We study the tunneling of Bogoliubov excitations through a barrier in a Bose-Einstein condensate. We extend our previous work [Phys. Rev. A \textbf{78}, 013628 (2008)] to the case when condensate densities are different between the left and right of the barrier potential. In the framework of the Bogoliubov mean-field theory, we calculate the transmission probability and phase shift, as well as the energy flux and quasiparticle current carried by Bogoliubov excitations. We find that Bogoliubov phonons twist the condensate phase due to a back-reaction effect, which induces the Josephson supercurrent. While the total current given by the sum of quasiparticle current and induced supercurrent is conserved, the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low energy region. When the condensate densities are different between the left and right of the barrier, the excess quasiparticle current, as well as the induced supercurrent, remains finite far away from the barrier. We also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions. We show that supercurrent can be generated inside the condensate by injecting free atoms from outside. On the other hand, atoms are emitted when the
Bogoliubov phonons propagate toward the phase boundary from the superfluid region.
The multi-terminal Josephson effect allows DC supercurrent to flow at finite commensurate voltages. Existing proposals to realize this effect rely on nonlocal Andreev processes in superconductor-normal-superconductor junctions. However, this approach requires precise control over microscopic states and is obscured by dissipative current. We show that standard tunnel Josephson circuits also support multiplet supercurrent mediated only by local tunneling processes. Furtheremore, we observe that the supercurrents persist even in the high charging energy regime in which only sequential Cooper tran…
We study the dynamics of the Bogoliubov wave packet in superconductors and calculate the supercurrent carried by the wave packet. We discover an anomalous contribution to the supercurrent, related to the quantum metric of the Bloch wave function. This anomalous contribution is most important for flat or quasiflat bands, as exemplified by the attractive Hubbard models on the Creutz ladder and sawtooth lattice. Our theoretical framework is general and can be used to study a wide variety of phenomena, such as spin transport and exciton transport.
We report current driven scanning tunneling spectroscopy (CDSTS) measurements at very low temperatures on vortices in 2H-NbSe2. We find that a current produces an increase of the density of states at the Fermi level in between vortices, and a reduction of the zero bias peak at the vortex center. This occurs well below the de-pairing current. We conclude that a supercurrent affects the low energy part of the superconducting gap structure of 2H-NbSe2.
We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. We find the anomalous enhancement of the quasiparticle current $J_{\rm q}$ carried by Bogoliubov phonons near a potential barrier, due to the supply of the excess current from the condensate. This effect leads to the increase of quasiparticle transmission probability in the low energy region found by Kovrizhin {\it et al.}. We also show that the quasiparticle current twists the phase of the condensate wavefunction across the barrier, leading to a finite Josephson supercurrent $J_{\rm s}$ through the barrie…
We present a version of acoustic black holes by using the principle of the Josephson effect. We find that in the case two superconductors $A$ and $B$ are separated by an insulating barrier, an acoustic black hole may be created in the middle region between the two superconductors. We discuss in detail how to describe an acoustic black hole in the Josephson junction and write the metric in the langauge of the superconducting electronics. Our final results infer that for big enough tunneling current and thickness of the junction, experimental verification of the Hawking temperature could be poss…
We study the Josephson effect in a triplet superconductor--ferromagnet--singlet superconductor junction. We show that the interaction of tunneling Cooper pairs with the interface magnetization can permit a Josephson current at the lowest order of a tunneling Hamiltonian perturbation theory. Two conditions must be satisfied for this to occur: the magnetization of the ferromagnet has a component parallel to the ${\bf d}$-vector of the triplet superconductor, and the gaps of the superconductors have the same parity with respect to the interface momentum. The resulting charge current displays an u…
The single-particle excitations of a superconductor are coherent superpositions of electrons and holes near the Fermi level, called Bogoliubov quasiparticles. They are Majorana fermions, meaning that pairs of quasiparticles can annihilate. We calculate the annihilation probability at a beam splitter for chiral quantum Hall edge states, obtaining a 1 +/- cos phi dependence on the phase difference phi of the superconductors from which the excitations originated (with the +/- sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in…
We have measured the tunneling density of states (DOS) in a superconductor carrying a supercurrent or exposed to an external magnetic field. The pair correlations are weakened by the supercurrent, leading to a modification of the DOS and to a reduction of the gap. As predicted by the theory of superconductivity in diffusive metals, we find that this effect is similar to that of an external magnetic field.
