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10.0

Jun 29, 2018
06/18

by
C. Karrasch

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We illustrate how finite-temperature charge and thermal Drude weights of one-dimensional systems can be obtained from the relaxation of initial states featuring global (left-right) gradients in the chemical potential or temperature. The approach is tested for spinless interacting fermions as well as for the Fermi-Hubbard model, and the behaviour in the vicinity of singular points (such as half filling or isotropic chains) is discussed. We present technical details on how to implement the...

Topics: Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1611.00573

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3.0

Jun 29, 2018
06/18

by
C. Karrasch

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One of the most straightforward ways to study thermal properties beyond linear response is to monitor the relaxation of an arbitrarily large left-right temperature gradient $T_L-T_R$. In one-dimensional systems which support ballistic thermal transport, the local energy currents $\langle j(t)\rangle$ acquire a non-zero value at long times, and it was recently investigated whether or not this steady state fulfills a simple additive relation $\langle j(t\to\infty)\rangle=f(T_L)-f(T_R)$ in...

Topics: Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1612.04964

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62

Sep 20, 2013
09/13

by
C. Karrasch

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We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries. A detailed derivation of a truncated set of RG flow equations that requires only basic knowledge of the functional integral approach to many-particle physics is given. Using fRG we study linear-response transport properties of a variety of quantum dots in...

Source: http://arxiv.org/abs/cond-mat/0612329v1

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49

Sep 19, 2013
09/13

by
C. Karrasch

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We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this...

Source: http://arxiv.org/abs/1009.3852v1

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52

Sep 23, 2013
09/13

by
C. Karrasch; V. Meden

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We study a quantum dot Josephson junction inside an Aharonov-Bohm environment. The geometry is modeled by an Anderson impurity coupled to two directly-linked BCS leads. We illustrate that the well-established picture of the low-energy physics being governed by an interplay of two distinct (singlet and doublet) phases is still valid for this interferometric setup. The phase boundary depends, however, non-monotonically on the coupling strength between the superconductors, causing the system to...

Source: http://arxiv.org/abs/0810.3847v2

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6.0

Jun 30, 2018
06/18

by
C. Karrasch; D. Schuricht

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We analyze the dynamics of the return amplitude following a sudden quench in the three-state quantum Potts chain. For quenches crossing the quantum critical point from the paramagnetic to the ferromagnetic phase, the corresponding rate function is non-analytic at critical times and behaves linearly in their vicinity. In particular, we find no indication of a link between the time evolution close to the critical times and the scaling properties of the quantum critical point in the Potts chain.

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1701.04214

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Sep 22, 2013
09/13

by
C. Karrasch; D. Schuricht

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We investigate the dynamics following sudden quenches across quantum critical points belonging to different universality classes. Specifically, we use matrix product state methods to study the quantum Ising chain in the presence of two additional terms which break integrability. We find that in all models the rate function for the return probability to the initial state becomes a non-analytic function of time in the thermodynamic limit. This so-called `dynamical phase transition' was first...

Source: http://arxiv.org/abs/1302.3893v2

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8.0

Jun 27, 2018
06/18

by
C. Karrasch; J. E. Moore

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We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over $10^4$ samples for lattices as large as $10^{5}$ sites. We identify regimes in which non-ohmic power law...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1506.00972

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75

Sep 20, 2013
09/13

by
C. Karrasch; J. E. Moore

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We study one-dimensional spinless fermions at zero and finite temperature T using the density matrix renormalization group. We consider nearest as well as next-nearest neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system alogrithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power law suppression...

Source: http://arxiv.org/abs/1207.0011v2

3
3.0

Jun 30, 2018
06/18

by
D. M. Kennes; C. Karrasch

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We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications almost effortlessly within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schroedinger and Heisenberg time evolutions of arbitrary pure states |psi> and operators A in...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1404.3704

3
3.0

Jun 28, 2018
06/18

by
D. M. Kennes; C. Karrasch

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We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered non-interacting system, where for comparison we compute a quasi-exact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of L~100 sites and large bond dimensions chi~1700, which allows us to quantitatively...

Topics: Disordered Systems and Neural Networks, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1511.02205

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Jul 20, 2013
07/13

by
C. Karrasch; V. Meden; K. Schönhammer

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We illustrate how to calculate the finite-temperature linear-response conductance of quantum impurity models from the Matsubara Green function. A continued fraction expansion of the Fermi distribution is employed which was recently introduced by Ozaki [Phys. Rev. B 75, 035123 (2007)] and converges much faster than the usual Matsubara representation. We give a simplified derivation of Ozaki's idea using concepts from many-body condensed matter theory and present results for the rate of...

