Subgap Conductance Research Articles

Theoretical valley-polarized subgap transport and intravalley pairing states in a silicene-based antiferromagnet–superconductor junction

We theoretically study the valley-polarized subgap transport and intravalley pairing states in silicene-based antiferromagnet/superconductor (AF/SC) junctions. It is found that in the absence of an electric field, the antiferromagnetic order induced in silicene can give rise to valley-polarized states that strongly affect the subgap conductance. With the increasing antiferromagnetic exchange field, the gap-edge Andreev-resonant peak is replaced by broadened features for the homo-SC model whereas by a sharp conductance dip for the bulk-SC one. This significant difference arises from the intravalley Andreev reflection caused by the valley-mixing scattering in the bulk-SC model, which can be enhanced by the antiferromagnetic order. Particularly, this intravalley pairing process can be switched on or off by adjusting the spin polarization through the electric field applied in the AF region. Our findings not only pave a new road to employ antiferromagnetic materials in valleytronics, but also facilitate the verification and detection of potential intravalley pairing state and valley polarization in silicene.

Hard Superconducting Gap in PbTe Nanowires

Semiconductor nanowires coupled to a superconductor provide a powerful testbed for quantum device physics such as Majorana zero modes and gate-tunable hybrid qubits. The performance of these quantum devices heavily relies on the quality of the induced superconducting gap. A hard gap, evident as vanishing subgap conductance in tunneling spectroscopy, is both necessary and desired. A hard gap has been achieved and extensively studied before in III–V semiconductor nanowires (InAs and InSb). In this study, we present the observation of a hard superconducting gap in PbTe nanowires coupled to a superconductor Pb. The gap size Δ is ∼ 1 meV (maximally 1.3 meV in one device). Additionally, subgap Andreev bound states can also be created and controlled through gate tuning. Tuning a device into the open regime can reveal Andreev enhancement of the subgap conductance. These results pave the way for diverse superconducting quantum devices based on PbTe nanowires.

Tunability of Andreev levels in a spin-active Ising superconductor/half-metal Josephson junction

We study the Andreev levels, supercurrent and tunnelling conductance in a clean Ising superconductor (ISC)/half-metal (HM)/ISC Josephson junction (JJ) with spin-active interfaces using Bogoliubov–de Gennes equations. We theoretically demonstrate the effect of spin mixing, spin flipping processes and spin–orbit coupling (SOC) of the ISC on Andreev bound states spectra, the current phase relation and tunnelling conductance in a transparent and opaque barrier limit. We witness an additional splitting of the Andreev levels due to the SOC of the ISC and transition for different barrier magnetic moments. Also, different φ-junctions can be achieved by tuning the strength of the barrier magnetic moment and spin mismatch angle. Moreover, a possible transition can also be achieved for a SOC stronger than the chemical potential of the ISC using suitable control parameters. The tunnelling conductance is found to be dependent on the spin mismatch angle. A finite subgap conductance is also observed, indicating different probabilities of Andreev reflected electrons and holes in the presence of SOC. Furthermore, anomalous Andreev levels are observed for different HM length scales, signifying their role in the tunability of the φ-phase JJ.

Junctions and Superconducting Symmetry in Twisted Bilayer Graphene.

Junctions provide a wealth of information on the symmetry of the order parameter of superconductors. We analyze junctions between a scanning tunneling microscope (STM) tip and superconducting twisted bilayer graphene (TBG) and TBG Josephson junctions (JJs). We compare superconducting phases that are even or odd under valley exchange (s- or f-wave). The critical current in mixed (s and f) JJs strongly depends on the angle between the junction and the lattice. In STM-TBG junctions, due to Andreev reflection, the f-wave leads to a prominent peak in subgap conductance, as seen in experiments.

