Andreev Bound States Research Articles

Andreev bound-state dynamics in quantum-dot Josephson junctions: a washing out of the 0-π transition.

We consider a Josephson junction formed by a quantum dot connected to two bulk superconductors in the presence of Coulomb interaction and coupling to both an electromagnetic environment and a finite density of electronic quasiparticles. In the limit of a large superconducting gap we obtain a Born-Markov description of the relevant Andreev bound-states dynamics. We calculate the current-phase relation and we find that the experimentally unavoidable presence of quasiparticles can dramatically modify the 0-π standard transition picture. We show that photon-assisted quasiparticle absorption allows the dynamic switching from the 0 to the π state and vice versa, washing out the 0-π transition predicted by purely thermodynamic arguments. Spectroscopic signatures of Andreev bound-states broadening are investigated by considering microwave irradiation.

Helical Andreev bound states in topological insulator f-wave Josephson junction

We study the effect of f-wave triplet superconductivity induced by proximity effect on the surface states of a three-dimensional topological insulator (3DTI). In fact, the gapless surface state for excitation spectrum of a triplet superconductor topological insulator gives rise to formation of helical Andreev bound states (ABSs) and, necessarily, suppression of Andreev reflection at the interface of a superconductor/ferromagnetic structure. By calculating the relevant form of Dirac spinors for two-dimensional time-reversal symmetric Hamiltonian, the normal and Andreev reflection coefficients and ABSs corresponding to tunneling and Josephson junctions, respectively, are obtained. It is shown, that the Andreev process vanishing occurs strongly, so that, the evanescent waves will be permissible in tunneling process. It is found that the dispersion of ABSs is an even function of electron incident angle θ for f1-wave and odd for f2-wave. In f1-order, for module of incident angle, θ>0.167π, the ABSs are independent of superconducting phase difference, ϕ, so that the Josephson current may vanish for this region. Effect of magnetization on flattening of ABSs occurs in f2 order faster than f1.

Spin supercurrent, magnetization dynamics, andφ-state in spin-textured Josephson junctions

The prospect of combining the dissipationless nature of superconducting currents with the spin-polarization of magnetic materials is interesting with respect to exploring superconducting analogues of topics in spintronics. In order to accomplish this aim, it is pivotal to understand how spin-supercurrents interact dynamically with magnetization textures. We investigate the appearance of a spin-supercurrent and the resulting magnetization dynamics in a textured magnetic Josephson current by using three experimentally relevant models: i) a S/F/S junction with spin-active interfaces, ii) a S/F1/F2/F3/S Josephson junction with a ferromagnetic trilayer, and iii) a Josephson junction containing a domain wall. In all of these cases, the supercurrent is spin-polarized and exerts a spin-transfer torque on the ferromagnetic interlayers which causes magnetization dynamics. Using a scattering matrix formalism in the clean limit, we compute the Andreev-bound states and free energy of the system which is used to solve the Landau-Lifshiftz-Gilbert equation. We compute both how the inhomogeneous magnetism influences the phase-dependence of the charge supercurrent as well as the magnetization dynamics caused by the spin-supercurrent. Using a realistic experimental parameter set, we find that the supercurrent can induce magnetization switching that is controlled by the superconducting phase difference. Moreover, we demonstrate that the combined effect of chiral spin symmetry breaking and interface scattering causes the system to act as a phase battery that may supply any superconducting phase difference phi in the ground state. Such a phi junction is accompanied by an anomalous supercurrent appearing even at zero phase difference, and we demonstrate that the flow direction of this current is controlled by the chirality of the magnetization configuration.

Effective manipulation of Andreev bound states, zero mode Majorana fermion and Josephson current in a superconductor–normal–superconductor junction on the surface of a topological insulator

Abstract We study the effective manipulation of the Andreev bound states (ABS), zero mode Majorana fermion and Josephson current (JC) in a superconductor–normal–superconductor junction on the surface of a topological insulator in unexplored regime of parameters. It is found that the energy of the ABS changes dramatically with the phase difference between both superconductors (SCs) in a certain range of the incident angle of quasiparticles. It is shown that the velocity of Majorana fermion and the JC can be effectively tuned in a wide range of the chemical potential in the normal region ( μ N ) and the separation width ( L ) of the two SCs. In addition, we expose that the critical JC and its product with the normal resistance are, respectively, a quarter and the same to those in a graphene-based Josephson junction. The dependence of the critical JC on the chemical potential in the superconducting region is not monotonous: it increases (decreases) for small (large) μ N .