Source: http://arxiv.org/abs/1007.3403v2

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69

Sep 22, 2013
09/13

by
C. Karrasch; T. Enss; V. Meden

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We investigate the effect of local Coulomb correlations on electronic transport through a variety of coupled quantum dot systems connected to Fermi liquid leads. We use a newly developed functional renormalization group scheme to compute the gate voltage dependence of the linear conductance, the transmission phase, and the dot occupancies. A detailed derivation of the flow equations for the dot level positions, the inter-dot hybridizations, and the effective interaction is presented. For...

Source: http://arxiv.org/abs/cond-mat/0603510v2

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48

Sep 17, 2013
09/13

by
C. Karrasch; A. Oguri; V. Meden

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We investigate the Josephson current J(\phi) through a quantum dot embedded between two superconductors showing a phase difference \phi. The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U. We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature T_K and the superconducting energy gap \Delta or, at...

Source: http://arxiv.org/abs/0711.0671v2

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Jul 20, 2013
07/13

by
C. Karrasch; S. Andergassen; V. Meden

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We investigate two serially-aligned quantum dots in the molecular regime of large tunnel couplings t. A Zeeman field B is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap Delta and phase difference phi gives rise to an equilibrium supercurrent J. To compute J in presence of Coulomb interactions U between the dot electrons, we employ the functional renormalization group (FRG). For B\simt -- where the...

Source: http://arxiv.org/abs/1107.5837v2

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4.0

Jun 30, 2018
06/18

by
C. Karrasch; R. G. Pereira; J. Sirker

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We generalize nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. Analyzing density-matrix renormalization group results for the spin autocorrelation function in the XXZ chain we provide, in particular, direct evidence for spin diffusion in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory. Furthermore, we discuss how the frequencies and exponents of the oscillatory...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1410.2226

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Sep 23, 2013
09/13

by
Y. Huang; C. Karrasch; J. E. Moore

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Many low-dimensional materials are well described by integrable one-dimensional models such as the Hubbard model of electrons or the Heisenberg model of spins. However, the small perturbations to these models required to describe real materials are expected to have singular effects on transport quantities: integrable models often support dissipationless transport, while weak non-integrable terms lead to finite conductivities. We use matrix-product-state methods to obtain quantitative values of...

Source: http://arxiv.org/abs/1212.0012v2

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6.0

Jun 29, 2018
06/18

by
C. Karrasch; T. Prosen; F. Heidrich-Meisner

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Integrable models such as the spin-1/2 Heisenberg chain, the Lieb-Liniger or the one-dimensional Hubbard model are known to avoid thermalization, which was also demonstrated in several quantum-quench experiments. Another dramatic consequence of integrability is the zero-frequency anomaly in transport coefficients, which results in ballistic finite-temperature transport, despite the presence of strong interactions. While this aspect of nonergodic dynamics has been known for a long time, there...

Topics: Quantum Physics, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1611.04832

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62

Sep 18, 2013
09/13

by
C. Karrasch; R. Ilan; J. E. Moore

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We study the real-time dynamics of spin chains driven out of thermal equilibrium by an initial temperature gradient T_L \neq T_R using density matrix renormalization group methods. We demonstrate that the nonequilibrium energy current saturates fast to a finite value if the linear-response thermal conductivity is infinite, i.e. if the Drude weight D is nonzero. Our data suggests that a nonintegrable dimerized chain might support such dissipationless transport (D>0). We show that the...

Source: http://arxiv.org/abs/1211.2236v2

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6.0

Jun 30, 2018
06/18

by
C. Karrasch; D. M. Kennes; F. Heidrich-Meisner

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We study the spin and thermal conductivity of spin-1/2 ladders at finite temperature. This is relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-1/2 XXZ...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1412.6047

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149

Sep 23, 2013
09/13

by
C. Karrasch; J. H. Bardarson; J. E. Moore

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We propose an easily implemented approach to study time-dependent correlation functions of one dimensional systems at finite temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long time behavior of current correlation...

Source: http://arxiv.org/abs/1111.4508v2

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Jun 28, 2018
06/18

by
C. Karrasch; D. M. Kennes; F. Heidrich-Meisner

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We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interactions and moreover, we compute its filling dependence at infinite temperature. The finite-frequency contributions originating from the fact that the energy current is...

Topics: Quantum Physics, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1506.05788

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57

Sep 23, 2013
09/13

by
C. Karrasch; J. H. Bardarson; J. E. Moore

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Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical operator. We demonstrate how the numerical effort of such calculations is reduced when the physical time evolution is augmented by an additional time evolution within the auxiliary Hilbert space. Specifically, we explore a variety of integrable and non-integrable,...

Source: http://arxiv.org/abs/1303.3942v2

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Sep 20, 2013
09/13

by
C. Karrasch; J. Rentrop; D. Schuricht; V. Meden

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We provide strong evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: The leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our...