Photoinduced spin-polarized transport and controllable valley-triplet pairing states in a silicene-superconductor junction

We theoretically investigate the spin-polarized subgap transport and valley-triplet pairing states in a silicene-superconductor junction. By using the nonequilibrium Green’s function, it is found that the subgap conductance is strongly affected by the spin polarization induced by an off-resonant circularly polarized light. More importantly, the presence of valley-mixing scattering at the interface could result in a valley-triplet Andreev reflection (AR) process, where the incident electrons and reflected holes come from the same valley. We also find that the amplitude of the valley-triplet AR is controllable by tuning the intensity of the light, the position of the Fermi level, and even the interface coupling strength. Particularly, the fully valley-polarized conductance spectrum shows distinctive behaviors, which is beneficial for us to verify and detect the possible valley-triplet pairing states as well as the spin/valley polarizations in silicene. Our results may pave the way for the applications of silicene in spin-valleytronics.

Andreev reflection spectroscopy in strongly paired superconductors

Motivated by recent experiments on low-carrier-density superconductors, including twisted multilayer graphene, we study signatures of the BCS to BEC evolution in Andreev reflection spectroscopy. We establish that in a standard quantum point contact geometry, Andreev reflection in a BEC superconductor is unable to mediate a zero-bias conductance beyond $e^2/h$ per lead channel. This bound is shown to result from a duality that links the sub-gap conductance of BCS and BEC superconductors. We then demonstrate that sharp signatures of BEC superconductivity, including perfect Andreev reflection, can be recovered by tunneling through a suitably designed potential well. We propose various tunneling spectroscopy setups to experimentally probe this recovery.

Role of interface and valley-mixing scattering in a ferromagnetic silicene/superconductor junction

We theoretically investigate the subgap transport in a ferromagnetic silicene/superconductor junction and highlight the role of the interface. It is demonstrated that the subgap conductance spectra for the continuous and discontinuous interface models are significantly different. In particular, the intravalley Andreev reflection (AR) may occur at the discontinuous interface, and then the subgap conductance will be remarkably enhanced when the silicene sheet is highly valley polarized. This novel AR resulted from the valley-mixing scattering, which is absent in the continuous interface model. The influence of the interface coupling strength on the subgap conductance is also computed. Our results can be directly tested experimentally using scanning tunnel microscope measurements and/or point-contact spectroscopy.

Thermal conductance and nonequilibrium superconductivity in a diffusive NSN wire probed by shot noise

We investigate diffusive nanowire-based structures with two normal terminals on the sides and a central superconducting island in the middle, which is either grounded or floating. Using a semiclassical calculation we demonstrate that both device layouts permit a quantitative measurement of the energy-dependent sub-gap thermal conductance $G_\mathrm{th}$ from the spectral density of the current noise. In the floating case this goal is achieved without the need to contact the superconductor provided the device is asymmetric, that may be attractive from the experimental point of view. In addition, we observe that the shot noise in the floating case is sensitive to a well-known effect of non-equilibrium suppression and bistability of the superconducting gap. Our calculations are directly applicable to the multi-mode case and can serve as a starting point to understand the shot noise response in open one dimensional Majorana device.

Electron-boson-interaction induced particle-hole symmetry breaking of conductance into subgap states in superconductors

Particle-hole symmetry (PHS) of conductance into subgap states in superconductors is a fundamental consequence of a noninteracting mean-field theory of superconductivity. The breaking of this PHS has been attributed to a noninteracting mechanism, i.e., quasiparticle poisoning (QP), a process detrimental to the coherence of superconductor-based qubits.Here, we show that the ubiquitous electron-boson interactions in superconductors can also break the PHS of subgap conductances. We study the effect of such couplings on the PHS of subgap conductances in superconductors using both the rate equation and Keldysh formalism, which have different regimes of validity. In both regimes, we found that such couplings give rise to a particle-hole $asymmetry$ in subgap conductances which increases with increasing coupling strength, increasing subgap-state particle-hole content imbalance and decreasing temperature. Our proposed mechanism is general and applies even for experiments where the subgap-conductance PHS breaking cannot be attributed to QP.

