltonian for the $\text{Bi}_2\text{Se}_3$class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of $\text{Bi}_2\text{Se}_3$. For the most experimentally relevant surface termination we analytically derive the surface state spectrum, revealing an anisotropic Dirac cone with elliptical constant energy contours giving rise to different velocities in different inplane directions. The spinmomentum locking of strained $\text{Bi}_2\text{Se}_3$ is shown to be modified and for some strain configurations we see a nonzero spin component perpendicular to the surface. We show that for a thin film of $\text{Bi}_2\text{Se}_3$ the surface state band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the surface state band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap.
Mathias Rosdahl Jensen, Jens Paaske, Anders Mathias Lunde, Morten Willatzen 1703.05259v1 [pdf]

Nematic Bond Theory of Heisenberg Helimagnets 
Abstract
 2016

Tunable Magnetic Anisotropy from HigherHarmonics Exchange Scattering on the Surface of a Topological Insulator 
Abstract
 We show that higherharmonics exchange scattering from a magnetic adatom on the surface of a three dimensional topological insulator leads to a magnetic anisotropy whose magnitude and sign may be tuned by adjusting the chemical potential of the helical surface band. As chemical potential moves from the Dirac point towards the surface band edge, the surface normal is found to change from magnetic easy, to hard axis. Hexagonal warping is shown to diminish the region with easy axis anisotropy, and to suppress the anisotropy altogether. This indirect contribution can be comparable in magnitude to the intrinsic term arising from crystal field splitting and atomic spinorbit coupling, and its tunability with chemical potential makes the two contributions experimentally discernible, and endows this source of anisotropy with potentially interesting magnetic functionality.
Jens Paaske, Erikas Gaidamauskas Journal reference: Phys. Rev. Lett. 117, 177201 (2016) [ 1602.08926v2 ] DOI: 10.1103/PhysRevLett.117.177201

Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a twodimensional superconductor 
Abstract
 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 `selforganized' 1D topologically nontrivial superconducting phase within the set of subgap YuShibaRusinov (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 shortrange ferromagnetic and longrange antiferromagnetic electroninduced 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 spinorbit 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.
M. H. Christensen, M. Schecter, K. Flensberg, B. M. Andersen, J. Paaske Journal reference: Phys. Rev. B 94, 144509 (2016) [ 1607.08190v2 ] DOI: 10.1103/PhysRevB.94.144509

Signatures of Majorana Kramers pairs in superconductorLuttinger liquid and superconductorquantum dotnormal lead junctions 
Abstract
 Timereversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a onedimensional superconductor is coupled to a normalmetal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electronelectron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquidMajorana Kramers pair junction and show that its lowenergy properties are determined by Andreev reflection scattering processes in the spintriplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spintriplet superconductor  normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slaveboson meanfield theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.
Younghyun Kim, Dong E. Liu, Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg, Roman M. Lutchyn Journal reference: Phys. Rev. B 94, 075439 (2016) [ 1605.02073v2 ] DOI: 10.1103/PhysRevB.94.075439

Selforganized topological superconductivity in a YuShibaRusinov chain 
Abstract
 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 spinspin interaction mediated through the subgap band of YuShibaRusinov states. Moreover, the simple spinspin 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 electrondriven topological superconductivity with Majorana boundary modes using magnetic atoms on superconducting surfaces.
M. Schecter, K. Flensberg, M. H. Christensen, B. M. Andersen, J. Paaske Journal reference: Phys. Rev. B 93, 140503 (2016) [pdf] DOI: 10.1103/PhysRevB.93.140503

YuShibaRusinov states in phasebiased superconductor–quantum dot–superconductor junctions 
Abstract
 We study the effects of a phase difference on YuShibaRusinov (YSR) states in a spinful Coulombblockaded quantum dot contacted by a superconducting loop. In the limit where charging energy is larger than the superconducting gap, we determine the subgap excitation spectrum, the corresponding supercurrent, and the differential conductance as measured by a normalmetal tunnel probe. In absence of a phase difference only one linear combination of the superconductor lead electrons couples to the spin, which gives a single YSR state. With finite phase difference, however, it is effectively a twochannel scattering problem and therefore an additional state emerges from the gap edge. The energy of the phasedependent YSR states depend on the gate voltage and one state can cross zero energy twice inside the valley with odd occupancy. These crossings are shifted by the phase difference towards the charge degeneracy points, corresponding to larger exchange couplings. Moreover, the zeroenergy crossings give rise to resonant peaks in the differential conductance with magnitude $4e^2/h$. Finally, we demonstrate that the quantum fluctuations of the dot spin do not alter qualitatively any of the results.
Gediminas Kiršanskas, Moshe Goldstein, Karsten Flensberg, Leonid I. Glazman, Jens Paaske Journal reference: Phys. Rev. B 92, 235422 (2015) [pdf] DOI: 10.1103/PhysRevB.92.235422