We study a Cooper-pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, due to the Coulomb blockade,mediate a supercurrent by coherent co-tunneling of Cooper pairs. We show that the supercurrent resulting from such co-tunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably,this phase offset persists wh…
We argue that a superconducting state with a Fermi-surface of Bogoliubov quasiparticles, a Bogoliubov Fermi-surface (BG-FS), can be identified by the dependence of physical quantities on disorder. In particular, we show that a linear dependence of the residual density of states at weak disorder distinguishes a BG-FS state from other nodal superconducting states. We further demonstrate the stability of supercurrent against impurities and a characteristic Drude-like behavior of the optical conductivity. Our results can be directly applied to electron irradiation experiments on candidate material…
Using tunneling spectroscopy, we have measured the local electron energy distribution function in the normal part of a superconductor-normal metal-superconductor (SNS) Josephson junction containing an extra lead to a normal reservoir. In the presence of simultaneous supercurrent and injected quasiparticle current, the distribution function exhibits a sharp feature at very low energy. The feature is odd in energy, and odd under reversal of either the supercurrent or the quasiparticle current direction. The feature represents an effective temperature gradient across the SNS Josephson junction th…
We show that a supercurrent carried by spinless singlet Cooper pairs can induce a spin accumulation in the normal metal interlayer of a Josephson junction. This phenomenon occurs when a nonequilibrium spin-energy mode is excited in the normal metal, for instance by an applied temperature gradient between ferromagnetic electrodes. Without supercurrent, the spin accumulation vanishes in the Josephson junction. With supercurrent, a spatially antisymmetric spin accumulation is generated that can be measured by tunneling to a polarized detector electrode. We explain the physical origin of the induc…
Supercurrent effect in a charge density wave intertwined superconductor
School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology（华中科技大学物理学院、武汉国家强磁场中心）；Department of Physics, Zhejiang University（浙江大学物理系）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））
Motivated by recent work on strain-induced pseudo-magnetic fields in Dirac and Weyl semimetals, we analyze the possibility of analogous fields in two-dimensional nodal superconductors. We consider the prototypical case of a d-wave superconductor, a representative of the cuprate family, and find that the presence of weak strain leads to pseudo-magnetic fields and Landau quantization of Bogoliubov quasiparticles in the low-energy sector. A similar effect is induced by the presence of generic, weak doping gradients. In contrast to genuine magnetic fields in superconductors, the strain- and doping…
The RCSJ model of resistively and capacitively shunted Josephson junctions is used to describe superconducting point contacts over a wide range of resistances up to the metallic -- tunneling transition. Their small dynamic capacitance of order $C = 0.1 $fF due to the point-contact geometry results in a huge plasma frequency. The critical current is then strongly suppressed and the contact resistance becomes finite because of quantum-mechanical zero-point fluctuations of the Josephson plasma and the rather large escape rate out of the zero-voltage state due to quantum tunneling. We test the pre…
We study a two-terminal graphene Josephson junction with contacts shaped to form a narrow constriction, less than 100nm in length. The contacts are made from type II superconducting contacts and able to withstand magnetic fields high enough to reach the quantum Hall (QH) regime in graphene. In this regime, the device conductance is determined by edge states, plus the contribution from the constricted region. In particular, the constriction area can support supercurrents up to fields of ~2.5T. Moreover, enhanced conductance is observed through a wide range of magnetic fields and gate voltages. …
We report a coherence-length scale phenomenon related to how the high-Tc order parameter (OP) evolves under a directly-applied supercurrent. Scanning tunneling spectroscopy was performed on current-carrying YBa_2Cu_3O_7-delta thin-film strips at 4.2K. At current levels well below the theoretical depairing limit, the low-energy Andreev states are suppressed by the supercurrent, while the gap-like structures remain unchanged. We rule out the likelihood of various extrinsic effects, and propose instead a model based on phase fluctuations in the d-wave BTK formalism to explain the suppression. Our…
We address the question of probing the supercurrents in superconducting (SC) samples on a local scale by performing Scanning Tunneling Spectroscopy (STS) experiments with a SC tip. In this configuration, we show that the tunneling conductance is highly sensitive to the Doppler shift term in the SC quasiparticle spectrum of the sample, thus allowing the local study of the superfluid velocity. Intrinsic screening currents, such as those surrounding the vortex cores in a type II SC in a magnetic field, are directly probed. With Nb tips, the STS mapping of the vortices, in single crystal 2H-NbSe_2…
We introduce a new approach to the Josephson effect in SIS tunnel junctions. The Josephson coupling energy is calculated from the overlap of real space Cooper pair wavefunctions in two superconductors through an insulating barrier. It is shown that the Josephson tunneling is limited by the size of the Cooper pair and its shrinking during the tunneling. Therefore, the Josephson coupling energy and the critical current become extremely small in high $T_{c}$ superconductors, including $MgB_{2}$. This shrinking also causes the observed DC supercurrent in low $T_{c}$ superconductors, such as Pb and…
Superconducting excitations --Bogoliubov quasiparticles -- are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). Depending on the applied voltage bias in STM one can sample the particle and hole content of such a superconducting excitation. Recent Scanning Tunneling Microscope (STM) experiments offer a unique insight into the inner workings of the superconducting state of superconductors. We propose a new observable quantity for STM studies that is the manifestation of the particle-hole dualism of the quasiparticles. We call it a {\em Bogoliub…
We have measured, in real time, individual quasiparticle tunneling in a single Cooper pair transistor, using rf reflectometry on the supercurrent branch. We have extracted the even-to-odd and odd-to-even transition rates directly by analyzing the distributions of dwell times in the even and odd states of the transistor. We discuss both the measurement and analysis techniques and report on the temperature and gate dependence of the quasiparticle tunneling rates.