Microscopic Theory of Tunneling Spectroscopy in Sr2RuO4

We study the surface Andreev bound state (ABS) of superconducting Sr$_2$RuO$_4$, which is a candidate material for the realization of the chiral $p$-wave superconducting state. In order to clarify the role of chiral edge modes as ABSs, the surface density of states and the tunneling conductance is calculated in the normal metal/Sr$_2$RuO$_4$ junction within the framework of recursive Green's function method, while taking into account the orbital degrees of freedom (including Spin-Orbit interactions) with realistic material parameters. In Sr$_2$RuO$_4$, there are two bands $\alpha$ and $\beta$ originating from quasi-one-dimensional orbitals $d_{yz}$ and $d_{zx}$ and a two-dimensional band $\gamma$ originating from $d_{xy}$ orbital. We discuss about the contributions of various electronic bands to LDOS and the influence of atomic spin-orbit interaction (SOI). In the light of our calculations, quasi-one-dimensional model with dominant pair potentials in $\alpha$ and $\beta$ bands is consistent with conductance measurements in Au/Sr$_{2}$RuO$_{4}$ junctions.

Dynamical gate-tunable supercurrents in topological Josephson junctions

Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has been attributed to a transition where the topologically trivial 2DEG at the surface is nearly depleted, causing a shift in the spatial location and change in nature of the helical surface states. We present measurements that support this picture by revealing qualitative changes in the temperature and magnetic field dependence of the critical current across this transition. In particular, we observe pronounced fluctuations in the critical current near total depletion of the 2DEG that demonstrate the dynamical nature of the supercurrent transport through topological low energy ABSs.

Quasi-Classical Theory of Tunneling Spectroscopy in Superconducting Topological Insulator

We develop a theory of tunneling spectroscopy in superconducting topological insulator (STI), i.e., superconducting state of a carrier-doped topological insulator. Based on the quasi-classical approximation, we obtain an analytical expression of the energy dispersion of surface Andreev bound states (ABSs) and a compact formula for tunneling conductance of normal metal/STI junctions. The obtained compact formula of tunneling conductance makes the analysis of experimental data easy. As an application of our theory, we study tunneling conductance in CuxBi2Se3. We reveal that our theory reproduces the previous results by Yamakage et al. [Phys. Rev. B 85, 180509(R) (2012)]. We further study magneto-tunneling spectroscopy in the presence of external magnetic fields, where the energy of quasiparticles is shifted by the Doppler effect. By rotating magnetic fields in the basal plane, we can distinguish between two different topological superconducting states with and without point nodes, in their magneto-tunneling spectra.

Tunable Josephson effect in hybrid parallel coupled double quantum dot-superconductor tunnel junction

Using non-equilibrium Green’s function approach, we study electronic transport through a parallel double quantum dot (DQD) system symmetrically coupled to conventional superconducting leads. Andreev bound states (ABS) and corresponding resonant Cooper pair electron transmission through such a DQD-superconductor tunnel junction around the Fermi energy, a manifestation of Josephson effect, occur due to proximity effect as a result of superconducting order parameter. Interdot tunnel coupling in parallel coupled DQD system and Coulomb interactions regulate the Josephson effect in a very significant manner. Further, it is also found that interdot tunnel coupling has reverse effect on ABS and Cooper pair tunneling in the presence and absence of Coulomb interactions.

Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot

Tunneling spectroscopy of a Nb coupled carbon nanotube quantum dot reveals the formation of pairs of Andreev bound states (ABS) within the superconducting gap. A weak replica of the lower ABS is found, which is generated by quasi-particle tunnelling from the ABS to the Al tunnel probe. An inversion of the ABS-dispersion is observed at elevated temperatures, which signals the thermal occupation of the upper ABS. Our experimental findings are well supported by model calculations based on the superconducting Anderson model.

Parity Measurement in Topological Josephson Junctions

We study the properties of a topological Josephson junction made of both edges of a two-dimensional topological insulator. We show that, due to fermion parity pumping across the bulk, the global parity of the junction has a clear signature in the periodicity and critical value of the Josephson current. In particular, we find that the periodicity with the flux changes from 4π in a junction with an even number of quasiparticles to 2π in the odd sector. In the case of long junctions, we exhibit a rigorous mathematical connection between the spectrum of Andreev bound states and the fermion parity anomaly, through bosonization. Additionally, we discuss the rather quantitative effects of Coulomb interactions on the Josephson current.