Tunable Magnetic Anisotropy from HigherHarmonics Exchange Scattering on the Surface of a Topological Insulator 
Abstract
 2015

Probing transverse magnetic anisotropy by electronic transport through a singlemolecule magnet 
Abstract
 By means of electronic transport, we study the transverse magnetic anisotropy of an individual Fe$_4$ singlemolecule magnet (SMM) embedded in a threeterminal 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.
M. Misiorny, E. Burzurí, R. Gaudenzi, K. Park, M. Leijnse, M. R. Wegewijs, J. Paaske, A. Cornia, H. S. J. van der Zant Journal reference: Physical Review B 91, 035442 (2015) [pdf] DOI: 10.1103/PhysRevB.91.035442

Probing transverse magnetic anisotropy by electronic transport through a singlemolecule magnet 
Abstract
 2014

Quantum interference in offresonant transport through single molecules 
Abstract
 We provide a simple set of rules for predicting interference effects in offresonant transport through singlemolecule junctions. These effects fall in two classes, showing respectively an odd or an even number of nodes in the linear conductance within a given molecular charge state, and we demonstrate how to decide the interference class directly from the contacting geometry. For neutral alternant hydrocarbons, we employ the CoulsonRushbrookeMcLachlan pairing theorem to show that the interference class is decided simply by tunneling on and off the molecule from same, or different sublattices. More generally, we investigate a range of smaller molecules by means of exact diag onalization combined with a perturbative treatment of the moleculelead tunnel coupling. While these results generally agree well with GW calculations, they are shown to be at odds with simpler meanfield treatments. For molecules with spindegenerate ground states, we show that for most junctions, interference causes no transmission nodes, but argue that it may lead to a nonstandard gatedependence of the zerobias Kondo resonance.
Kim G. L. Pedersen, Mikkel Strange, Martin Leijnse, Per Hedegård, Gemma Solomon, Jens Paaske Journal reference: Phys. Rev. B 90, 125413 (2014) [pdf] DOI: 10.1103/PhysRevB.90.125413

Majorana Bound States in TwoChannel TimeReversalSymmetric Nanowire Systems 
Abstract
 We consider timereversalsymmetric twochannel semiconducting quantum wires proximity coupled to an swave superconductor. We analyze the requirements for a nontrivial topological phase and find that necessary conditions are 1) the determinant of the pairing matrix in channel space must be negative, 2) inversion symmetry must be broken, and 3) the two channels must have different spinorbit couplings. The first condition can be implemented in semiconducting nanowire systems where interactions suppress intrachannel pairing, while the inversion symmetry can be broken by tuning the chemical potentials of the channels. For the case of collinear spinorbit directions, we find a general expression for the topological invariant by block diagonalization into two blocks with chiral symmetry only. By projection to the lowenergy sector, we solve for the zero modes explicitly and study the details of the gap closing, which in the general case happens at finite momenta.
Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg Journal reference: Phys. Rev. Lett. 122, 126402 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.126402

Quantum interference in offresonant transport through single molecules 
Abstract
 2012

Manipulation of organic polyradicals in a singlemolecule transistor 
Abstract
 Inspired by cotunneling spectroscopy of spinstates in a single OPE5based molecule, we investigate the prospects for electric control of magnetism in purely organic molecules contacted in a threeterminal 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 lowenergy Heisenberg model, which we substantiate microscopically by a simple valence bond description of the molecule. These preliminary findings suggest an interesting route towards functionalized allorganic molecular magnetism.
J. Fock, M. Leijnse, K. Jennum, A. S. Zyazin, J. Paaske, P. Hedegård, M. Brøndsted Nielsen, H. S. J. van der Zant Journal reference: Phys. Rev. B 86, 235403 (2012) [5 pages] [pdf] DOI: 10.1103/PhysRevB.86.235403

