arXiv subjects

A. O. Gogolin

Publications and source records attributed to A. O. Gogolin.

At least 19 recordsLinked to original sources

arXiv2009

Phonon-phonon interactions and phonon damping in carbon nanotubes

We formulate and study the effective low-energy quantum theory of interacting long-wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory. A general and analytical derivation of all three- and four-phonon processes is provided, and the relevant coupling constants are determined in terms of few elastic coefficients. Due to the low dimensionality and the parabolic dispersion, the finite-temperature density of noninteracting flexural phonons diverges, and a nonperturbative approach to their interactions is necessary. Within a mean-field description, we find that a dynamical gap opens. In practice, this gap is thermally smeared, but still has important consequences. Using our theory, we compute the decay rates of acoustic phonons due to phonon-phonon and electron-phonon interactions, implying upper bounds for their quality factor.

cond-mat.mes-hall↗

arXiv2008

Interaction-induced harmonic frequency mixing in quantum dots

We show that harmonic frequency mixing in quantum dots coupled to two leads under the influence of time-dependent voltages of different frequency is dominated by interaction effects. This offers a unique and direct spectroscopic tool to access correlations, and holds promise for efficient frequency mixing in nano-devices. Explicit results are provided for an Anderson dot and for a molecular level with phonon-mediated interactions.

cond-mat.mes-hall↗

arXiv2008

Counting statistics for the Anderson impurity model: Bethe ansatz and Fermi liquid study

We study the counting statistics of charge transport in the Anderson impurity model (AIM) employing both Keldysh perturbation theory in a Fermi liquid picture and the Bethe ansatz. In the Fermi liquid approach, the object of our principal interest is the generating function for the cumulants of the charge current distribution. We derive an exact analytic formula relating the full counting statistic (FCS) generating function to the self-energy of the system in the presence of a measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM perturbatively in the Coulomb interaction. By comparing this perturbative analysis with a strong coupling expansion, we arrive at a conjecture for an expression for the FCS generating function at O(V^3) (V is the voltage across the impurity) valid at all orders in the interaction. In the second part of the article, we examine a Bethe ansatz analysis of the current noise for the AIM. Unlike the Fermi liquid approach, here the goal is to obtain qualitative, not quantitative, results for a wider range of voltages both in and out of a magnetic field. Particularly notable are finite field results showing a double peaked structure in the current noise for voltages satisfying eV ~ mu H$. This double peaked structure is the ``smoking gun'' of Kondo physics in the current noise and is directly analogous to the single peak structure predicted for the differential conductance of the AIM.

cond-mat.mes-hall↗

arXiv2008

Vibration-induced correction to the current through a single molecule

We provide analytical results for the perturbative correction to the current-voltage relation through a vibrating molecule for weak electron-phonon coupling. The nonlinear conductance exhibits a step-like feature at $eV=\hbar ω_0$, where $ω_0$ is the vibration frequency. We establish criteria for the sign change of the step in the conductance (up or down). This transition turns out to be nonuniversal and is governed by essentially all system parameters.

cond-mat.mes-hall↗

arXiv2007

Full counting statistics of spin transfer through ultrasmall quantum dots

We analyze the spin-resolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modelling the setup by the Anderson Hamiltonian, we explicitly take into account the onsite Coulomb repulsion $U$. We calculate the cumulant generating function for the probability to transfer a certain number of electrons with a preselected spin orientation during a fixed time interval. With the cumulant generating function at hand we are then able to calculate the spin current correlations which are of outmost importance in the emerging field of spintronics. We confirm the existing results for the charge statistics and report the discovery of the new type of correlation between the spin-up and -down polarized electrons flows, which has a potential to become a powerful new instrument for the investigation of the Kondo effect in nanostructures.

