Subgap Structures Research Articles

Proximity-induced superconductivity in type-II Weyl semimetal NbIrTe4

Heterostructures between conventional superconductors and materials with different electronic ground states have emerged as a powerful method for exploring the exotic superconducting properties induced by the proximity effect. Here, we investigate Andreev transport through the interface between an s-wave superconductor Nb and a type-II Wely semimetal NbIrTe4. The differential conductance measurement reveals an anomalous zero-bias conductance peak and prominent subgap structures at low temperatures. Furthermore, we found that these subgap structures are not only related to the interface coupling strength but also influenced by the thickness of the NbIrTe4 flake. For thin devices (≤100 nm), the differential conductance spectra only exhibit a single-gap structure. While in thicker devices (∼150 nm), we observed the distinct double-gap structure, which is likely to originate from the proximity-induced superconductivity gap on the bulk and surface of the NbIrTe4 flakes. These results can provide a good reference for understanding the superconducting phase in type-II Weyl semimetals and take a step toward its future application in the field of superconducting electronics.

Intrinsic cluster-shaped density waves in cellular dynamical mean-field theory

It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows us to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster---cluster density waves---in all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunneling microscopy. We relate these subgap structures to nodal and antinodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.

How does the break-junction quasiparticle tunnel conductance look like for d-wave superconductors?

The bias-voltage, V, dependences of the differential tunnel conductance G(V) = dJ/DV were calculated for the quasiparticle current J flowing in the ab plane across the break junction made of d-wave superconductors. The tunnel directionality effect was taken into account by introducing an effective tunneling cone described by the angle 2θ0. It was shown that G(V) looks like predominantly d-wave or isotropic s-wave ones, depending on the magnitude of θ0 and the rotation angles of the crystal lattices of electrodes with respect to the junction plane. In certain configurations, the G(V) dependences of nominally symmetric S-I-S junctions may turn out similar to those for non-symmetric S–I–N junctions (here, S, I, and N denote superconductors, insulators, and normal metals, respectively) and provide misleading information about the actual energy gap. At finite temperatures, sub-gap structures appear, which possess features appropriate to both d- and s-wave superconductors and are dependent on the problem parameters.

Subgap structures and pseudogap in cuprate superconductors: Role of density waves

In scanning tunneling microscopy (STM) conductance curves, the superconducting gap of cuprates is sometimes accompanied by small sub-gap structures at very low energy. This was documented early on near vortex cores and later at zero magnetic field. Using mean-field toy models of coexisting d-wave superconductivity ($d$SC), \emph{d}-form factor density wave ($d$FF-DW), and extended s-wave pair density wave ($s'$PDW), we find agreement with this phenomenon, with $s'$PDW playing a critical role. We explore the high variability of the gap structure with changes in band structure and density wave (DW) wave vector, thus explaining why sub-gap structures may not be a universal feature in cuprates. In the absence of nesting, non-superconducting results never show signs of pseudogap, even for large density waves magnitudes, therefore reinforcing the idea of a distinct origin for the pseudogap, beyond mean-field theory. Therefore, we also briefly consider the effect of DWs on a pre-existing pseudogap.

Quantum Coherence of the Quartet Scheme Observed by Shapiro Resonance Under Radio-Frequency Irradiation in Three Terminal Josephson Junctions

We have investigated three-terminal superconductor (S)–normal metal (N)–superconductor (S) Josephson junctions. In a geometry where a T-shaped normal metal (Cu) is connected to three superconducting reservoirs (Al), new subgap structures appear in the differential resistance when the bias voltages on two of the three terminals compensate each other exactly. These features correspond to the correlated motion of Cooper pairs within the structure. They are consistent with the prediction of quartets formed by the simultaneous splitting of two Cooper pairs at one of the superconducting contacts and the emission of two phase correlated Cooper pairs in the two other electrodes. To test the quantum coherence of such mechanism, we have studied the effect of a radio-frequency irradiation at 14 GHz down to 100 mK. Well known Shapiro steps involving two terminals are measured, and in particular, half-integer steps are observed. This is consistent with the transfer of two Cooper pairs between two terminals. This paper reveals that the quartet resonances also show Shapiro steps in agreement with the quartet mechanism. Our findings confirm the quartet scenario and demonstrate its coherent nature.