Charge-neutral nonlocal response in superconductor-InAs nanowire hybrid devices

Nonlocal quasiparticle transport in normal-superconductor-normal (NSN) hybrid structures probes sub-gap states in the proximity region and is especially attractive in the context of Majorana research. Conductance measurement provides only partial information about nonlocal response composed from both electron-like and hole-like quasiparticle excitations. In this work, we show how a nonlocal shot noise measurement delivers a missing puzzle piece in NSN InAs nanowire-based devices. We demonstrate that in a trivial superconducting phase quasiparticle response is practically charge-neutral, dominated by the heat transport component with a thermal conductance being on the order of conductance quantum. This is qualitatively explained by numerous Andreev reflections of a diffusing quasiparticle, that makes its charge completely uncertain. Consistently, strong fluctuations and sign reversal are observed in the sub-gap nonlocal conductance, including occasional Andreev rectification signals. Our results prove conductance and noise as complementary measurements to characterize quasiparticle transport in superconducting proximity devices.

Conductance asymmetries in mesoscopic superconducting devices due to finite bias

Tunneling conductance spectroscopy in normal metal-superconductor junctions is an important tool for probing Andreev bound states in mesoscopic superconducting devices, such as Majorana nanowires. In an ideal superconducting device, the subgap conductance obeys specific symmetry relations, due to particle-hole symmetry and unitarity of the scattering matrix. However, experimental data often exhibits deviations from these symmetries or even their explicit breakdown. In this work, we identify a mechanism that leads to conductance asymmetries without quasiparticle poisoning. In particular, we investigate the effects of finite bias and include the voltage dependence in the tunnel barrier transparency, finding significant conductance asymmetries for realistic device parameters. It is important to identify the physical origin of conductance asymmetries: in contrast to other possible mechanisms such as quasiparticle poisoning, finite-bias effects are not detrimental to the performance of a topological qubit. To that end we identify features that can be used to experimentally determine whether finite-bias effects are the source of conductance asymmetries.

Photon-assisted resonant Andreev reflections: Yu-Shiba-Rusinov and Majorana states

Photon-assisted tunneling frequently provides detailed information on the underlying charge-transfer process. In particular, the Tien-Gordon approach and its extensions predict that the sideband spacing in bias voltage is a direct fingerprint of the number of electrons transferred in a single tunneling event. Here, we analyze photon-assisted tunneling into subgap states in superconductors in the limit of small temperatures and bias voltages where tunneling is dominated by resonant Andreev processes and does not conform to the predictions of simple Tien-Gordon theory. Our analysis is based on a systematic Keldysh calculation of the subgap conductance and provides a detailed analytical understanding of photon-assisted tunneling into subgap states, in excellent agreement with a recent experiment. We focus on tunneling from superconducting electrodes and into Yu-Shiba-Rusinov states associated with magnetic impurities or adatoms, but we also explicitly extend our results to include normal-metal electrodes or other types of subgap states in superconductors. In particular, we argue that photon-assisted Andreev reflections provide a high-accuracy method to measure small, but nonzero energies of subgap states which can be important for distinguishing conventional subgap states from Majorana bound states.

Conductance spectra of (Nb, Pb, In)/NbP superconductor/Weyl semimetal junctions

The possibility of inducing superconductivity in type-I Weyl semimetal through coupling its surface to a superconductor was investigated. A single crystal of NbP, grown by chemical vapor transport method, was carefully characterized by XRD, EDX, SEM, ARPES techniques and by electron transport measurements. The mobility spectrum of the carriers was determined. For the studies of interface transmission, the (001) surface of the crystal was covered by several hundred nm thick metallic layers of either Pb, or Nb, or In. DC current-voltage characteristics and AC differential conductance through the interfaces as a function of the DC bias were investigated. When the metals become superconducting, all three types of junctions show conductance increase, pointing out the Andreev reflection as a prevalent contribution to the subgap conductance. In the case of Pb-NbP and Nb-NbP junctions, the effect is satisfactorily described by modified Blonder-Tinkham-Klapwijk model. The absolute value of the conductance is much smaller than that for the bulk crystal, indicating that the transmission occurs through only a small part of the contact area. An opposite situation occurs in In-NbP junction, where the conductance at the peak reaches the bulk value indicating that almost whole contact area is transmitting and, additionally, a superconducting proximity phase is formed in the material. We interpret this as a result of indium diffusion into NbP, where the metal atoms penetrate the surface barrier and form very transparent superconductor-Weyl semimetal contact inside. However, further diffusion occurring already at room temperature leads to degradation of the effect, so it is observed only in the pristine structures. Despite of this, our observation directly demonstrates possibility of inducing superconductivity in a type-I Weyl semimetal.