cond-mat.mes-hall↗

arXiv2007

Full counting statistics of spin transfer through the Kondo dot

We calculate the spin current distribution function for a Kondo dot in two different regimes. In the exactly solvable Toulouse limit the linear response, zero temperature statistics of the spin transfer is trinomial, such that all the odd moments vanish and the even moments follow a binomial distribution. On the contrary, the corresponding spin-resolved distribution turns out to be binomial. The combined spin and charge statistics is also determined. In particular, we find that in the case of a finite magnetic field or an asymmetric junction the spin and charge measurements become statistically dependent. Furthermore, we analyzed the spin counting statistics of a generic Kondo dot at and around the strong-coupling fixed point (the unitary limit). Comparing these results with the Toulouse limit calculation we determine which features of the latter are generic and which ones are artifacts of the spin symmetry breaking.

cond-mat.mes-hall↗

arXiv2006

Hanbury-Brown-Twiss correlations and noise in the charge transfer statistics through a multiterminal Kondo dot

We analyze the full counting statistics of charge transfer through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. At the unitary Kondo fixed point and for N>2 we recover distinct anticorrelations of currents in concurring transport channels, which are related to the fermionic Hanbury Brown and Twiss (HBT) antibunching. This effect weakens as one moves away from the fixed point. Furthermore, we identify a special class of current correlations that are due entirely to the virtual polarization of the Kondo singlet. These can be used for extracting information on the parameters of the underlying Fermi-liquid model.

cond-mat.str-el↗

arXiv2006

Full counting statistics for the Kondo dot in the unitary limit

We calculate the charge transfer probability distribution function $χ(λ)$ for the Kondo dot in the strong coupling limit within the framework of the Nozières--Fermi--liquid theory of the Kondo effect. At zero temperature, the ratio of the moments $C_n$ of the charge distribution to the backscattering current $I_{\rm bs}$ follows a universal law $C_n/2I_{\rm bs}=(-1)^n(1+2^n)/6$. The functional form of $χ(λ)$ is consistent with tunnelling of electrons and, possibly, electron pairs. We then discuss the cross-over behaviour of $χ(λ)$ from weak to strong Coulomb repulsion in the underlying Anderson impurity model and relate this to the existing results. Finally, we extend our analysis to the case of finite temperatures.

cond-mat.mes-hall↗

arXiv2005

Towards full counting statistics for the Anderson impurity model

We analyse the full counting statistics (FCS) of the charge transport through the Anderson impurity model (AIM) and similar systems with a single conducting channel. The object of principal interest is the generating function for the cumulants of charge current distribution. We derive an exact analytic formula relating the FCS generating function to the self energy of the system in the presence of the measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM both perturbatively in the Coulomb interaction and in the Kondo regime at the Toulouse point (we also study a related model of a spinless single-site quantum dot coupled to two half-infinite metallic leads in the Luttinger liquid phase at a special interaction strength). At zero temperature the FCS turns out to be binomial for small voltages. For the generic case of arbitrary energy scales the FCS is shown to be captured very well by generalisations of the Levitov-Lesovik type formula. Surprisingly, the FCS for the AIM indicates a presence of coherent electron pair tunnelling in addition to conventional single-particle processes. By means of perturbative expansions around the Toulouse point we succeeded in showing the universality of the binomial FCS at zero temperature in linear response. Based on our general formula for the FCS we then argue for a more general binomial theorem stating that the linear response zero-temperature FCS for any interacting single-channel set-up is always binomial.

cond-mat.mes-hall↗

arXiv2005

Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length $a_{aa}$ displays a confinement-induced resonance. We compute the dimer-dimer scattering length $a_{dd}$, and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.

cond-mat.stat-mech↗

arXiv2005

Three-body problem for ultracold atoms in quasi-one-dimensional traps

We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\perp$. For this quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$, and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.

cond-mat.stat-mech↗

arXiv2005

Full counting statistics for the Kondo dot

The generating function for the cumulants of charge current distribution is calculated for two generalised Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter $g=1/2$. We find that the low--temperature non-equilibrium transport in the Kondo case occurs via tunnelling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant (`skewness') explicitly and analyse it for different couplings, temperatures, and magnetic fields. For the $g=1/2$ set-up the statistics simplifies and is given by a modified version of the Levitov--Lesovik formula.

