Nonlinear Differential Conductance Research Articles

Tunneling spectroscopy between one-dimensional helical conductors

We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the nonlinear differential conductance as a function of the voltage bias between the conductors and the orbital momentum shift induced on tunneling electrons by an orthogonal magnetic field. We show that the conductance map exhibits an interference pattern which is characteristic to the interacting helical liquid. This can be contrasted with the different interference pattern from tunneling between regular Luttinger liquids which is governed by the spin-charge separation of the elementary collective excitations.

At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. --- We extend a recently-eveloped Fermi-liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora $et al.$, Phys. Rev. B, 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe Ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, $c_A$, describing its leading $\sim\varepsilon^2$ term, and the transport coefficients $c_V$ and $c_T$, describing the leading $\sim V^2$ and $\sim T^2$ terms in the nonlinear differential conductance. A sign change in $c_A$ or $c_V$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. We find that the fields $B_A$, $B_T$ and $B_V$ at which $c_A$, $c_T$ and $c_V$ change sign, respectively, are all of order $T_K$, as expected, with $B_A = B_T = B_V = 0.75073\,T_K$ in the Kondo limit.

At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

We extend a recently-developed Fermi-liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora et al., Phys. Rev. B, 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe Ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, $c_A$, describing its leading $\sim \varepsilon^2$ term, and the transport coefficients $c_V$ and $c_T$, describing the leading $\sim V^2$ and $\sim T^2$ terms in the nonlinear differential conductance. A sign change in $c_A$ or $c_V$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. Surprisingly, we find that the fields $B_A$ and $B_V$ at which $c_A$ and $c_V$ change sign are parametrically different, with $B_A$ of order $T_K$ but $B_V$ much larger. In fact, in the Kondo limit $c_V$ never vanishes, implying that the conductance retains a (weak) zero-bias maximum even for strong magnetic field and that the two finite-bias conductance side peaks caused by the Zeeman splitting of the local level do not emerge from zero bias voltage.

Functional renormalization group study of the Anderson–Holstein model

We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode.

Bistability and nonlinear negative differential conductance in semiconductor superlattices illuminated by laser light

We have experimentally and theoretically investigated negative differential conductance regions in the current-voltage characteristic of undoped semiconductor superlattice surrounded by barriers and illuminated by laser light. The negative differential conductances are nonlinear and show bistable behavior as a function of the applied voltage. These phenomena are quantitatively described by a self-consistent analysis of the field-dependent Wannier-Stark absorption and accumulation of photocarriers in the presence of barriers at the superlattice borders.

Detecting Majorana bound states by nanomechanics

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.

Many-body enhanced nonlinear conductance resonance in quantum channels

We measure a strong enhancement of the nonlinear differential conductance ($g=dI/dV$), the amplitude of which exceeds the universal quantum conductance ($2{e}^{2}/h$), under finite bias voltage in quantum point contacts (QPCs). By developing a spin-based model in the low-electron-density limit, we demonstrate that this resonance is an intrinsic nonequilibrium phenomenon that arises from many-body induced modifications to the QPC potential. A comparison with the linear conductance ($G=I/V$) shows that this phenomenon is driven by many-body dynamics within a single one-dimensional sub-band.

Kramers polarization in strongly correlated carbon nanotube quantum dots

Ferromagnetic contacts put in proximity with carbon nanotubes induce spin and orbital polarizations. These polarizations affect dramatically the Kondo correlations occurring in quantum dots formed in a carbon nanotube, inducing effective fields in both spin and orbital sectors. As a consequence, the carbon nanotube quantum dot spectral density shows a four-fold split SU(4) Kondo resonance. Furthermore, the presence of spin-orbit interactions leads to the occurrence of an additional polarization among time-reversal electronic states (polarization in the time-reversal symmetry or Kramers sector). Here, we estimate the magnitude for the Kramer polarization in realistic carbon nanotube samples and find that its contribution is comparable to the spin and orbital polarizations. The Kramers polarization generates a new type of effective field that affects only the time-reversal electronic states. We report new splittings of the Kondo resonance in the dot spectral density which can be understood only if Kramers polarization is taken into account. Importantly, we predict that the existence of Kramers polarization can be experimentally detected by performing nonlinear differential conductance measurements. We also find that, due to the high symmetry required to build SU(4) Kondo correlations, its restoration by applying an external field is not possible in contrast to the compensated SU(2) Kondo state observed in conventional quantum dots.