Nonlocal Conductance Spectroscopy of Andreev Bound States: Symmetry Relations and BCS Charges.

Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments.

End-to-end correlated subgap states in hybrid nanowires

End-to-end correlated bound states are investigated in superconductor-semiconductor hybrid nanowires at zero magnetic field. Peaks in subgap conductance are independently identified from each wire end, and a cross-correlation function is computed that counts end-to-end coincidences, averaging over thousands of subgap features. Strong correlations in a short, $300~\mathrm{nm}$ device are reduced by a factor of four in a long, $900~\mathrm{nm}$ device. In addition, subgap conductance distributions are investigated, and correlations between the left and right distributions are identified based on their mutual information.

Asymmetric d-wave superconducting topological insulator in proximity with a magnetic order

In the framework of the Dirac–Bogoliubov–de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet d-wave symmetry. The asymmetric role of this gap respect to the electron–hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of d-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region mzfs and orbital rotated angle α of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.

Andreev bound states probed in three-terminal quantum dots

Andreev bound states (ABSs) are well-defined many-body quantum states that emerge from the hybridization of individual quantum dot (QD) states with a superconductor and exhibit very rich and fundamental phenomena. We demonstrate several electron transport phenomena mediated by ABSs that form on three-terminal carbon nanotube (CNT) QDs, with one superconducting (S) contact in the center and two adjacent normal-metal (N) contacts. Three-terminal spectroscopy allows us to identify the coupling to the N contacts as the origin of the Andreev resonance (AR) linewidths and to determine the critical coupling strengths to S, for which a ground state (or quantum phase) transition in such S-QD systems can occur. In addition, we ascribe replicas of the lowest-energy ABS resonance to transitions between the ABS and odd-parity excited QD states, a process we call excited state ABS resonances. In the conductance between the two N contacts we find a characteristic pattern of positive and negative differential subgap conductance, which we explain by considering two nonlocal processes, the creation of Cooper pairs in S by electrons from both N terminals, and a transport mechanism we call resonant ABS tunneling, possible only in multiterminal QD devices. In the latter process, electrons are transferred via the ABS without effectively creating Cooper pairs in S. The three-terminal geometry also allows spectroscopy experiments with different boundary conditions, for example by leaving S floating. Surprisingly, we find that, depending on the boundary conditions and the device parameters, the experiments either show single-particle Coulomb blockade resonances, ABS characteristics, or both in the same measurements, seemingly contradicting the notion of ABSs replacing the single-particle states as eigenstates of the QD. We qualitatively explain these results as originating from the finite time scale required for the coherent oscillations between the superposition states after a single-electron tunneling event. These experiments demonstrate that three-terminal experiments on a single complex quantum object can also be useful to investigate charge dynamics otherwise not accessible due to the very high frequencies.

Conduction spectroscopy of a proximity induced superconducting topological insulator

The combination of superconductivity and the helical spin-momentum locking at the surface state of a topological insulator (TI) has been predicted to give rise to p-wave superconductivity and Majorana bound states. The superconductivity can be induced by the proximity effect of a s-wave superconductor (S) into the TI. To probe the superconducting correlations inside the TI, dI/dV spectroscopy has been performed across such S–TI interfaces. Both the alloyed Bi1.5Sb0.5Te1.7Se1.3 and the stoichiometric BiSbTeSe2 have been used as three-dimensional TI. In the case of Bi1.5Sb0.5Te1.7Se1.3, the presence of disorder induced electron–electron interactions can give rise to an additional zero-bias resistance peak. For the stoichiometric BiSbTeSe2 with less disorder, tunnel barriers were employed in order to enhance the signal from the interface. The general observations in the spectra of a large variety of samples are conductance dips at the induced gap voltage, combined with an increased sub-gap conductance, consistent with p-wave predictions. The induced gap voltage is typically smaller than the gap of the Nb superconducting electrode, especially in the presence of an intentional tunnel barrier. Additional uncovered spectroscopic features are oscillations that are linearly spaced in energy, as well as a possible second order parameter component.