cond-mat.str-el↗

arXiv2004

Atom-dimer scattering for confined ultracold fermion gases

We solve the three-body problem of an ultracold Fermi gas with parabolic confinement length $a_\perp$ and 3D scattering length $a$. On the two-body level, there is a Feshbach-type resonance at $a_\perp/a\approx 1.46$, and a dimer state for arbitrary $a_\perp/a$. The three-body problem is shown to be universal, an d described by the atom-dimer scattering length $a_{ad}$ and a range parameter $b_{ad}$. In the dimer limit $a_\perp/a\gg 1$, we find a repulsive zero-range atom-dimer interaction. For $a_\perp/a\ll -1$, however, the potential has long range, with $a_{ad}>0$ and $b_{ad}\gg a_{ad}$. There is no trimer state, and despite $a_{ad}=0$ at $a_\perp/a\approx 2.6$, there is no resonance enhancement of the interaction.

cond-mat.stat-mech↗

arXiv2004

Mean-field results on the Anderson impurity model out of equilibrium

We investigate the mean-field phase diagram of the Anderson impurity model out of equilibrium. Generalising the unrestricted Hartree-Fock approach to the non-equilibrium situation we derive and analyse the system of equations defining the critical surface separating the magnetic regime from the non-magnetic one. An exact analytic solution for the phase boundary as a function of the applied voltage is found in the symmetric case. Surprisingly, we find that as soon as there is an asymmetry, even small, between the contacts, no finite voltage is able to destroy the magnetic regime which persists at arbitrary high voltages.

cond-mat.mes-hall↗

arXiv2004

Resonant tunnelling in interacting 1D systems with an AC modulated gate

We present an analysis of transport properties of a system consisting of two half-infinite interacting one-dimensional wires connected to a single fermionic site, the energy of which is subject to a periodic time modulation. Using the properties of the exactly solvable Toulouse point we derive an integral equation for the localised level Keldysh Green's function which governs the behaviour of the linear conductance. We investigate this equation numerically and analytically in various limits. The period-averaged conductance G displays a surprisingly rich behaviour depending on the parameters of the system. The most prominent feature is the emergence of an intermediate temperature regime at low frequencies, where G is proportional to the line width of the respective static conductance saturating at a non-universal frequency dependent value at lower temperatures.

cond-mat.mes-hall↗

arXiv2003

Rashba coupling in quantum dots: exact solution

We present an analytic solution to the problem of the Rashba spin-orbit coupling in semiconductor quantum dots. We calculate the exact energy spectrum, wave-functions, and spin--flip relaxation times. We discuss various effects inaccessible via perturbation theory. In particular, we find that the effective gyromagnetic ratio is strongly suppressed by the spin-orbit coupling. The spin-flip relaxation rate has a maximum as a function of the spin-orbit coupling and is therefore suppressed in both the weak- and strong coupling limits.

cond-mat.str-el↗

arXiv2003

Transport, optical properties and quantum ratchet effects for quantum dots and molecules coupled to Luttinger liquids

We present non-perturbative solutions for multi-level quantum dot structures coupled to interacting one-dimensional electrodes out of equilibrium. At a special correlation strength the Hamiltonian can be mapped to the Kondo problem which possesses a solvable Toulouse point, where all conductance and noise properties can be calculated exactly. Special attention is paid to the fully asymmetric setup when each dot level is coupled to only one of the leads and the electron transport through the structure is accompanied by photon absorption (emission). A relation between the optical spectra and the energy dependent current noise power is established. Experimental implications of the results, specifically for the Fano factor, the ratchet current, and field emission via localised states, are discussed. In particular, we predict that the peak in the ratchet current as function of the irradiation frequency splits up in two due to correlation effects.

cond-mat.str-el↗

arXiv2002

Resonant tunnelling between Luttinger liquids: solvable case

We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonisation and re-fermionisation methods, we find a mapping to a Kondo-type problem which possesses a non-trivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the non-linear current-voltage characteristics and analyse the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.

cond-mat.str-el↗