Inelastic tunneling of electrons through a quantum dot with an embedded single molecular magnet

We report a theoretical analysis of electron transport through a quantum dot with an embedded biaxial single-molecule magnet (SMM) based on mapping of the many-body interaction-system onto a one-body problem by means of the non-equilibrium Green function technique. It is found that the conducting current exhibits a stepwise behavior and the nonlinear differential conductance displays additional peaks with variation of the sweeping speed and the magnitude of magnetic field. This observation can be interpreted by the interaction of electron-spin with the SMM and the quantum tunneling of magnetization. The inelastic conductance and the corresponding tunneling processes are investigated with normal as well as ferromagnetic electrodes. In the case of ferromagnetic configuration, the coupling to the SMM leads to an asymmetric tunneling magnetoresistance (TMR), which can be enhanced or suppressed greatly in certain regions. Moreover, a sudden TMR-switch with the variation of magnetic field is observed, which is seen to be caused by the inelastic tunneling.

Phonon-assisted Kondo effect in single-molecule quantum dots coupled to ferromagnetic leads

Based on the infinite- U Anderson model spin-polarized transport through the tunnel magnetoresistance (TMR) system of single-molecule quantum dot is investigated under the interplay of strong electron correlation and electron–phonon (e–ph) coupling. The spectral density and the nonlinear differential conductance are studied using the extended non-equilibrium Green's function method through calculating the dot-level splitting self-consistently. The results exhibit that a serial of peaks emerge on the two sides of the main Kondo peak for the antiparallel magnetic configuration of electrodes, while for the parallel case both the main and phonon-assisted satellite Kondo peaks all split up into two asymmetric peaks even at zero-bias. Correspondingly, the nonlinear differential conductance displays a set of satellite-peaks around the Kondo-peak in the presence of the e–ph interaction. Furthermore, extra maxima and minima appear in the TMR curve. The TMR alternates between the positive and the negative values along with the variation of bias voltage.

Linear and nonlinear conductance of ballistic quantum wires with hybrid confinement

We characterize the linear and nonlinear electron transport in quantum point contacts (QPCs) realized by a hybrid combination of etching and gating. We demonstrate that the strong electron confinement generated through this hybrid QPC process results in quantized subbands with a large energy separation, leading to the observation of robust one-dimensional quantum-transport effects. Measurements of the nonlinear differential conductance reveal an unexpected bunching of curves at 0.20−0.25×2e2/h, rather than at the expected value of 0.5×2e2/h. Application of a simple analytical model indicates that this bunching is associated with the highly asymmetric manner in which the source-drain voltage is dropped across the QPC near pinch-off and under nonequilibrium conditions.

Quantum interference and Coulomb correlation effects in spin-polarized transport through two coupled quantum dots

Spin-dependent transport through two coupled single-level quantum dots attached to ferromagnetic leads with collinear (parallel and antiparallel) magnetizations is analyzed theoretically by the nonequilibrium Green function technique. Transport characteristics, in particular, linear and nonlinear differential conductance and tunnel magnetoresistance associated with the magnetization rotation from antiparallel to parallel alignment, are calculated numerically with intradot Coulomb interaction taken into account. The relevant Green functions are derived by the equation of motion method within the Hartree-Fock decoupling scheme. The dot occupations and Green functions are calculated self-consistently, and the numerical analysis is focused on the interference (Fano antiresonance) and Coulomb interaction effects. It is shown that the presence of Fano antiresonance depends on the sign of the nondiagonal coupling elements.

Nonequilibrium Kondo effect in a quantum dot coupled to ferromagnetic leads

We study the Kondo effect in the electron transport through a quantum dot coupled to ferromagnetic leads, using a real-time diagrammatic technique that provides a systematic description of the nonequilibrium dynamics of a system with strong local electron correlations. We evaluate the theory in an extension of the ``resonant tunneling approximation,'' introduced earlier, by introducing the self-energy of the off-diagonal component of the reduced propagator in spin space. In this way we develop a charge and spin conserving approximation that accounts not only for Kondo correlations but also for the spin splitting and spin accumulation out of equilibrium. We show that the Kondo resonances, split by the applied bias voltage, may be spin polarized. A left-right asymmetry in the coupling strength and/or spin polarization of the electrodes significantly affects both the spin accumulation and the weight of the split Kondo resonances out of equilibrium. The effects are observable in the nonlinear differential conductance. We also discuss the influence of decoherence on the Kondo resonance in the frame of the real-time formulation.

Inelastic Scattering and Local Heating in Atomic Gold Wires

We present a method for including inelastic scattering in a first-principles density-functional computational scheme for molecular electronics. As an application, we study two geometries of four-atom gold wires corresponding to two different values of strain and present results for nonlinear differential conductance vs device bias. Our theory is in quantitative agreement with experimental results and explains the experimentally observed mode selectivity. We also identify the signatures of phonon heating.

