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This theory is based on a linearization ... [more ▼]For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the low-energy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained. [less ▲]Detailed reference viewed: 126 (2 UL) Inelastic Electron Backscattering in a Generic Helical Edge ChannelSchmidt, Thomas ; Rachel, Stephan; von Oppen, Felix et alin Physical Review Letters (2012), 108We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single ... [more ▼]We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, $G T^4$. In addition, $G$ is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling. [less ▲]Detailed reference viewed: 103 (4 UL) Rydberg crystallization detection by statistical meansBreyel, D.; Schmidt, Thomas ; Komnik, A.in Physical Review. A (2012), 86We investigate an ensemble of atoms which can be excited into a Rydberg state. Using a disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the ... [more ▼]We investigate an ensemble of atoms which can be excited into a Rydberg state. Using a disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function $P(M)$ to create a certain number of Rydberg atoms $M$, as well as their pair-correlation function. Using the latter, we identify the critical interaction strength above which the system undergoes a phase transition to a Rydberg crystal. We then show that this phase transition can be detected using $P(M)$ alone. [less ▲]Detailed reference viewed: 84 (1 UL) Detecting Majorana bound states by nanomechanicsWalter, Stefan; Schmidt, Thomas ; Borkje, Kjetil et alin Physical Review. B (2011), 84We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a ... [more ▼]We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an s-wave superconductor. The detector makes use of an oscillating electrode, which can be realized using a doubly clamped metallic beam, tunnel coupled to one edge of the topological superconductor. We find that a measurement of the nonlinear differential conductance provides the necessary information to uniquely identify Majorana bound states. [less ▲]Detailed reference viewed: 98 (1 UL) Nanoscale investigations of the electronic surface properties of Cu(In,Ga)Se$_2$ thin films by scanning tunneling spectroscopyMönig, H.; Caballero, R.; Kaufmann, C. A. et alin Solar Energy Materials and Solar Cells (2011), 95In this work we investigate the electronic surface properties of polycrystalline Cu(In,Ga)Se$_2$ thin films by locally resolved scanning tunneling spectroscopy (STS). From current imaging tunneling ... [more ▼]In this work we investigate the electronic surface properties of polycrystalline Cu(In,Ga)Se$_2$ thin films by locally resolved scanning tunneling spectroscopy (STS). From current imaging tunneling spectroscopy (CITS) maps of an area of we observe distinct granular inhomogeneities, where current-voltage ($I(U)$) spectra differ from grain to grain and vary between metallic and semiconducting characteristics. Due to the high density of defect states at the Cu(In,Ga)Se$_2$ surface, the metallic $I(U)$ characteristics is not surprising. In the case of the semiconducting $I(U)$ characteristics, we suggest a preferential oxidation of particular grains, which passivates defect levels at the surface. This is supported by the presence of gallium and indium oxides detected by global X-ray photoelectron spectroscopy. Furthermore, we recorded $I(U)$ spectra from different grains under supra band gap laser illumination, which always show semiconducting characteristics. This behavior can be explained by a saturated occupation of defect states by photoexcited charge carriers. By evaluating differential conductance $(dI/dU)$ spectra under illumination from various grains, we estimate the average surface band gap to and compare the valence band onset with results from macroscopic ultraviolet photoelectron spectroscopy. The high lateral resolution of our CITS data allows also to study electronic properties at grain boundaries, which are discussed with regard to a recent STS study on a non-oxidized sample. [less ▲]Detailed reference viewed: 106 (4 UL) Current Correlations in Quantum Spin Hall InsulatorsSchmidt, Thomas in Physical Review Letters (2011), 107We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical ... [more ▼]We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the inter-edge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross-correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states. [less ▲]Detailed reference viewed: 100 (5 UL) Charge transfer statistics of a molecular quantum dot with strong electron-phonon interactionMaier, S.; Schmidt, Thomas ; Komnik, A.in Physical Review. B (2011), 83We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics. By using the ... [more ▼]We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics. By using the Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data, the formalism is shown to capture the basic properties of the strong-coupling regime. [less ▲]Detailed reference viewed: 98 (4 UL) Detection of qubit-oscillator entanglement in nanoelectromechanical systemsSchmidt, Thomas ; Borkje; Bruder, Christoph et alin Physical Review Letters (2010), 104Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an ... [more ▼]Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg uncertainty limit. Therefore, it is just a question of time before we will routinely see true quantum effects in nanomechanical systems. One of the hallmarks of quantum mechanics is the existence of entangled states. We propose a realistic scenario making it possible to detect entanglement of a mechanical resonator and a qubit in a nanoelectromechanical setup. The detection scheme is all done by standard current and noise measurements of an atomic point contact coupled to an oscillator and a qubit. This setup could allow for the first observation of entanglement between a continuous and a discrete quantum system in the solid state. [less ▲]Detailed reference viewed: 90 (1 UL) Fate of 1D Spin-Charge Separation Away from Fermi PointsSchmidt, Thomas ; Imambekov, Adilet; Glazman, Leonid I.in Physical Review Letters (2010), 104We consider the dynamic response functions of interacting one dimensional spin-$1/2$ fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using ... [more ▼]We consider the dynamic response functions of interacting one dimensional spin-$1/2$ fermions at arbitrary momenta. We build a nonperturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum. [less ▲]Detailed reference viewed: 90 (1 UL) Spin-charge separation in one-dimensional fermion systems beyond Luttinger liquid theorySchmidt, Thomas ; Imambekov, Adilet; Glazman, Leonid I.in Physical Review. B (2010), 82We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take ... [more ▼]We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take into account the nonlinearity of the fermion dispersion exactly. We calculate the power-law singularities of