arXiv subjects

H. Grabert

Publications and source records attributed to H. Grabert.

At least 19 recordsLinked to original sources

arXiv2011

Defect-induced multicomponent electron scattering in single-walled carbon nanotubes

We present a detailed comparison between theoretical predictions on electron scattering processes in metallic single-walled carbon nanotubes with defects and experimental data obtained by scanning tunneling spectroscopy of Ar$^+$ irradiated nanotubes. To this purpose we first develop a formalism for studying quantum transport properties of defected nanotubes in presence of source and drain contacts and an STM tip. The formalism is based on a field theoretical approach describing low-energy electrons. We account for the lack of translational invariance induced by defects within the so called extended kp approximation. The theoretical model reproduces the features of the particle-in-a-box-like states observed experimentally. Further, the comparison between theoretical and experimental Fourier-transformed local density of state maps yields clear signatures for inter- and intra-valley electron scattering processes depending on the tube chirality.

cond-mat.mes-hall↗

arXiv2009

Massless Dirac-Weyl Fermions in a T_3 Optical Lattice

We propose an experimental setup for the observation of quasi-relativistic massless Fermions. It is based on a T_3 optical lattice, realized by three pairs of counter-propagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the T_3 Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudo-spin S=1. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.

cond-mat.quant-gas↗

arXiv2009

Electron Scattering in Intrananotube Quantum Dots

Intratube quantum dots showing particle-in-a-box-like states with level spacings up to 200meV are realized in metallic single-walled carbon nanotubes by means of low dose medium energy Ar irradiation. Fourier transform scanning tunneling spectroscopy compared to results of a Fabry-Perot electron resonator model yields clear signatures for inter- and intra-valley scattering of electrons confined between consecutive irradiation-induced defects (inter-defects distance < 10nm). Effects arising from lifting the degeneracy of the Dirac cones within the first Brillouin zone are also observed.

cond-mat.mes-hall↗

arXiv2007

Electronic and atomic shell structure in aluminum nanowires

We report experiments on aluminum nanowires in ultra-high vacuum at room temperature that reveal a periodic spectrum of exceptionally stable structures. Two "magic" series of stable structures are observed: At low conductance, the formation of stable nanowires is governed by electronic shell effects whereas for larger contacts atomic packing dominates. The crossover between the two regimes is found to be smooth. A detailed comparison of the experimental results to a theoretical stability analysis indicates that while the main features of the observed electron-shell structure are similar to those of alkali and noble metals, a sequence of extremely stable wires plays a unique role in Aluminum. This series appears isolated in conductance histograms and can be attributed to "superdeformed" non-axisymmetric nanowires.

cond-mat.mes-hall↗

arXiv2007

Negativity of the excess noise in a quantum wire capacitively coupled to a gate

The electrical current noise of a quantum wire is expected to increase with increasing applied voltage. We show that this intuition can be wrong. Specifically, we consider a single channel quantum wire with impurities and with a capacitive coupling to nearby metallic gates and find that its excess noise, defined as the change in the noise caused by the finite voltage, can be negative at zero temperature. This feature is present both for large ($c \gg c_q$) and small ($c \ll c_q$) capacitive coupling, where $c$ is the geometrical and $c_q$ the quantum capacitance of the wire. In particular, for $c \gg c_q$, negativity of the excess noise can occur at finite frequency when the transmission coefficients are energy dependent, i.e. in the presence of Fabry-Pérot resonances or band curvature. In the opposite regime $c \lesssim c_q$, a non trivial voltage dependence of the noise arises even for energy independent transmission coefficients: at zero frequency the noise decreases with voltage as a power law when $c < c_q/3$, while, at finite frequency, regions of negative excess noise are present due to Andreev-type resonances.

cond-mat.str-el↗

arXiv2006

Cohesion, Conductance, and Charging Effects in a Metallic Nanocontact

The conducting and thermodynamic properties of ballistic metallic nanocontacts with smooth shapes are investigated. All properties are related to the electronic scattering matrix, which is evaluated in the WKB approximation for independent electrons and in the self-consistent Hartree approximation for interacting electrons. Mesoscopic oscillations of order 1nN in the cohesive force and of order e in the contact charge are predicted when a metallic nanocontact is pulled apart, which are synchronized with quantized jumps in the conductance.

cond-mat.mes-hall↗

arXiv2006

Universality in metallic nanocohesion: a quantum chaos approach

Convergent semiclassical trace formulae for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, are derived. It is shown that mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force: the amplitude of the oscillations depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1 nano-Newton, in agreement with recent experiments. Interestingly, quantum tunneling is shown to be described quantitatively in terms of the instability of the classical periodic orbits.

cond-mat.mes-hall↗

arXiv2005

Fractional charge in the noise of Luttinger liquid systems

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency v_F/gL, where v_F is the Fermi velocity, g the Luttinger liquid interaction parameter, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections of plasmons at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=e g of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.

cond-mat.mtrl-sci↗

arXiv2004

Appearance of fractional charge in the noise of non-chiral Luttinger liquids

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency $ω$ relative to the ballistic frequency $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Luttinger liquid interaction parameter, and $L$ the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge $e^*=e g$ of the bulk excitations.