Spin valve effect in electronic transport through quantum dots

Spin polarized transport through a quantum dot coupled to two ferromagnetic leads is analyzed theoretically by the non-equilibrium Green function technique. The relevant correlation and retarded (advanced) Green functions have been calculated within a consistent approach in the Hartree-Fock approximation. Magnetic configuration of the system can vary continuously from parallel to antiparallel alignment of the electrode magnetizations. When coupling of the dot to the leads is spin dependent, transport characteristics depend on the angle between magnetic moments of the leads. Nonlinear transport characteristics, including conductance, differential conductance and tunnel magnetoresistance have been analyzed numerically.

Low-temperature transport through a quantum dot between two superconductor leads

We consider a quantum dot coupled to two BCS superconductors with same gap energies $\Delta$. The transport properties are investigated by means of infinite-$U$ noncrossing approximation. In equilibrium density of states, Kondo effect shows up as two sharp peaks around the gap bounds. Application of a finite voltage bias leads these peaks to split, leaving suppressed peaks near the edges of energy gap of each lead. The clearest signatures of the Kondo effect in transport are three peaks in the nonlinear differential conductance: one around zero bias, another two at biases $\pm 2\Delta$. This result is consistent with recent experiment. We also predict that with decreasing temperature, the differential conductances at biases $\pm 2\Delta$ anomalously increase, while the linear conductance descends.

Photon-phonon-assisted tunneling through a single-molecule quantum dot

Based on exactly mapping of a many-body electron-phonon interaction problem onto a one-body problem, we apply the well-established nonequilibrium Green function technique to solve the time-dependent phonon-assisted tunneling at low temperature through a single-molecular quantum dot connected to two leads, which is subject to a microwave irradiation field. It is found that in the presence of the electron-phonon interaction and the microwave irradiation field, the time-average transmission and the nonlinear differential conductance display additional peaks due to pure photon absorption or emission processes and photon-absorption-assisted phonon emission processes. The variation of the time-average current with frequency of the microwave irradiation field is also studied.

Kondo-type transport through an interacting quantum dot coupled to ferromagneticleads

We investigate the equilibrium and out-of-equilibrium Kondo effects in a single-levelinteracting quantum dot connected to two ferromagnetic leads. Within the noncrossingapproximation, we calculate the total density of states (DOS), the linear conductance andthe nonlinear differential conductance for both the parallel and the antiparallel alignmentsof the spin polarization orientation in the leads, followed by a brief discussionregarding the validity of this approach. Numerical calculations show that, for theantiparallel alignment, a single Kondo peak always appears in the equilibriumDOS, resulting in conventional temperature behaviour in the linear conductanceand the zero-bias maximum in the differential conductance. The strength of theDOS peak is gradually suppressed with increasing polarization, due to the factthat formation of the Kondo-correlated state is more difficult in the presence ofhigher polarization. In contrast, for the parallel configuration the Kondo peak inthe DOS descends precipitately and splits into two peaks to form a very steepvalley between them. This splitting contributes to the appearance of a ‘hump’ inthe temperature-dependent linear conductance and a nonzero-bias maximum inthe differential conductance. Moreover, application of a bias voltage can spliteach Kondo peak into two in the nonequilibrium DOS for both configurations.Finally we point out that the tunnel magnetoresistance could be an effective tool todemonstrate the different Kondo effects in the different spin configurations found here.

Consistent picture of strong electron correlation from magnetoresistance and tunneling conductance measurements in multiwall carbon nanotubes

Both the magnetoconductance and the nonlinear differential conductance of multiwall carbon nanotube ropes have been studied at low temperture. Suppression in the differential conductance was observed at low bias voltages and at low temperatures, indicating the formation of a Coulomb gap. The magnetoconductance was found to follow a scaling law at both high and low temperatures, but with different mechanisms. The analysis of the data provides a sign of a non-Fermi-liquid-like behavior through magnetotransport measurement.

Self-consistent theory of current and voltage noise in multimode ballistic conductors

Electron transport in a self-consistent potential along a ballistic two-terminal conductor has been investigated. We have derived general formulas which describe the nonlinear current-voltage characteristics, differential conductance, and low-frequency current and voltage noise assuming an arbitrary distribution function and correlation properties of injected electrons. The analytical results have been obtained for a wide range of biases: from equilibrium to high values beyond the linear-response regime. The particular case of a three-dimensional Fermi-Dirac injection has been analyzed. We show that the Coulomb correlations are manifested in the negative excess voltage noise, i.e., the voltage fluctuations under high-field transport conditions can be less than in equilibrium.