the spectral function and the charge- and spin-density structure factors for arbitrary momenta and interaction strengths. The exponents characterizing the singularities are functions of momenta and differ significantly from the predictions of the linear Luttinger liquid theory. We generalize the notion of the spin-charge separation to the nonlinear spectrum. This generalization leads to phenomenological relations between threshold exponents and the threshold energy. [less ▲]Detailed reference viewed: 92 (1 UL) Transport properties of a superconducting single-electron transistor coupled to a nanomechanical oscillatorKoerting, V.; Schmidt, Thomas ; Doiron, C. B. et alin Physical Review. B (2009), 79We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent ... [more ▼]We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper-pair tunneling events is shown to lead to pronounced back action effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor. [less ▲]Detailed reference viewed: 115 (3 UL) Transient dynamics of a molecular quantum dot with a vibrational degree of freedomRiwar, Roman-Pascal; Schmidt, Thomas in Physical Review. B (2009), 80We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In ... [more ▼]We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon interaction, we use perturbation theory to determine the time dependence of the dot population and the average current. The limit of strong coupling is accessed by means of a self-consistent time-dependent mean-field approximation. These complementary approaches allow us to investigate the dynamics of the inelastic effects occurring when the applied bias voltage exceeds the phonon frequency and the emergence of bistability. [less ▲]Detailed reference viewed: 88 (2 UL) Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedomSchmidt, Thomas ; Komnik, A.in Physical Review. B (2009), 80We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the ... [more ▼]We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the contributions due to quasielastic and inelastic transport processes in the cumulant generating function and discuss their influence on the transport properties of the dot. We find that in the low-energy sector, the inelastic term causes a sign change in the shot noise correction at certain universal values of the transmission. Furthermore, we show that when the correction to the current due to inelastic processes vanishes, all odd order cumulants vanish as well. [less ▲]Detailed reference viewed: 87 (4 UL) Transient dynamics of the Anderson impurity model out of equilibriumSchmidt, Thomas ; Werner, P.; Mühlbacher, L. et alin Physical Review. B (2008), 78We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the ... [more ▼]We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material. [less ▲]Detailed reference viewed: 97 (1 UL) Full counting statistics of spin transfer through the Kondo dotSchmidt, Thomas ; Gogolin, A. O.; Komnik, A.in Physical Review. B (2007), 75We 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 ... [more ▼]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. [less ▲]Detailed reference viewed: 118 (5 UL) Hanbury Brown--Twiss Correlations and Noise in the Charge Transfer Statistics through a Multiterminal Kondo DotSchmidt, Thomas ; Komnik, A.; Gogolin, A. O.in Physical Review Letters (2007), 98We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between ... [more ▼]We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between concurring transport channels, which show distinct Hanbury Brown?Twiss antibunching for N>2 reflecting the fermionic nature of charge carriers. While this effect weakens as one moves away from the Kondo fixed point, a new type of correlations between nonconcurring channels emerges which are due entirely to the virtual polarization of the Kondo singlet. As these are not obscured by the background from fixed-point correlations they provide a promising means for extracting information on the parameters of the underlying Fermi-liquid model from the experimental data. [less ▲]Detailed reference viewed: 105 (1 UL) Full counting statistics of spin transfer through ultrasmall quantum dotsSchmidt, Thomas ; Komnik, A.; Gogolin, A. O.in Physical Review. B (2007), 76We analyze the spin-resolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modeling the setup by the Anderson Hamiltonian, we explicitly ... [more ▼]We analyze the spin-resolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modeling the setup by the Anderson Hamiltonian, we explicitly take into account the on-site 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 utmost importance in the emerging field of spintronics. We confirm the existing results for the charge statistics and report the discovery of a different type of correlation between the spin-up and -down polarized electron flows, which has the potential to become a powerful instrument for the investigation of the Kondo effect in nanostructures. [less ▲]Detailed reference viewed: 109 (2 UL) Nonlinear transport through a dynamic impurity in a strongly interacting one-dimensional electron gasSchmidt, Thomas ; Komnik, A.in Physical Review. B (2007), 76We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to ... [more ▼]We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to the voltage sources. Assuming the impurity time dependence to be oscillatory, we present a full analytic perturbative result in impurity strength for arbitrary interaction parameter calculated with the help of Coulomb gas expansion (CGE). Moreover, a full analytic solution beyond the above restriction is possible for a special nontrivial interaction strength which has been achieved independently by full resummation of CGE series as well as via refermionization technique. The resulting nonlinear current-voltage characteristic turns out to be very rich due to the presence of the additional energy scale associated with the impurity oscillation frequency. In accordance with the previous studies, we also find an enhancement of the linear conductance of the wire to values above the unitary limit G0=2e2/h. [less ▲]Detailed reference viewed: 97 (1 UL) On the visibility of electron--electron interaction effects in field emission spectraSchmidt, Thomas ; Komnik, A.in Solid State Communications (2005), 135One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current $j(\omega)$ in field ... [more ▼]One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current $j(\omega)$ in field emission (FE) experiments. Its high energy tail $j_>(\omega)$ (above the Fermi edge) contains invaluable information about the nature of the electron--electron interactions inside the emitter. Thus far, $j_>(\omega)$ has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around $E_F$. We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of $j_>(\omega)$. We apply our results to the FE from Luttinger liquids and single-wall carbon nanotubes. [less ▲]Detailed reference viewed: 84 (1 UL)     1 2 3 4 5