Source: http://arxiv.org/abs/1205.2091v1

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4.0

Jun 30, 2018
06/18

by
C. Karrasch; D. M. Kennes; J. E. Moore

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We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is two-fold: First, we compute both the charge and the spin current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity sigma(omega) in presence of small integrability-breaking next-nearest...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1408.1891

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50

Sep 21, 2013
09/13

by
C. Karrasch; J. Hauschild; S. Langer; F. Heidrich-Meisner

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We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementrary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical...

Source: http://arxiv.org/abs/1301.6401v2

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63

Sep 23, 2013
09/13

by
D. M. Kennes; S. G. Jakobs; C. Karrasch; V. Meden

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We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a nonequilibrium initial state into a (potentially) steady state driven by a bias voltage and (ii) the dynamics governed by an explicitly time-dependent Hamiltonian. All time regimes from transient to asymptotic can be tackled; the only approximation is the...

Source: http://arxiv.org/abs/1111.6982v1

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Sep 18, 2013
09/13

by
C. Karrasch; R. Hedden; R. Peters; Th. Pruschke; K. Schönhammer; V. Meden

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We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle vertex in order to address finite-energy properties (e.g, spectral functions). By comparing with data obtained from the numerical renormalization group (NRG) framework, the FRG approximation is shown to work well for arbitrary parameters (particularly finite...

Source: http://arxiv.org/abs/0806.0246v2

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Sep 23, 2013
09/13

by
V. Kashcheyevs; C. Karrasch; T. Hecht; A. Weichselbaum; V. Meden; A. Schiller

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Understanding the charging of exceptionally narrow levels in quantum dots in the presence of interactions remains a challenge within mesoscopic physics. We address this fundamental question in the generic model of a narrow level capacitively coupled to a broad one. Using bosonization we show that for arbitrary capacitive coupling charging can be described by an analogy to the magnetization in the anisotropic Kondo model, featuring a low-energy crossover scale that depends in a power-law fashion...

Source: http://arxiv.org/abs/0810.2538v2

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6.0

Jun 29, 2018
06/18

by
D. M. Kennes; J. C. Pommerening; J. Diekmann; C. Karrasch; V. Meden

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We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic (`gapless') fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as...

Topics: Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1610.03284

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Sep 20, 2013
09/13

by
C. Karrasch; T. Hecht; A. Weichselbaum; J. von Delft; Y. Oreg; V. Meden

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We investigate the appearance of pi lapses in the transmission phase theta of a two-level quantum dot with Coulomb interaction U. Using the numerical and functional renormalization group methods we study the entire parameter space for spin-polarized as well as spin-degenerate dots, modeled by spinless or spinful electrons, respectively. We investigate the effect of finite temperatures T. For small T and sufficiently small single-particle spacings delta of the dot levels we find pi phase lapses...

Source: http://arxiv.org/abs/cond-mat/0612490v1

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Jul 20, 2013
07/13

by
C. Karrasch; T. Hecht; A. Weichselbaum; Y. Oreg; J. von Delft; V. Meden

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Transmission phase \alpha measurements of many-electron quantum dots (small mean level spacing \delta) revealed universal phase lapses by \pi between consecutive resonances. In contrast, for dots with only a few electrons (large \delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multi-level quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal...

Source: http://arxiv.org/abs/cond-mat/0609191v3

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Sep 23, 2013
09/13

by
S. Becker; C. Karrasch; T. Mashoff; M. Pratzer; M. Liebmann; V. Meden; M. Morgenstern

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Using low-temperature scanning tunneling spectroscopy applied to the Cs-induced two-dimensional electron system (2DES) on p-type InSb(110), we probe electron-electron interaction effects in the quantum Hall regime. The 2DES is decoupled from p-doped bulk states and exhibits spreading resistance within the insulating quantum Hall phases. In quantitative agreement with calculations we find an exchange enhancement of the spin splitting. Moreover, we observe that both the spatially averaged as well...

Source: http://arxiv.org/abs/1012.1968v2

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Sep 23, 2013
09/13

by
A. Eichler; R. Deblock; M. Weiss; C. Karrasch; V. Meden; C. Schonenberger; H. Bouchiat

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We investigate the Josephson current in a single wall carbon nanotube connected to superconducting electrodes. We focus on the parameter regime in which transport is dominated by Kondo physics. A sizeable supercurrent is observed for odd number of electrons on the nanotube when the Kondo temperature Tk is sufficiently large compared to the superconducting gap. On the other hand when, in the center of the Kondo ridge, Tk is slightly smaller than the superconducting gap, the supercurrent is found...

Source: http://arxiv.org/abs/0810.1671v2