Anomalous Josephson Effect in Triplet Superconductor–Ferromagnet–Triplet Superconductor Junctions

We study the anomalous Josephson current appearing at zero phase difference in triplet superconductor–ferromagnet–triplet superconductor (TFT) junctions. The anomalous Josephson current appears when the magnetization orientation of the ferromagnet layer and two d vectors of triplet superconductors are noncoplanar. The Josephson junction involving two triplet superconductors with noncolinear d vectors exhibits two spin-split Andreev bound states which have opposite phase shifts compared with the conventional current-phase relation. The ferromagnet layer can transmit one of the Andreev bound states while block the other completely. The survived Andreev bound state gives rise to the anomalous Josephson current and have arbitrary equilibrium phase difference. The equilibrium phase difference of the supercurrent can be tuned continuously by the junction parameters.

Phase-sensitive transport at a normal metal–superconductor interface close to a Josephson junction

Phase- and voltage bias-sensitive quasiparticle transport at a double $NI{S}_{1}I{S}_{2}$ interface is considered. The barriers $I$ range from tunnel to transparent, and the intermediate region ${S}_{1}$ has a width comparable to the superconducting coherence length. A phase difference $\ensuremath{\varphi}$ is applied to the Josephson junction ${S}_{1}I{S}_{2}$. The normal and Andreev reflections at the $NI{S}_{1}$ interface become $\ensuremath{\varphi}$ sensitive, and transport is governed by interferences within the narrow ${S}_{1}$ region in both the normal and the anomalous channels. The subgap conductance is separately (energy $E$) and (phase $\ensuremath{\varphi}$) symmetric. Above the superconducting gap, the conductance is, in general, not symmetric even if $(E,\ensuremath{\varphi})$ is changed in $(\ensuremath{-}E,\ensuremath{-}\ensuremath{\varphi})$, but the symmetry is restored by averaging Fermi oscillations. The Tomasch oscillations are amplified by the phase difference. The subgap conductance exhibits a resonant structure at the energy of the Andreev bound states (ABSs) of the ${S}_{1}I{S}_{2}$ junction, providing a side spectroscopy of such states. Depending on the relative transparencies of the junctions, the resonance can increase or reduce the conductance, and it can even vanish for $\ensuremath{\varphi}=\ensuremath{\pi}$, featuring total reflection of quasiparticles at $N{S}_{1}$ by the ABS at ${S}_{1}{S}_{2}$.

Nonlocal spectroscopy of Andreev bound states

We experimentally investigate Andreev bound states (ABSs) in a carbon nanotube quantum dot (QD) connected to a superconducting Nb lead (S). A weakly coupled normal metal contact acts as a tunnel probe that measures the energy dispersion of the ABSs. Moreover, we study the response of the ABS to nonlocal transport processes, namely, Cooper pair splitting and elastic co-tunnelling, which are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable nonlocal conductance with a rich structure, including a sign reversal at the ground-state transition from the ABS singlet to a degenerate magnetic doublet. We describe our device by a simple rate equation model that captures the key features of our observations and demonstrates that the sign of the nonlocal conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes $u$ and $v$.

Impurity Effects in a Vortex Core in a Chiral p-Wave Superconductor Within the t-Matrix Approximation

We study the effects of non-magnetic impurity scattering on the Andreev bound states (ABS) in an isolated vortex in a two-dimensional chiral p-wave superconductor numerically. We incorporate the impurity scattering effects into the quasiclassical Eilenberger formulation through the self-consistent $t$-matrix approximation. Within this scheme, we calculate the local density of states (LDOS) around two types of vortices: "parallel" ("anti-parallel") vortex where the phase winding of the pair-potential coming from vorticity and that coming from chirality have the same (opposite) sign. When the scattering phase-shift $\delta_0$ of each impurity is small, we find that impurities affect differently low energy quasiparticle spectrum around the two types of vortex in a way similar to that in the Born limit ($\delta_0\rightarrow 0$). For a larger $\delta_0(\leq \pi/2)$ however we find that ABS in the vortex is strongly suppressed by impurities for both types of vortex. We found that there are some correlations between the suppression of ABS near vortex cores and the low energy density of states due to impurity bands in the bulk.

Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions

Currently, much effort is being put into detecting unconventional p-wave superconductivity in Josephson junctions based on topological insulators (TIs). For that purpose we propose to use superconducting Klein tunneling, i.e. the reflectionless passage of Cooper pairs through a potential barrier in a gated ballistic junction. This phenomenon occurs due to the fact that the supercurrent is carried by helical Andreev bound states (ABSs) characterized by spin-momentum locking similar to the normal-state carriers. We derive the spectrum of the helical ABSs and the corresponding Josephson current for a junction made on the surface of a three-dimensional TI. The superconducting Klein tunneling is predicted to yield a non-sinusoidal current-phase relation and an anomalous critical current $I_c$ that does not vanish with increasing barrier strength. We also analyze the dependence of the I_cR_n product (where R_n is the normal-state junction resistance) on the microscopic parameters of the superconductor/TI interface, which leads to lower I_cR_n values than expected from previous models of the proximity-effect Josephson junctions.

The Higher Andreev State

Physics In superconductors, materials capable of perfect conduction of electricity, the associated supercurrent is carried by pairs of electrons known as Cooper pairs. If a superconductor is placed in contact with a nonsuperconducting material, a single electron impinging on the interface from the nonsuperconducting side is reflected as a hole and forms a Cooper pair on the superconductor side—a process known as Andreev reflection. For a nonsuperconducting material sandwiched between two superconductors (as is the case in devices such as tunnel Josephson junctions), the reflections on the two interfaces will cause the formation of standing waves—Andreev bound states (ABSs)—which are responsible for carrying the supercurrent across the weak link. The ABSs have a discrete spectrum, but usually only the lowest energy state is accessed in experiments. Bretheau et al. directly detected an excited ABS in a less common form of a Josephson junction, where the weak link is an atomic contact. Their apparatus consisted of an atomic contact junction in parallel with a tunnel junction, and with another tunnel junction acting as a source and detector of microwaves. By measuring the current and voltage dependence of the latter, and by varying the phase difference across the atomic contact, they were able to precisely map out the energy needed to excite the ground ABS. It is expected that the existence of two ABSs can be used as a basis for a quantum bit or as a stage for exploring fundamental mesoscopic phenomena. Nature 499 , 312 (2013).

Tunneling spectroscopy of a single quantum dot coupled to a superconductor: From Kondo ridge to Andreev bound states

We performed tunneling spectroscopy of a carbon nanotube quantum dot (QD) coupled to a metallic reservoir either in the normal or in the superconducting state. We explore how the Kondo resonance, observed when the QD's occupancy is odd and the reservoir is normal, evolves towards Andreev bound states (ABS) in the superconducting state. Within this regime, the ABS spectrum observed is consistent with a quantum phase transition from a singlet to a degenerate magnetic doublet ground state, in quantitative agreement with a single-level Anderson model with superconducting leads.

Theory of tunneling spectroscopy in a superconducting topological insulator

We calculate tunneling conductance of normal metal and superconducting topological insulator CuxBi2Se3 junctions for the possible pairing symmetries. In the presence of gapless Andreev bound states (ABSs), the tunneling conductance shows a zero-bias peak even for the three-dimensional full-gap superconducting state. This zero-bias conductance peak stems from the enhancement of the surface density of states induced by the surface-state transition in momentum space.

Andreev bound states and current-phase relations in three-dimensional topological insulators

To guide the search for the Majorana fermion, we theoretically study superconductor/topological/superconductor (S/TI/S) junctions in an experimentally relevant regime. We find that the striking features present in these systems, including the doubled periodicity of the Andreev bound states (ABSs) due to tunneling via Majorana states, can still be present at high electron densities. We show that via the inclusion of magnetic layers, this 4pi periodic ABS can still be observed in three-dimensional topological insulators, where finite angle incidence usually results in the opening of a gap at zero energy and hence results in a 2pi periodic ABS. Furthermore, we study the Josephson junction characteristics and find that the gap size can be controlled and decreased by tuning the magnetization direction and amplitude. These findings pave the way for designing experiments on S/3DTI/S junctions.

Suppression of Andreev current due to transverse current flow in an InAs two-dimensional electrons

In a superconductor–normal–superconductor (SNS) structure, the effect of transverse current across the normal part on the transport through Andreev bound states (ABSs) has been examined. Here, a ballistic InAs two-dimensional electron system (2DES) is used as the N-layer to form ABSs. At the same time the 2DES has strong spin–orbit interaction, hence there should emerge the spin-Hall effect associated with the transverse current. We have observed strong reduction of characteristic oscillation in the conductance versus bias voltage, which may be attributed to spin polarization due to the spin-Hall effect.