Differential Shot Noise Research Articles

Effect of the mixing of s-wave and chiral p-wave pairings on electrical shot noise properties of normal metal/superconductor tunnel junctions

Abstract We study theoretically the electrical shot noise properties of tunnel junctions between a normal metal and a superconductor with the mixture of singlet $s$-wave and chiral triplet $p$-wave pairing due to broken inversion symmetry. We investigate how the shot noise properties vary as the relative amplitude between the two parity components in the pairing potential is changed. It is demonstrated that some characteristics of the electrical shot noise properties of such tunnel junctions may depend sensitively on the relative amplitude between the two parity components in the pairing potential, and some significant changes may occur in the electrical shot noise properties when the relative amplitude between the two parity components is varied from the singlet $s$-wave pairing dominated regime to the chiral triplet $p$-wave pairing dominated regime. In the chiral triplet $p$-wave pairing dominated regime, the ratio of noise power to electric current is close to $2e$ both in the in-gap and in the out-gap region. In the singlet $s$-wave pairing dominated regime, the value of this ratio is close to $4e$ in the inner gap region but may reduce to about $2e$ in the outer gap region as the relative amplitude of the chiral triplet pairing component is increased. The variations of the differential shot noise with the bias voltage also exhibit some significantly different features in different regimes. Such different features can serve as useful diagnostic tools for the determination of the relative magnitude of the two parity components in the pairing potential.

Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

AbstractConsidering models with tilted linear and quadratic band touching dispersions, the effect of the transverse linear tilt on the transmission spectra is analyzed through a harmonically driven potential well oriented longitudinally. Employing the Floquet scattering matrix formalism, Fano resonances are found as an outcome of matching between the Floquet sidebands and quasi‐bound states, where the tilt renormalizes their energies and wave vectors. It is found that the Fano resonance energy decreases (increases) for linear (quadratic) band touchings as the magnitude of the transverse momentum increases, indicating a distinct signature of the underlying band dispersion in the transmission profile. The sign of the product of the transverse momentum and the tilt also determines the relative shift in the Fano resonance energy with respect to the untilted case for both band dispersions, suggesting a possible tunability of the Fano resonance for tilted systems. Importantly, the tilt strength can also be directly determined by measuring the Fano resonance energy as function of the transverse momenta direction. The shot noise spectra and their differential property are further studied where an inflection region and undulation, respectively, is found around the Fano resonance energy. Interestingly, differential shot noise and transmission spectra both qualitatively behave in a similar fashion and might thus serve as important observables for future experiments on driven solid‐state systems.

Shot noise in topological insulator-based ferromagnet/p-wave superconductor junctions

The differential shot noise and Fano factor in topological insulator-based ferromagnet/p-wave superconductor (TI-based FM/p-wave SC) junctions is theoretically investigated based on the Dirac-Bogoliubov-de Gennes equation. Three kinds of pairings px, py, and px+ipy-waves for SC are chosen. It is found that the shot noise spectrum strongly depends on the finite-quasi-particle lifetime, the magnetic gap m induced by an applied magnetization, the Fermi-energy mismatch between FM and SC as well as the type of the pair potential symmetry. Shortening the quasi-particles lifetime leads to the dips in the shot noise smoothed out. Increasing the magnetic gap can suppress the shot noise and Fano factor when the conventional Andreev retro-reflection is the dominant process but the shot noise can be enhanced when the dominant process is the specular Andreev reflection. Which type of reflection dominates the tunneling process with a turning point at the Fermi energy EF =m, where the values of shot noise in all energy ranges become zero. This result can be used not only to distinguish the specular Andreev reflection from the Andreev retro-reflection in thin film TI-based FM/p-wave SC structures but also to determine the energy-mass gap induced by the applied magnetization.