Finitebias conductance anomalies at a singlettriplet crossing 
Abstract
 Quantum dots and singlemolecule transistors may exhibit level crossings induced by tuning external parameters such as magnetic field or gate voltage. For Coulomb blockaded devices, this shows up as an inelastic cotunneling threshold in the differential conductance, which can be tuned to zero at the crossing. Here we show that, in addition, level crossings can give rise to a nearly vertical stepedge, ridge or even a Fanolike ridgevalley feature in the differential conductance inside the relevant Coulomb diamond. We study a gatetunable quasidegeneracy between singlet and triplet ground states, and demonstrate how these different shapes may result from a competition between nonequilibrium occupations and weak (spinorbit) mixing of the states. Our results are shown to be in qualitative agreement with recent transport measurements on a Mn complex [E. A. Osorio, et al., Nano Lett. 10, 105 (2010)]. The effect remains entirely general and should be observable in a wide range of Coulomb blockaded devices.
Chiara Stevanato, Martin Leijnse, Karsten Flensberg, Jens Paaske Journal reference: Phys. Rev. B 86, 165427 (2012) [pdf] DOI: 10.1103/PhysRevB.86.165427

Cotunneling renormalization in carbon nanotube quantum dots 
Abstract
 We determine the levelshifts induced by cotunneling in a Coulomb blockaded carbon nanotube quantum dot using leading order quasidegenerate perturbation theory within a single nanotube quartet. It is demonstrated that otherwise degenerate and equally tunnelcoupled $K$ and $K'$ states are mixed by cotunneling and therefore split up in energy except at the particle/holesymmetric midpoints of the Coulomb diamonds. In the presence of an external magnetic field, we show that cotunneling induces a gatedependent $g$factor renormalization, and we outline different scenarios which might be observed experimentally, depending on the values of both intrinsic $KK'$ splitting and spinorbit coupling.
Gediminas Kiršanskas, Jens Paaske, Karsten Flensberg Journal reference: Phys. Rev. B 86, 075452 (2012) [pdf] DOI: 10.1103/PhysRevB.86.075452

MagneticField Dependence of Tunnel Couplings in Carbon Nanotube Quantum Dots 
Abstract
 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 weaktunnel couplings, leading to gatedependent level renormalization. By comparison to a one and twoshell model, this is shown to be a consequence of disorderinduced valley mixing in the nanotube. Moreover, a parallel magnetic field is shown to reduce this mixing and thus suppress the effects of tunnel renormalization.
K. GroveRasmussen, S. Grap, J. Paaske, K. Flensberg, S. Andergassen, V. Meden, H. I. Jørgensen, K. Muraki, T. Fujisawa Journal reference: Phys. Rev. Lett. 108, 176802 (2012) [pdf] DOI: 10.1103/PhysRevLett.108.176802

Manipulation of organic polyradicals in a singlemolecule transistor 
Abstract
 2011

Sources of negative tunneling magnetoresistance in multilevel quantum dots with ferromagnetic contacts 
Abstract
 We analyze distinct sources of spindependent 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.
S. Koller, J. Paaske, M. Grifoni Journal reference: Phys. Rev. B, 045313 (2012) [pdf] DOI: 10.1103/PhysRevB.85.045313

Nonequilibrium Transport through a Spinful Quantum Dot with Superconducting Leads 
Abstract
 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 IVcharacteristics 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 spininduced YuShibaRussinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IVcharacteristics in the crossover regime of intermediate symmetry, consistent with recent experimental observations of negative differential conductance and repositioned conductance peaks in subgap cotunneling spectroscopy.
B. M. Andersen, K. Flensberg, V. Koerting, J. Paaske Journal reference: Phys. Rev. Lett. 107, 256802 (2011) [pdf] DOI: 10.1103/PhysRevLett.107.256802

Inelastic cotunneling in quantum dots and molecules with weakly broken degeneracies 
Abstract
 We calculate the nonlinear cotunneling conductance through interacting quantum dot systems in the deep Coulomb blockade regime using a rate equation approach based on the Tmatrix formalism, which shows in the concerned regions very good agreement with a generalized master equation approach. Our focus is on inelastic cotunneling in systems with weakly broken degeneracies, such as complex quantum dots or molecules. We find for these systems a characteristic gate dependence of the nonequilibrium cotunneling conductance. While on one side of a Coulomb diamond the conductance decreases after the inelastic cotunneling threshold towards its saturation value, on the other side it increases monotonously even after the threshold. We show that this behavior originates from an asymmetric gate voltage dependence of the effective cotunneling amplitudes.
Georg Begemann, Sonja Koller, Milena Grifoni, Jens Paaske Journal reference: Phys. Rev. B 82, 045316 (2010) [pdf] DOI: 10.1103/PhysRevB.82.045316