cond-mat.str-el↗

arXiv2003

Long wavelength spatial oscillations of high frequency current noise in 1D electron systems

Finite frequency current noise is studied theoretically for a 1D electron system in presence of a scatterer. In contrast to zero frequency shot noise, finite frequency noise shows spatial oscillations at high frequencies with wavelength $πv_F/ω$. Band curvature leads to a decay of the amplitude of the noise oscillations as one moves away from the scatterer, superimposed by a beat. Furthermore, Coulomb interaction reduces the amplitude and modifies the wavelength of the oscillations, which we inspect in the framework of the Luttinger liquid (LL) model. The oscillatory noise contributions are only suppressed altogether when the LL interaction parameter $g \to 0$.

cond-mat.mes-hall↗

arXiv2002

Conductance of the single-electron transistor: A comparison of experimental data with Monte Carlo calculations

We report on experimental results for the conductance of metallic single-electron transistors as a function of temperature, gate voltage and dimensionless conductance. In contrast to previous experiments our transistor layout allows for a direct measurement of the parallel conductance and no ad hoc assumptions on the symmetry of the transistors are necessary. Thus we can make a comparison between our data and theoretical predictions without any adjustable parameter. Even for rather weakly conducting transistors significant deviations from the perturbative results are noted. On the other hand, path integral Monte Carlo calculations show remarkable agreement with experiments for the whole range of temperatures and conductances.

cond-mat.mes-hall↗

arXiv2002

Cohesion and Stability of Metal Nanowires: A Quantum Chaos Approach

A remarkably quantitative understanding of the electrical and mechanical properties of metal wires with a thickness on the scale of a nanometer has been obtained within the free-electron model using semiclassical techniques. Convergent trace formulas for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, are derived. Mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force, whose amplitude depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1nN, in agreement with experiments on gold nanowires. A linear stability analysis shows that the classical instability of a long wire under surface tension can be completely suppressed by quantum effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the conductance quantum, in accord with recent results on alkali metal nanowires.

cond-mat.mes-hall↗

arXiv2002

Exact c-number Representation of Non-Markovian Quantum Dissipation

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr{ö}dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born--Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.

cond-mat.stat-mech↗

arXiv2002

Magnetic field effects in energy relaxation mediated by Kondo impurities

We study the energy distribution function of quasiparticles in voltage biased mesoscopic wires in presence of magnetic impurities and applied magnetic field. The system is described by a Boltzmann equation where the collision integral is determined by coupling to spin 1/2 impurities. We derive an effective coupling to a dissipative spin system which is valid well above Kondo temperature in equilibrium or for sufficiently smeared distribution functions in non-equilibrium. For low magnetic field an enhancement of energy relaxation is found whereas for larger magnetic fields the energy relaxation decreases again meeting qualitatively the experimental findings by Anthore et al. (cond-mat/0109297). This gives a strong indication that magnetic impurities are in fact responsible for the enhanced energy relaxation in copper wires. The quantitative comparison, however, shows strong deviations for energy relaxation with small energy transfer whereas the large energy transfer regime is in agreement with our findings.

cond-mat.mes-hall↗

arXiv2002

Coulomb drag shot noise in coupled Luttinger liquids

Coulomb drag shot noise has been studied theoretically for 1D interacting electron systems, which are realized e.g. in single-wall nanotubes. We show that under adiabatic coupling to external leads, the Coulomb drag shot noise of two coupled or crossed nanotubes contains surprising effects, in particular a complete locking of the shot noise in the tubes. In contrast to Coulomb drag of the average current, the noise locking is based on a symmetry of the underlying Hamiltonian and is not limited to asymptotically small energy scales.

cond-mat.mes-hall↗

arXiv2001

Shot Noise in Schottky's Vacuum Tube

In these notes we discuss the origin of shot noise ('Schroteffekt') of vacuum tubes in detail. It will be shown that shot noise observed in vacuum tubes and first described by W. Schottky in 1918 is a purely classical phenomenon. This is in pronounced contrast to shot noise investigated in mesoscopic conductors which is due to quantum mechanical diffraction of electron waves.

cond-mat.mes-hall↗

arXiv2000

Static and dynamic image potential for tunneling into a Luttinger liquid

We study electron tunneling from a tip or a lead into an interacting quantum wire described by Luttinger liquid theory. Within a WKB-type approach, the Coulomb interaction between the wire and the tunneling electrons, as well as the finite traversal time are taken into account. Although the static image potential is only logarithmically suppressed against the bare Coulomb interaction, the dynamic image potential is not strong enough to alter power-law exponents entering the tunneling density of states.

cond-mat.str-el↗

arXiv2000

Current bistability and hysteresis in strongly correlated quantum wires

Nonequilibrium transport properties are determined exactly for an adiabatically connected single channel quantum wire containing one impurity. Employing the Luttinger liquid model with interaction parameter $g$, for very strong interactions $g\lapx 0.2$, and sufficiently low temperatures, we find an S-shaped current-voltage relation. The unstable branch with negative differential conductance gives rise to current oscillations and hysteretic effects. These non perturbative and non linear features appear only out of equilibrium.

cond-mat↗