Study of Andreev reflection in topological insulator-based ferromagnet/ [formula omitted] wave superconductor structures

The Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk theory are used to calculate the tunneling conductance and shot noise in topological insulator-based ferromagnet/ dx2−y2+idxy mixed wave superconductor (TI-based FM/ dx2−y2+idxy SC) junctions. The Andreev reflection is investigated by analyzing the conductance and shot noise. Results show that the Andreev reflection process strongly depend on the magnetic gap m in FM, the gate potential U applied to the electrode on top of SC, and the magnitude of the ratio of Δ1/Δ0 with Δ0(Δ1) the absolute of pair potential of dx2−y2(dxy) component. The specular Andreev reflection can be enhanced by m as well as U. The conventional Andreev retro-reflection, however, can be enhanced by U but be suppressed by m. Which of the two reflections dominates the tunneling phenomenon exists a turning point at m = EF where both the tunneling conductance and differential shot noise become zero. This can be used as a criterion for distinguishing between the specular Andreev reflection and the Andreev retro-reflection in thin film TI-based FM/ dx2−y2+idxy SC structures. In addition, the dx2−y2+idxy pairing symmetry as well as the magnitude of magnetic gap can be determined by the experiment of scanning tunnel spectroscopy.

Majorana differential shot noise and its universal thermoelectric crossover

Nonequilibrium states driven by both electric bias voltages $V$ and temperature differences $\Delta T$ (or thermal voltages $eV_T\equiv k_B\Delta T$) are unique probes of various systems. Whereas average currents $I(V,V_T)$ are traditionally measured in majority of experiments, an essential part of nonequilibrium dynamics, stored particularly in fluctuations, remains largely unexplored. Here we focus on Majorana quantum dot devices, specifically on their differential shot noise $\partial S^>(V,V_T)/\partial V$, and demonstrate that in contrast to the differential electric or thermoelectric conductance, $\partial I(V,V_T)/\partial V$ or $\partial I(V,V_T)/\partial V_T$, it reveals a crossover from thermoelectric to pure thermal nonequilibrium behavior. It is shown that this Majorana crossover in $\partial S^>(V,V_T)/\partial V$ is induced by an interplay of the electric and thermal driving, occurs at an energy scale determined by the Majorana tunneling amplitude, and exhibits a number of universal characteristics which may be accessed in solely noise experiments or in combination with measurements of average currents.

Spin transport properties in ferromagnet/superconductor junctions on topological insulator

The spin-dependent Andreev reflection is investigated theoretically by analyzing the electronic transport in a thin-film topological insulator (TI) ferromagnet/superconductor (FM/SC) junction. The tunneling conductance and shot noise are calculated based on the Dirac–Bogoliubov–de Gennes equation and Blonder–Tinkham–Klapwijk theory. It is found that the magnetic gap in ferromagnet can enhance the Andreev retro-reflection but suppress the specular Andreev reflection. The gate potential applied to the electrode on top of superconductor can enhance the two types of reflections. There is a transition between the two types of reflections at which both the tunneling conductance and differential shot noise become zero. These results provide a method to realize and detect experimentally the intra-band specular Andreev reflection in thin film TI-based FM/SC structures.

Shot noise and differential conductance as signatures of putative topological superconductivity in FeSe0.45Te0.55

We present a theory for the differential shot noise, $dS/dV$, as measured via shot-noise scanning tunneling spectroscopy, and the differential conductance, $dI/dV$, for tunneling into Majorana zero modes (MZMs) in the putative topological superconductor ${\mathrm{FeSe}}_{0.45}{\mathrm{Te}}_{0.55}$. We demonstrate that for tunneling into chiral Majorana edge modes near domain walls, as well as MZMs localized in vortex cores and at the end of defect lines, $dS/dV$ vanishes whenever $dI/dV$ reaches a quantized value being equal to the quantum of conductance. These results are independent of the particular orbital tunneling path, thus establishing a vanishing $dS/dV$ concomitant with a quantized $dI/dV$, as universal signatures for Majorana modes in two-dimensional topological superconductors, irrespective of the material's specific complex electronic band structure.