Spinorbit interaction and asymmetry effects on Kondo ridges at finite magnetic field 
Abstract
 We study electron transport through a serial double quantum dot with Rashba spinorbit 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 timereversal symmetry is preserved. Resulting from the crossing of a spinup and a spindown 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. Leftright asymmetric levellead couplings and detuned onsite energies lead to a simultaneous breaking of leftright and bondingantibonding state symmetry. In this case the finiteB Kondo ridges in the VgB plane are bent with respect to the Vgaxis. For the Kondo ridge to develop different level renormalizations must be compensated by adjusting B.
S. Grap, S. Andergassen, J. Paaske, V. Meden Journal reference: Phys. Rev. B 83, 115115 (2011) [pdf] DOI: 10.1103/PhysRevB.83.115115

Sources of negative tunneling magnetoresistance in multilevel quantum dots with ferromagnetic contacts 
Abstract
 2010

Nonequilibrium transport via spininduced subgap states in superconductor/quantum dot/normal metal cotunnel junctions 
Abstract
 We study lowtemperature 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 Tmatrix, from which we obtain the nonlinear cotunneling conductance. For even occupied dots the system can be conceived as an effective S/Ncotunnel junction with subgap transport mediated by Andreev reflections. The net spin of an odd occupied dot, however, leads to the formation of subgap resonances inside the superconducting gap which gives rise to a characteristic peakdip structure in the differential conductance, as observed in recent experiments.
V. Koerting, B. M. Andersen, K. Flensberg, J. Paaske Journal reference: Phys. Rev. B 82, 245108 (2010) [pdf] DOI: 10.1103/PhysRevB.82.245108

Gatedependent spinorbit coupling in multielectron carbon nanotubes 
Abstract
 Understanding how the orbital motion of electrons is coupled to the spin degree of freedom in nanoscale systems is central for applications in spinbased electronics and quantum computation. We demonstrate this coupling of spin and orbit in a carbon nanotube quantum dot in the general multielectron regime in presence of finite disorder. Further, we find a strong systematic dependence of the spinorbit coupling on the electron occupation of the quantum dot. This dependence, which even includes a sign change is not demonstrated in any other system and follows from the curvatureinduced spinorbit split Diracspectrum of the underlying graphene lattice. Our findings unambiguously show that the spinorbit coupling is a general property of nanotube quantum dots which provide a unique platform for the study of spinorbit effects and their applications.
Thomas Sand Jespersen, Kasper GroveRasmussen, Jens Paaske, Koji Muraki, Toshimasa Fujisawa, Jesper Nygård, Karsten Flensberg 1008.1600v2 [pdf]

Exchange cotunneling through quantum dots with spinorbit coupling 
Abstract
 We investigate the effects of spinorbit 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 timereversal 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 finitefield cotunneling spectroscopy thus provides valuable information about orbital, and spin degrees of freedom and their mutual coupling.
J. Paaske, A. Andersen, K. Flensberg DOI: 10.1103/PhysRevB.82.081309 1006.2371v1 [pdf]

Transport via coupled states in a C60 peapod quantum dot 
Abstract
 We have measured systematic repetitions of avoided crossings in low temperature threeterminal transport through a carbon nanotube with encapsulated C60 molecules. We show that this is a general effect of the hybridization of a host quantum dot with an impurity. The welldefined nanotube allows identification of the properties of the impurity, which we suggest to be a chain of C60 molecules inside the nanotube. This electronic coupling between the two subsystems opens the interesting and potentially useful possibility of contacting the encapsulated molecules via the tube.
Anders Eliasen, Jens Paaske, Karsten Flensberg, Sebastian Smerat, Martin Leijnse, Maarten R. Wegewijs, Henrik I. Jørgensen, Marc Monthioux, Jesper Nygård DOI: 10.1103/PhysRevB.81.155431 1002.0477v1 [pdf]

Nonequilibrium transport via spininduced subgap states in superconductor/quantum dot/normal metal cotunnel junctions 
Abstract
 2009