The Andreev conductance in superconductor–insulator–normal metal structures

The Andreev subgap conductance at 0.08–0.2 K in thin-film superconductor (aluminum)–insulator–normal metal (copper, hafnium, or aluminum with iron-sublayer-suppressed superconductivity) structures is studied. The measurements are performed in a magnetic field oriented either along the normal or in the plane of the structure. The dc current–voltage (I–U) characteristics of samples are described using a sum of the Andreev subgap current dominating in the absence of the field at bias voltages U < (0.2–0.4)Δc/e (where Δc is the energy gap of the superconductor) and the single-carrier tunneling current that predominates at large voltages. To within the measurement accuracy of 1–2%, the Andreev current corresponds to the formula $${I_n} + {I_s} = {K_n}\tanh \left( {{{eU} \mathord{\left/ {\vphantom {{eU} {2k{T_{eff}}}}} \right. \kern-\nulldelimiterspace} {2k{T_{eff}}}}} \right) + {K_s}{{\left( {{{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} \right)} {\sqrt {1 - {{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - {{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} }}$$ following from a theory that takes into account mesoscopic phenomena with properly selected effective temperature T eff and the temperature- and fieldindependent parameters K n and K s (characterizing the diffusion of electrons in the normal metal and superconductor, respectively). The experimental value of K n agrees in order of magnitude with the theoretical prediction, while K s is several dozen times larger than the theoretical value. The values of T eff in the absence of the field for the structures with copper and hafnium are close to the sample temperature, while the value for aluminum with an iron sublayer is several times greater than this temperature. For the structure with copper at T = 0.08–0.1 K in the magnetic field B|| = 200–300 G oriented in the plane of the sample, the effective temperature T eff increases to 0.4 K, while that in the perpendicular (normal) field B ⊥ ≈ 30 G increases to 0.17 K. In large fields, the Andreev conductance cannot be reliably recognized against the background of single- carrier tunneling current. In the structures with hafnium and in those with aluminum on an iron sublayer, the influence of the magnetic field is not observed.

Spin-triplet f-wave symmetry in superconducting monolayer [formula omitted

The proximity-induced spin-triplet f-wave symmetry pairing in a monolayer molybdenum disulfide-superconductor hybrid features an interesting electron-hole excitations and also effective superconducting subgap, giving rise to a distinct Andreev resonance state. Owing to the complicated Fermi surface and momentum dependency of f-wave pair potential, monolayer MoS2 with strong spin-orbit coupling can be considered an intriguing structure to reveal the superconducting state. Actually, this can be possible by calculating the peculiar spin-valley polarized transport of quasiparticles in a related normal metal/superconductor junction. We theoretically study the formation of effective gap at the interface and resulting normalized conductance on top of a MoS2 under induction of f-wave order parameter, using Blonder-Tinkham-Klapwijk formalism. The superconducting excitations shows that the gap is renormalized by a bias limitation coefficient including dynamical band parameters of monolayer MoS2, especially, ones related to the Schrodinger-type momentum of Hamiltonian. The effective gap is more sensitive to the n-doping regime of superconductor region. The signature of spin-orbit coupling, topological and asymmetry mass-related terms in the resulting subgap conductance and, in particular, maximum conductance is presented. In the absence of topological term, the effective gap reaches to its maximum value. The unconventional nature of superconducting order leads to the appearance of zero-bias conductance. In addition, the maximum value of conductance can be controlled by tuning the doping level of normal and superconductor regions.