Revealing universal Majorana fractionalization using differential shot noise and conductance in nonequilibrium states controlled by tunneling phases

Universal fractionalization of quantum transport characteristics in Majorana quantum dot devices is expected to emerge for well separated Majorana bound states. We show that the Majorana universality of the differential shot noise $\partial S^>/\partial V$ and conductance $\partial I/\partial V$ at low bias voltages $V$ arises only in ideal setups with only one Majorana mode entangled with the quantum dot. In realistic devices, where both Majorana modes are entangled with the quantum dot, $\partial S^>/\partial V$ and $\partial I/\partial V$ become very sensitive to tunneling phases and their universal fractional values are hard to observe even for well separated Majorana bound states. In contrast, as revealed here, the ratio $(\partial S^>/\partial V)/(\partial I/\partial V)$ weakly depends on the tunneling phases and is fractional when the Majorana bound states are well separated or integer when they significantly overlap. Importantly, for very large $V$ we demonstrate that this ratio becomes fully independent of the tunneling phases and its universal fractional Majorana value may be observed in state-of-the-art experiments.

Study of differential shot noise in ferromagnet-insulator-superconductor graphene junction with TRSB

In this paper, we study differential shot noise in ferromagnet-insulator- superconductor graphene junction with time-reversal symmetry broken (TRSB) where we consider two different Cooper pairing states: one unconventional TRSB D ​+ ​iS-wave and an unconventional TRSB D ​+ ​iDxy-wave. We consider two regimes: the first one is the equal Fermi energies on both sides of the junction and the second regime is the Fermi energies that are far from each other. In the first regime, for D ​+ ​iS when the main part i. e. D-wave is dominant, we have obtained the shot noise peaks at the edge of the superconducting gap. The height of peaks reduces with the increase of the ferromagnetic exchange field. For D ​+ ​iS, when the s-wave part plays the main role, the peaks split in high exchange fields. For D ​+ ​iDxy-wave, the peaks split as well, but the distance between the peaks for D ​+ ​iDxy is smaller than D ​+ ​iS. Also, differential shot noise at zero-bias shows an oscillating behavior with respect to the barrier potential of the insulator such that its absolute value decreases when the exchange field enhances.In the second regime (Fermi energies are selected far from each other in the both sides of the junction), zero-bias peaks are formed when the main part i. e. D-wave is dominant while the peaks are shifted to non-zero voltages when the sub-dominant s-wave part is significant compared with the main part. Also, differential shot noise at zero-bias does not show any oscillating behavior versus the strength of barrier potential while its absolute value enhances with the increase of the exchange fields.Therefore, differential shot noise may serve as a valuable tool to understand more about various candidates of pair symmetries including TRSB states.

The interplay of intralead and dot-lead Coulomb electrons on shot noise in the Kondo regime

The interplay of intralead and dot-lead Coulomb interactions on shot noise of a quantum dot coupled to Luttinger-liquid leads is systematically investigated in the Kondo regime. By equation of motion and canonical transformation methods, a general shot noise formula with transmission coefficient is derived, the factors of the above two types of interactions and on-dot Coulomb interaction being taken into account. Then we study in detail the shot noise and Fano factor as a function of bias voltage. Numerical results show for weak and moderately strong intralead Coulomb interactions, the dot-lead interaction not only helps to improve the shot noise, but also narrows the zero-bias Kondo dip. A series of polaron peaks appear in the differential shot noise when the renormalized parameter Y<1, a combination effect of the intralead and dot-lead Coulomb interactions. For Y>1, a novel type of excitonic dips appear only in the case of moderately strong intralead interaction. In the very strong intralead interaction limit, all features of excitonic peaks or dips disappear, and shot noise shows power-law dependence on the voltage with the renormalized exponent Y. The Fano factor is always sub-Poisson noise no matter whether Y is greater or less than 1.

Effect of magnetic fields on the shot noise of a quantum dot with Luttinger leads

We study the shot noise of a strongly correlated quantum dot system in the Kondo regime, concentrating on the joint effect of a magnetic field B and intralead Coulomb interaction. A shot noise formula is derived. The shot noise is suppressed by the magnetic field when the intralead interaction is weak, but improved by the field when the interaction is strong. The differential shot noise has a peak or valley at eV = ±gμBB for weak or moderately strong intralead interaction. As the interactions increase, these singular behaviours gradually disappear. In the strong interaction limit, the shot noise's curve has a power-law dependence on the voltage. The intralead Coulomb interaction also modulates the Fano line shape of shot noise. The Fano factor is enhanced by the magnetic field and dot-lead asymmetric coupling and is always sub-Poissonian noise.