Electrical manipulation of spin states in a single electrostatically
gated transitionmetal complex 
Abstract
 We demonstrate an electrically controlled highspin (S=5/2) to lowspin (S=1/2) transition in a threeterminal device incorporating a single Mn2+ ion coordinated by two terpyridine ligands. By adjusting the gatevoltage we reduce the terpyridine moiety and thereby strengthen the ligandfield on the Mnatom. Adding a single electron thus stabilizes the lowspin configuration and the corresponding sequential tunnelling current is suppressed by spinblockade. From lowtemperature inelastic cotunneling spectroscopy, we infer the magnetic excitation spectrum of the molecule and uncover also a strongly gatedependent singlettriplet splitting on the lowspin side. The measured biasspectroscopy is shown to be consistent with an exact diagonalization of the Mncomplex, and an interpretation of the data is given in terms of a simplified effective model.
Edgar A. Osorio, Kasper MothPoulsen, Herre S. J. van der Zant, Jens Paaske, Per Hedegard, Karsten Flensberg, Jesper Bendix, Thomas Bjornholm DOI: 10.1021/nl9029785 0912.2640v1 [pdf]

Superconductivityenhanced bias spectroscopy in carbon nanotube quantum dots 
Abstract
 We study lowtemperature transport through carbon nanotube quantum dots in the Coulomb blockade regime coupled to niobiumbased superconducting leads. We observe pronounced conductance peaks at finite sourcedrain 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 tunnelingrenormalizations of the two subbands in the nanotube. Finally, we discuss the origin of an especially pronounced subgap structure observed in every fourth Coulomb diamond.
K. GroveRasmussen, H. I. Jørgensen, B. M. Andersen, J. Paaske, T. S. Jespersen, J. Nygård, K. Flensberg, P. E. Lindelof Journal reference: Phys. Rev. B 79, 134518 (2009) [pdf] DOI: 10.1103/PhysRevB.79.134518

Nonequilibrium cotunneling through a threelevel quantum dot 
Abstract
 We calculate the nonlinear cotunneling conductance through a quantum dot with 3 electrons occupying the three highest lying energy levels. Starting from a 3orbital Anderson model, we apply a generalized SchriefferWolff 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 quantumwire quantum dots. Further predictions of the model like cascade resonances and a magneticfield 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.
S. Schmaus, V. Koerting, J. Paaske, T. S. Jespersen, J. Nygård, P. Wölfle Journal reference: Phys. Rev. B 79, 045105 (2009) [pdf] DOI: 10.1103/PhysRevB.79.045105

Electrical manipulation of spin states in a single electrostatically
gated transitionmetal complex 
Abstract
 2008

Gatedependent tunnelinginduced level shifts observed in carbon nanotube quantum dots 
Abstract
 We have studied electron transport in clean singlewalled 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 gatedependence 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 secondorder perturbation theory in the tunnel coupling.
J. V. Holm, H. I. Jørgensen, K. GroveRasmussen, J. Paaske, K. Flensberg, P. E. Lindelof Journal reference: Phys. Rev. B 77, 161406(R) (2008) [pdf] DOI: 10.1103/PhysRevB.77.161406

Electron transport in the fourlead twoimpurity Kondo model: Nonequilibrium perturbation theory with almost degenerate levels 
Abstract
 The eigenstates of an isolated nanostructure may get mixed by the coupling to external leads. This effect is the stronger, the smaller the level splitting on the dot and the larger the broadening induced by the coupling to the leads. We describe how to calculate the nondiagonal density matrix of the nanostructure efficiently in the cotunneling regime. As an example, we consider a system of two quantum dots in the Kondo regime, the two spins coupled by an antiferromagnetic exchange interaction and each dot tunnel coupled to two leads. Calculating the nonequilibrium density matrix and the corresponding current, we demonstrate the importance of the offdiagonal terms in the presence of an applied magnetic field and a finite bias voltage.
V. Koerting, J. Paaske, P. Wölfle Journal reference: Phys. Rev. B 77, 165122 (2008) (10 pages) [pdf] DOI: 10.1103/PhysRevB.77.165122

Gatedependent tunnelinginduced level shifts observed in carbon nanotube quantum dots 
Abstract
 2007

Electronic Excitations of a Single Molecule Contacted in a ThreeTerminal Configuration 
Abstract
 Lowtemperature threeterminal transport measurements through a thiol endcapped Pi conjugated molecule have been carried out. Electronic excitations, including zero and finitebias Kondoeffects have been observed and studied as a function of magnetic field. Using a simplified twoorbital model we have accounted for the spin and the electronic configuration of the first four charge states of the molecule. The chargedependent couplings to gate, source and drain electrodes suggest a scenario in which charges and spins are localized at the ends of the molecule, close to the electrodes.
Edgar A. Osorio, Kevin O'Neill, Maarten Wegewijs, Nicolai StuhrHansen, Jens Paaske, Thomas Bjornholm, Herre S. J. van der Zant Journal reference: Nano lett. 2007, 7, 3336 [pdf] DOI: 10.1021/nl0715802