Subgap structure in the conductance of a three-terminal Josephson junction

Three-terminal superconductor $(S)$-normal metal $(N)$-superconductor $(S)$ Josephson junctions are investigated. In a geometry where a T-shape normal metal is connected to three superconducting reservoirs, new subgap structures appear in the differential resistance for specific combinations of the superconductor chemical potentials. Those correspond to a correlated motion of Cooper pairs within the device that persist well above the Thouless energy and is consistent with the prediction of quartets formed by two entangled Cooper pairs. A simplified nonequilibrium Keldysh-Green's function calculation is presented that supports this interpretation.

Zero-Bias Anomaly in a Nanowire Quantum Dot Coupled to Superconductors

We studied the low-energy states of spin-1/2 quantum dots defined in InAs/InP nanowires and coupled to aluminum superconducting leads. By varying the superconducting gap Δ with a magnetic field B we investigated the transition from strong coupling Δ << T(K) to weak-coupling Δ >> T(K), where T(K) is the Kondo temperature. Below the critical field, we observe a persisting zero-bias Kondo resonance that vanishes only for low B or higher temperatures, leaving the room to more robust subgap structures at bias voltages between Δ and 2Δ. For strong and approximately symmetric tunnel couplings, a Josephson supercurrent is observed in addition to the Kondo peak. We ascribe the coexistence of a Kondo resonance and a superconducting gap to a significant density of intragap quasiparticle states, and the finite-bias subgap structures to tunneling through Shiba states. Our results, supported by numerical calculations, own relevance also in relation to tunnel-spectroscopy experiments aiming at the observation of Majorana fermions in hybrid nanostructures.

Sensing with Superconducting Point Contacts

Superconducting point contacts have been used for measuring magnetic polarizations, identifying magnetic impurities, electronic structures, and even the vibrational modes of small molecules. Due to intrinsically small energy scale in the subgap structures of the supercurrent determined by the size of the superconducting energy gap, superconductors provide ultrahigh sensitivities for high resolution spectroscopies. The so-called Andreev reflection process between normal metal and superconductor carries complex and rich information which can be utilized as powerful sensor when fully exploited. In this review, we would discuss recent experimental and theoretical developments in the supercurrent transport through superconducting point contacts and their relevance to sensing applications, and we would highlight their current issues and potentials. A true utilization of the method based on Andreev reflection analysis opens up possibilities for a new class of ultrasensitive sensors.

Superconducting Junction of a Single-Crystalline Au Nanowire for an Ideal Josephson Device

We report on the fabrication and measurements of a superconducting junction of a single-crystalline Au nanowire, connected to Al electrodes. The current-voltage characteristic curve shows a clear supercurrent branch below the superconducting transition temperature of Al and quantized voltage plateaus on application of microwave radiation, as expected from Josephson relations. Highly transparent (0.95) contacts very close to an ideal limit of 1 are formed at the interface between the normal metal (Au) and the superconductor (Al). The very high transparency is ascribed to the single crystallinity of a Au nanowire and the formation of an oxide-free contact between Au and Al. The subgap structures of the differential conductance are well explained by coherent multiple Andreev reflections (MAR), the hallmark of mesoscopic Josephson junctions. These observations demonstrate that single crystalline Au nanowires can be employed to develop novel quantum devices utilizing coherent electrical transport.

Switching current distributions and subgap structures of underdoped (Hg,Re)Ba2Ca2Cu3O8+δ intrinsic Josephson junctions

We have investigated the intrinsic Josephson properties in slightly underdoped (Hg,Re)Ba2Ca2Cu3Oy [Hg(Re)1223] intrinsic Josephson junctions (IJJs) with a dimension of 1.0×1.5×0.11 μm3. The current-voltage characteristics of the IJJs exhibit clear multiple branches with subgap structures similar to those of other cuprate superconductors. The switching current distributions P(I) from the zero-voltage to the nonzero-voltage state in the current-biased IJJs agree well with the theoretical curves of the thermally assisted escape model at temperatures above ≈5 K. The plasma frequency fp of the IJJs is estimated to be 1.3 THz from the fluctuation-free critical current density of 2.0×105 A/cm2, which is one of the highest among cuprate superconductors, reflecting the high Tc and a relatively low anisotropy of the Re doped Hg system. The P(I) gradually becomes independent of temperature below ≈5 K, which suggests a crossover of the escape process from thermal activation to quantum tunneling at such a high temperature.