Current correlations of Cooper-pair tunneling into a quantum Hall system

We study Cooper pair transport through a quantum point contact between a superconductor and a quantum Hall edge state at integer and fractional filling factors. We calculate the tunnelling current and its finite-frequency noise to the leading order in the tunneling amplitude for dc and ac bias voltage in the limit of low temperatures. At zero temperature and in case of tunnelling into a single edge channel both the conductance and differential shot noise vanish as a result of Pauli exclusion principle. In contrast, in the presence of two edge channels, this Pauli blockade is softened and a non-zero conductance and shot noise are revealed.

Differential conductance and shot noise of a graphene quantum dot coupled with Majorana bound states

Zigzag and armchair hexagonal graphene quantum dots (GQDs) are employed as tunneling spectrometers to detect the signature of Majorana bound states (MBSs) located at the ends of a hybrid nanowire-superconductor junction. The formulas of tunneling current and shot noise are derived to exhibit the local and non-local Andreev reflections induced by MBSs. When the energy splitting of MBSs in the nanowire (e M ) is zero, the hybridization of zero-bias state which comes from normal tunneling and MBSs appears in the zigzag hexagonal GQD system. For the armchair hexagonal GQD under the condition e M = 0, the zero-bias conductance peak emerges in the energy gap to show the absolute contribution of MBSs. When e M ≠ 0, the zero-bias conductance peak splits into symmetrically distributed multi-peaks. These signify that the connected MBSs open novel channels for electrons to tunnel through the metallic and semiconducting GQDs. Shot noise is enhanced by MBSs to form different appearances depending on concrete GQDs. The zigzag GQD system always displays sub-Poissonian shot noise, while super-Poissonian shot noise appears in the armchair GQD system due to the coupling of MBSs. We can distinguish the contributions of MBSs from that of normal tunneling electrons by shot noise and Fano factor at low energy region.

The photon-assisted shot noise of a strongly correlated quantum dot coupled to the Luttinger liquid leads

Abstract The joint effects of an ac field and intralead interaction on shot noise of a Kondo quantum dot coupled to Luttinger liquid leads is investigated. A general photon-assisted zero-frequency shot noise formula is derived by use of the extended equation of motion of the nonequilibrium Green function. The photon-assisted shot noise demonstrates antiresonant-like behavior. The differential shot noise versus bias voltage exhibits steps the widths of which are just the ac frequency. With the increase of the intralead interaction, the antiresonances and step-structure are gradually smoothed and eventually disappear in the limit of the strong intralead interaction. In the limit, the shot noise scales as a power law in bias voltage, a signature of strong intralead interactions. The measurements of the photon-assisted zero-frequency shot noise can provide valuable information of the intralead interaction.

Shot Noise in Superconducting Wires Applied with a Periodic Electric Field.

We have investigated the differential conductance and shot noise for the system of superconducting nanowires irradiated with a periodic electric field by nonequilibrium Green's functions. The numerical results show that the coupling between the Majorana bound states (MBSs) can be tuned by the periodic electric field. The width of barriers has huge influence on the coupling of MBSs, however, the separation between barriers affect the coupling faintly. The coupling increases with the width of barriers, the number of barriers and the strength of barriers. In addition, super-Poissonian shot noise emerges as the coupling increases.