Electricfieldcontrolled spin reversal in a quantum dot with ferromagnetic contacts 
Abstract
 Manipulation of the spinstates of a quantum dot by purely electrical means is a highly desirable property of fundamental importance for the development of spintronic devices such as spinfilters, spintransistors and singlespin memory as well as for solidstate qubits. An electrically gated quantum dot in the Coulomb blockade regime can be tuned to hold a single unpaired spin1/2, which is routinely spinpolarized by an applied magnetic field. Using ferromagnetic electrodes, however, the properties of the quantum dot become directly spindependent and it has been demonstrated that the ferromagnetic electrodes induce a local exchangefield which polarizes the localized spin in the absence of any external fields. Here we report on the experimental realization of this tunnelinginduced spinsplitting in a carbon nanotube quantum dot coupled to ferromagnetic nickelelectrodes. We study the intermediate coupling regime in which singleelectron states remain well defined, but with sufficiently good tunnelcontacts to give rise to a sizable exchangefield. Since charge transport in this regime is dominated by the Kondoeffect, we can utilize this sharp manybody resonance to read off the local spinpolarization from the measured biasspectroscopy. We show that the exchangefield can be compensated by an external magnetic field, thus restoring a zerobias Kondoresonance, and we demonstrate that the exchangefield itself, and hence the local spinpolarization, can be tuned and reversed merely by tuning the gatevoltage. This demonstrates a very direct electrical control over the spinstate of a quantum dot which, in contrast to an applied magnetic field, allows for rapid spinreversal with a very localized addressing.
J. R. Hauptmann, J. Paaske, P. E. Lindelof Journal reference: Nature Physics 4, 373  376 (01 May 2008) [pdf] DOI: 10.1038/nphys931

Inelastic scattering rates in dwave superconductors 
Abstract
 The inelastic scattering rates of quasiparticles in a twodimensional dwave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We discover a strong enhancement of scattering with collinear momenta, brouth about by the special kinematics of the twodimensional fermions with Diraclike spectrum near the nodes of the dwave order parameter. In the case of a local instantaneous interparticle potential we find that either an RPAtype resummation of the perturbation series or an inclusion of nonlinear corrections to the Dirac spectrum is called for in order to obtain a finite scattering rate in the limit $\omega/T\to 0$. In either way, we find drastic changes in the scattering rate, as compared to the naively expected cubic temperature dependence.
J. Paaske, D. V. Khveshchenko Journal reference: Physica C 341, 265 (2000) [pdf] DOI: 10.1016/S09214534(00)00472X

Transconductance of a Double Quantum Dot System in the Kondo Regime 
Abstract
 We consider a lateral doubledot system in the Coulomb blockade regime with a single spin1/2 on each dot, mutually coupled by an antiferromagnetic exchange interaction. Each of the two dots is contacted by two leads. We demonstrate that the voltage across one of the dots will have a profound influence on the current passing through the other dot. Using Poor Man's scaling, we find that the Kondoeffect can lead to a strong enhancement of this {\it transconductance}.
V. Koerting, P. Wölfle, J. Paaske Journal reference: Phys. Rev. Lett. 99, 036807 (2007) [ condmat/0612566v2 ] DOI: 10.1103/PhysRevLett.99.036807

KondoEnhanced Andreev Tunneling in InAs Nanowire Quantum Dots 
Abstract
 We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with subgappeaks at $V_{sd}=\Delta/e$ markedly stronger(weaker) than the quasiparticle tunneling peaks at $V_{sd}=2\Delta/e$ for odd(even) occupation. We attribute the enhanced $\Delta$peak to an interplay between Kondocorrelations and Andreev tunneling in dots with an odd number of spins, and substantiate this interpretation by a poor man's scaling analysis.
T. SandJespersen, J. Paaske, B. M. Andersen, K. GroveRasmussen, H. I. Jørgensen, M. Aagesen, C. Sørensen, P. E. Lindelof, K. Flensberg, J. Nygård Journal reference: Phys. Rev. Lett. 99, 126603 (2007) [ condmat/0703264v1 ] DOI: 10.1103/PhysRevLett.99.126603

Electronic Excitations of a Single Molecule Contacted in a ThreeTerminal Configuration 
Abstract
 2006