The Behavior of Subgap Structures of Intrinsic Josephson Junctions in $({\rm Bi},{\rm Pb})_{2}{\rm Sr}_{2}{\rm CaCu}_{2}{\rm O}_{\rm y}$Under Magnetic Field and Microwave Irradiation

We have extensively studied the behavior of pronounced subgap structures on the quasiparticle branches of the current-voltage (I-V) characteristics of intrinsic Josephson junctions (IJJs) in (Bi1-xPbx)2Sr2CaCu2Oy (x=0.15, 0.2) single crystals for their applications in THz range. Six subgap structures are successfully observed between 6.3 and 26.2 mV on the first quasiparticle branch at 4.2 K. The intensities of two typical subgap structures at 6.3 and 8.2 mV are found to be approximately proportional to Ic 2 (critica current)2 over a wide range of temperature between 4.2 and ~ 80 K. They are interpreted with regard to the interference of Raman-active optical phonons with ac Josephson currents in IJJs. Under magnetic field up to 2.5 T they have been affected somewhat in the respect to return current, though the vortex flow also has been induced in IJJs. By microwave application of 2-100 GHz they have been strongly affected so that their peak intensities decrease and then each peak splits into two, with increasing microwave power.

Cluster-glass wave function in the two-dimensional extendedt−Jmodel

The recent observation of an electronic cluster glass state composed of random domains with unidirectional modulation of charge density and/or spin density on ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ reinvigorates the debate of existence of competing interactions and their importance in high-temperature superconductivity. By using a variational approach, here we show that the presence of the cluster glass state is actually an inherent nature of the model based on the antiferromagnetic interaction $(J)$ only, i.e., the well-known $t\text{\ensuremath{-}}J$ model. There is no need yet to introduce a competing interaction to understand the existence of the cluster glass state. The long-range pairing correlation is not much influenced by the disorder in the glass state which also has nodes and linear density of states. In the antinodal region, the spectral weight is almost completely suppressed. The modulation also produces subgap structures inside the ``coherent'' peaks of the local density of states.

Fabrication and characteristics of intrinsic Josephson junctions in Bi2Sr2CaCu2O8+x single crystals

Mesa-structured intrinsic Josephson junctions are fabricated in Bi2Sr2CaCu2O8+x single crystals. Typical current-voltage characteristics of intrinsic Josephson junctions are observed, which include multiple quasi-particle branches, surface junction with critical current lower than those of inner junctions, and subgap structures on quasiparticle branches. The corresponding physical explanations are also given. The energy gap voltage of the intrinsic Josephson junctions at 30 K is about 20 mV. Besides, the measuredI c -T relationship agrees quite well with the theoretical computations based on\(d_{x^2 - y^2 } - wave\) superconductor. Our measureddI/dV−V relationship shows theV-shaped gap structure, obviously differing from the U-shaped gap structure of the s-wave superconductor.

Local and macroscopic tunneling spectroscopy ofY1−xCaxBa2Cu3O7−δfilms: Evidence for a doping-dependentisoridxycomponent in the order parameter

Tunneling spectroscopy of epitaxial (110) Y1-xCaxBa2Cu3O7-d films reveals a doping dependent transition from pure d(x2-y2) to d(x2-y2)+is or d(x2-y2)+idxy order parameter. The subdominant (is or idxy) component manifests itself in a splitting of the zero bias conductance peak and the appearance of subgap structures. The splitting is seen in the overdoped samples, increases systematically with doping, and is found to be an inherent property of the overdoped films. It was observed in both local tunnel junctions, using scanning tunneling microscopy (STM), and in macroscopic planar junctions, for films prepared by either RF sputtering or laser ablation. The STM measurements exhibit fairly uniform splitting size in [110] oriented areas on the order of 10 nm2 but vary from area to area, indicating some doping inhomogeneity. U and V-shaped gaps were also observed, with good correspondence to the local faceting, a manifestation of the dominant d-wave order parameter.