Differential shot noise and Fano factor in a ferromagnet-Graphene-superconductor junction

Differential shot noise and Fano factor are investigated theoretically in a ferromagnet-Graphene-superconductor junctions, where ferromagnetism and superconductivity are induced by proximity effect, while the intermediate layer is Graphene. We have found that sub-gap region in shot noise and Fano factor is strongly affected by the ferromagnetic exchange energy. We have found that shot noise and Fano factor are suppressed when the exchange energy increases and the Andreev retro-reflection is the dominant process. When the dominant process is specular Andreev reflection, shot noise and Fano factor enhance by increasing the exchange energy. Also, for a wide intermediate Graphene layer, the shot noise oscillates vs applied bias voltage while there is no oscillation in the curves of Fano factor vs bias voltage. The calculation of Fano factor at zero bias shows that the Fano factor vs spin-polarization displays a clear distinction between Andreev retro-reflection and specular Andreev reflection. Our finding can be used not only to understand more about Andreev retro-reflection and specular Andreev reflection but also to discriminate between them through the differential shot noise and Fano factor.

Fano resonance via bonding and antibonding states in nonadiabatically-pumped double-quantum-well systems

In this work, transport properties of the nonadiabatically pumped double-quantum-well (DQW) structure are studied. Different from a single quantum well, band mixing in the DQW generates bonding and antibonding states, whose wave functions have different spatial symmetry. By applying a time-dependent electric potential to the two well regions simultaneously, Floquet sidebands are formed, which constitutes additional quantum tunneling paths. When one of the Floquet sidebands coincides with the bonding or antibonding quasibound states within the DQW structure, sharp Fano resonances are found in the transmission coefficients as well as in the differential shot noise spectra. While such Fano resonances originate from quantum interference, their shapes are strikingly different for transport via the bonding state and via the antibonding state. The Fano resonance via the even-parity bonding state shows a perfect transmission followed by a total reflection and the Fano resonance via the odd-parity antibonding state has a reversed symmetry and shows a total reflection before a perfect transmission.

Low-energy spectra of differential conductivity and shot noise in tunnel junctions based on superconductors with suppression of the order parameter at the S-N interface

The possibility of an anomalous structure in the differential conductivity of tunnel junctions based on high-temperature superconductors as a result of degradation of their surface layer is analyzed. This feature is in the form of two peaks near an energy gap separated by a region of suppressed conductivity. One peak is usually high and sharp, while the other is much more spread out. Differential conductivity and shot noise spectra in contacts of a normal injector with s- and d-type superconductors are calculated and compared. It is shown that combined measurements of these two characteristics can provide new information on the kinetics of transport processes in these structures.

Dynamic shot noise in a quantum dot coupled with Majorana fermions under the perturbation of microwave fields

The dynamic properties of a quantum dot (QD) coupled with Majorana fermions under the perturbation of microwave fields (MWFs) have been investigated through the nonequilibrium Green’s function (NGF) technique. The photon-assisted differential conductance, current, shot noise, and Fano factor have been evaluated in the Nambu representation. The normal electron tunneling and Andreev reflections contribute to the transport effectively, and novel conductance peaks appear around each photon-induced side channel. The shot noise is enhanced by increasing the interaction strength of Majorana fermions evidently, while it is suppressed accompanying with peak-valley structures by the MWFs. For the symmetric transmission where the QD energy E d = 0, terminal current disappears when the source-drain bias eV is removed. For the asymmetric transmission where E d ≠ 0, there exists nonzero pumping current induced by the applied MWF. The saturate pumping current increases with increasing E d as eV = 0 and E d ≠ 0, but the shot noise increases with decreasing E d . As the coupling energy between the Majorana fermions becomes zero, the Fano factor reaches the robust value F ≈ 0.38 as eV → 0.

Transport through graphenelike flakes with intrinsic spin-orbit interactions

It has been shown recently [J. L. Lado et al., Phys. Rev. Lett. 113, 027203 (2014)] that edge magnetic moments in graphene-like nanoribbons are strongly influenced by the intrinsic spin-orbit interaction. Due to this interaction an anisotropy comes about which makes the in-plane arrangement of magnetic moments energetically more favorable than that corresponding to the out-of-plane configuration. In this paper we raise both the edge magnetism problem as well as differential conductance and shot noise Fano factor issues, in the context of finite-size flakes within the Coulomb blockade (CB) transport regime. Our findings elucidate the following problems: (i) modification of the CB diamonds by the appearance of the in-plane magnetic moments, (ii) modification of the CB diamonds by intrinsic spin-orbit interaction.