Nonequilibrium singlet–triplet Kondo effect in carbon nanotubes 
Abstract
 The Kondoeffect is a manybody phenomenon arising due to conduction electrons scattering off a localized spin. Coherent spinflip scattering off such a quantum impurity correlates the conduction electrons and at low temperature this leads to a zerobias conductance anomaly. This has become a common signature in biasspectroscopy of singleelectron transistors, observed in GaAs quantum dots as well as in various singlemolecule transistors. While the zerobias Kondo effect is well established it remains uncertain to what extent Kondo correlations persist in nonequilibrium situations where inelastic processes induce decoherence. Here we report on a pronounced conductance peak observed at finite biasvoltage in a carbon nanotube quantum dot in the spin singlet ground state. We explain this finitebias conductance anomaly by a nonequilibrium Kondoeffect involving excitations into a spin triplet state. Excellent agreement between calculated and measured nonlinear conductance is obtained, thus strongly supporting the correlated nature of this nonequilibrium resonance.
J. Paaske, A. Rosch, P. Woelfle, N. Mason, C. M. Marcus, J. Nygard Journal reference: Nature Physics, vol. 2, p.460  464 (2006) [ condmat/0602581v1 ] DOI: 10.1038/nphys340

Nonequilibrium singlet–triplet Kondo effect in carbon nanotubes 
Abstract
 2004

The Kondo Effect in NonEquilibrium Quantum Dots: Perturbative Renormalization Group 
Abstract
 While the properties of the Kondo model in equilibrium are very well understood, much less is known for Kondo systems out of equilibrium. We study the properties of a quantum dot in the Kondo regime, when a large bias voltage V and/or a large magnetic field B is applied. Using the perturbative renormalization group generalized to stationary nonequilibrium situations, we calculate renormalized couplings, keeping their important energy dependence. We show that in a magnetic field the spin occupation of the quantum dot is nonthermal, being controlled by V and B in a complex way to be calculated by solving a quantum Boltzmann equation. We find that the wellknown suppression of the Kondo effect at finite V>>T_K (Kondo temperature) is caused by inelastic dephasing processes induced by the current through the dot. We calculate the corresponding decoherence rate, which serves to cut off the RG flow usually well inside the perturbative regime (with possible exceptions). As a consequence, the differential conductance, the local magnetization, the spin relaxation rates and the local spectral function may be calculated for large V,B >> T_K in a controlled way.
A. Rosch, J. Paaske, J. Kroha, P. Wölfle Journal reference: J. Phys. Soc. Jpn. 74, 118 (2005) [ condmat/0408506v2 ] DOI: 10.1143/JPSJ.74.118

Vibrational Sidebands and the Kondo Effect in Molecular Transistors 
Abstract
 Electron transport through molecular quantum dots coupled to a single vibrational mode is studied in the Kondo regime. We apply a generalized SchriefferWolff transformation to determine the effective lowenergy spinspinvibroninteraction. From this model we calculate the nonlinear conductance and find Kondo sidebands located at biasvoltages equal to multiples of the vibron frequency. Due to selection rules, the sidepeaks are found to have strong gatevoltage dependences, which can be tested experimentally. In the limit of weak electronvibron coupling, we employ a perturbative renormalization group scheme to calculate analytically the nonlinear conductance.
Jens Paaske, Karsten Flensberg Journal reference: Phys. Rev. Lett. 94, 176801 (2005) [ condmat/0409158v1 ] DOI: 10.1103/PhysRevLett.94.176801

Nonequilibrium transport through a Kondo dot: Decoherence effects 
Abstract
 We investigate the effects of voltage induced spinrelaxation in a quantum dot in the Kondo regime. Using nonequilibrium perturbation theory, we determine the joint effect of selfenergy and vertex corrections to the conduction electron Tmatrix in the limit of transport voltage much larger than temperature. The logarithmic divergences, developing near the different chemical potentials of the leads, are found to be cut off by spinrelaxation rates, implying that the nonequilibrium Kondoproblem remains at weak coupling as long as voltage is much larger than the Kondo temperature.
J. Paaske, A. Rosch, J. Kroha, P. Wölfle Journal reference: Phys. Rev. B 70, 155301 (2004) [ condmat/0401180v1 ] DOI: 10.1103/PhysRevB.70.155301

The Kondo Effect in NonEquilibrium Quantum Dots: Perturbative Renormalization Group 
Abstract
 2003