The influence of microwave irradiation on the pronounced subgap structures in intrinsic Josephson junctions of (Bi 1− xPb x) 2Sr 2CaCu 2O y

We have studied the behavior of pronounced subgap structures in the current–voltage ( I– V) characteristics of intrinsic Josephson junctions in (Bi 1− x Pb x ) 2Sr 2CaCu 2O y (with x=∼0.15, ∼0.2) mesas at 4.2 K without and with 2–20 GHz microwave irradiation. Without microwave irradiation, the I– V characteristics exhibited a set of superconducting and resistive quasiparticle branches corresponding to the constituent intrinsic Josephson junctions, with accompanying small subgap structures on the quasiparticle branches. Under irradiation of relatively high power of microwaves, the pronounced hysteretic subgap structures reduced, and new fine structures appeared beside them on the quasiparticle branches. The appearance of both original and new fine subgap structures was interpreted with regard to the interference of Raman-optical phonons with ac Josephson current in the intrinsic Josephson junctions.

Subgap structures in the current–voltage properties of La 2− xSr xCuO 4 intrinsic Josephson junctions

We investigated current–voltage ( I– V) properties of intrinsic Josephson junctions in c-axis micro-bridges (∼20 μm 2 area for ab plane and ∼1 μm length along the c-axis) of La 2− x Sr x CuO 4 single crystals. The micro-bridges were fabricated by the focused-ion-beam etching technique. We found periodic conductance peaks below the gap voltage in the RCSJ-like I– V curves of the intrinsic Josephson junctions. We discuss possible explanations and show that the subgap structures can be explained by coupling between ac Josephson oscillation and Josephson plasma oscillation in La 2− x Sr x CuO 4.

New features of subgap structures in intrinsic Josephson junctions of (Bi 1− xPb x) 2Sr 2CaCu 2O y

We have investigated the pronounced subgap structures in intrinsic Josephson junctions of (Bi 1− x Pb x ) 2Sr 2CaCu 2O y mesas with x≲0.2. The structures appear to be composed of multiple subbranches on quasiparticle branches in the current–voltage characteristics, independent of x, junction geometry, weak magnetic field and temperature T lower than the disappearance temperatures of subbranches T d. The excess current densities of the subbranches are approximately proportional to the critical current density of the intrinsic Josephson junctions at 4.2 K, and tend to increase, when T approaches T d. These features of the structures are discussed within the framework of the recently proposed coupling mechanisms between optical phonons and Josephson oscillations.

Theory for the coupling between longitudinal phonons and intrinsic Josephson oscillations in layered superconductors

In this publication a microscopic theory for the coupling of intrinsic Josephson oscillations in layered superconductors with longitudinal c-axis-phonons is developed. It is shown that the influence of lattice vibrations on the c-axis transport can be fully described by introducing an effective longitudinal dielectric function. Resonances in the I-V-characteristic appear at van Hove singularities of both acoustical and optical longitudinal phonon branches. This provides a natural explanation of the recently discovered subgap structures in the I-V-characteristic of highly anisotropic cuprate superconductors. The effect of the phonon dispersion on the damping of these resonances and the coupling of Josephson oscillations in different resistive junctions due to phonons are discussed in detail.

Subgap conductance structures of a normal-conductor–superconductor junction induced by a magnetic impurity

The transport properties in a normal-conductor–superconductor (NS) junction are investigated when a magnetic impurity is present in the normal region. As the spin of quasiparticles is reversed when they are Andreev-reflected from the NS interface, spin-flip scattering takes place regardless the spin alignment of an incident quasiparticle with respect to the magnetic impurity. The magnetic coupling between the quasiparticle and the impurity gives rise to subgap conductance peaks. The resonance state responsible for the subgap structures is found to be a hybrid of singlet and triplet states.

Photon-assisted Andreev transport and sub-gap structures

We report new measurements of microwave-induced perturbations of the sub-harmonic energy gap structures in the current–voltage characteristics of superconductor–semiconductor-superconductor junctions. Around the sub-gap bias voltages associated with the enhanced quasi-particle transfer mediated by multiple Andreev reflection processes we observe microwave induced satellites, shifted in voltage by multiples of hf/ en, where hf is the photon energy and n is the number of quasi-particle traversals as determined by the Andreev processes. The observed behavior is the analogue of the so-called photon-assisted tunneling but here associated with the multiple Andreev reflections.