Nonequilibrium transport through a Kondo dot in a magnetic field: Perturbation theory 
Abstract
 Using nonequilibrium perturbation theory, we investigate the nonlinear transport through a quantum dot in the Kondo regime in the presence of a magnetic field. We calculate the leading logarithmic corrections to the local magnetization and the differential conductance, which are characteristic of the Kondo effect out of equilibrium. By solving a quantum Boltzmann equation, we determine the nonequilibrium magnetization on the dot and show that the application of both a finite bias voltage and a magnetic field induces a novel structure of logarithmic corrections not present in equilibrium. These corrections lead to more pronounced features in the conductance, and their form calls for a modification of the perturbative renormalization group.
J. Paaske, A. Rosch, P. Wölfle Journal reference: Phys. Rev. B 69, 155330 (2004) [ condmat/0307365v1 ] DOI: 10.1103/PhysRevB.69.155330

Spectral function of the Kondo model in high magnetic fields 
Abstract
 Using a recently developed perturbative renormalization group (RG) scheme, we calculate analytically the spectral function of a Kondo impurity for either large frequencies w or large magnetic field B and arbitrary frequencies. For large w >> max[B,T_K] the spectral function decays as 1/ln^2[ w/T_K ] with prefactors which depend on the magnetization. The spinresolved spectral function displays a pronounced peak at w=B with a characteristic asymmetry. In a detailed comparison with results from numerical renormalization group (NRG) and bare perturbation theory in nexttoleading logarithmic order, we show that our perturbative RG scheme is controlled by the small parameter 1/ln[ max(w,B)/T_K]. Furthermore, we assess the ability of the NRG to resolve structures at finite frequencies.
A. Rosch, T. A. Costi, J. Paaske, P. Wölfle Journal reference: Phys. Rev. B 68, 014430 (2003) [ condmat/0301106v3 ] DOI: 10.1103/PhysRevB.68.014430

Nonequilibrium Transport through a Kondo Dot in a Magnetic Field: Perturbation Theory and Poor Man’s Scaling 
Abstract
 We consider electron transport through a quantum dot described by the Kondo model in the regime of large transport voltage V in the presence of a magnetic field B with max(V,B) >> T_K. The electric current I and the local magnetization M are found to be universal functions of V/T_K and B/T_K, where T_K is the equilibrium Kondo temperature. We present a generalization of the perturbative renormalization group to frequency dependent coupling functions, as necessitated by the structure of bare perturbation theory. We calculate I and M within a poor man's scaling approach and find excellent agreement with experiment.
A. Rosch, J. Paaske, J. Kroha, P. Wölfle Journal reference: Phys. Rev. Lett. 90, 076804 (2003) [ condmat/0202404v2 ] DOI: 10.1103/PhysRevLett.90.076804

Nonequilibrium transport through a Kondo dot in a magnetic field: Perturbation theory 
Abstract
 2001

Incipient nodal pairing in planar dwave superconductors 
Abstract
 The possibility of a second pairing transition $d\to d+is$ ($d+id^\prime$) in planar $d$wave superconductors which occurs in the absence of external magnetic field, magnetic impurities or boundaries is established in the framework of the nonperturbative phenomenon of dynamical chiral symmetry breaking in the system of $2+1$dimensional Diraclike nodal quasiparticles. We determine the critical exponents and quasiparticle spectral functions that characterize the corresponding quantum critical behavior and discuss some of its potentially observable spectral and transport features.
D. V. Khveshchenko, J. Paaske Journal reference: Phys. Rev. Lett. v.86, p.4672 (2001) [ condmat/0009117v3 ] DOI: 10.1103/PhysRevLett.86.4672

Incipient nodal pairing in planar dwave superconductors 
Abstract
 1998

Intrinsic temperature dependences of transport coefficients within the
hotspot model for normal state YBCO 
Abstract
 The temperature dependences of the galvanomagnetic and thermoelectric transport coefficients within a generic hotspot model are reconsidered. Despite the recent success in explaining ac Hall effect data in YBa_{2}Cu_{3}O_{7}, a general feature of this model is a departure from the approximately universal temperature dependences observed for normal state transport in the optimally doped cuprates. In this paper, we discuss such systematic deviations and illustrate some of their effects through a concrete numerical example using the calculated band structure for YBa_{2}Cu_{3}O_{7}.
J. Paaske, D. V. Khveshchenko Journal reference: Phys. Rev. B 57, R8127 (1998) [ condmat/9801126v1 ] DOI: 10.1103/PhysRevB.57.R8127

Intrinsic temperature dependences of transport coefficients within the
hotspot model for normal state YBCO 
Abstract