Using a numerical tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method we describe Josephson junctions made of multilayer graphene contacted by top superconducting gates. Both Bernal (ABA) and rhombohedral (ABC) stacking are considered and we find that the type of stacking has a strong effect on the proximity effect and the supercurrent flow. For both cases the pair amplitude shows a polarization between dimer and non-dimer atoms, being more pronounced for rhombohedral stacking. Even though the proximity effect in non-dimer sites is enhanced when compared to single layer g…
Polarization Controlled Supercurrent in Ferroelectric Josephson Junction
Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学开利纳米科学研究所）；Department of Quantum Nanoscience, Delft University of Technology（代尔夫特理工大学量子纳米科学系）；WPI-AIMR & IMR & CSIS, Tohoku University（东北大学世界顶尖科学家研究中心、材料科学高等研究院及化学系统信息学中心）；Kavli Institute for Theoretical Sciences, University of the Chinese Academy of Sciences（中国科学院大学理论科学研究所）
In copper- and iron-based unconventional superconductors, the Bogoliubov quasiparticles interact with a spin resonance at momentum $(π,π)$. This interaction is revealed by specific signatures in the quasiparticle spectroscopies, like kinks in photoemission and dips in tunneling. We study these signatures, as they appear inside and around a vortex core in the local density of states (LDOS), a property accessible experimentally by scanning tunneling spectroscopy. Our model retains the whole nonlocal structure of the self-energy in space and time and is therefore not amenable to a Hamiltonian tre…
Based on the Bogoliubov-de Gennes equations, we investigate the transport of the Josephson current in a S/$f_L$-F$_1$-$f_C$-F$_2$-$f_R$/S junction, where S and F$_{1,2}$ are superconductors and ferromagnets, and $f_{L, C, R}$ are the left, central, and right spin-active interfaces. These interfaces have noncollinear magnetizations, and the azimuthal angles of the magnetizations at the $f_{L, C, R}$ interfaces are $χ_{L, C, R}$. We demonstrate that, if both the ferromagnets have antiparallel magnetizations, the critical current oscillates as a function of the exchange field and the thickness of…
Electronic transport through nanostructures is greatly affected by the presence of superconducting leads. If the interface between the nanostructure and the superconductors is sufficiently transparent, a dissipationless current (supercurrent) can flow through the device due to the Josephson effect. A Josephson coupling, as measured via the zero-resistance supercurrent, has been obtained via tunnel barriers, superconducting constrictions, normal metals, and semiconductors. The coupling mechanisms vary from tunneling to Andreev reflection. The latter process has always occurred via a normal-type…
Motivated by theory and experiments on strain induced pseudo-Landau levels (LLs) of Dirac fermions in graphene and topological materials, we consider its extension for Bogoliubov quasiparticles (QPs) in a nodal superconductor (SC). We show, using an effective low energy description and numerical lattice calculations for a d-wave SC, that a spatial variation of the electronic hopping amplitude or a spatially varying s-wave pairing component can act as a pseudo-magnetic field for the Bogoliubov QPs, leading to the formation of pseudo-LLs. We propose realizations of this phenomenon in the cuprate…
From measurements of the c-axis I-V characteristics of intrinsic Josephson junctions in Bi_2Sr_2CaCu_2O_{8+delta} (Bi-2212) mesas we obtain the field dependence (H || c) of the quasiparticle (QP) conductivity, sigma_q(H,T), and of the Josephson critical current density, J_c(H,T). The quasiparticle conductivity sigma_q(H) increases sharply with H and reaches a plateau at 0.05 T <H< 0.3 T. We explain such behavior by the dual effect of supercurrents around vortices. First, they enhance the QP DOS, leading to an increase of sigma_q with H at low H and, second, they enhance the scattering rate for…
We present a consistent theory of superconductive tunneling in single-mode junctions within a scattering formulation of Bogoliubov-de Gennes quantum mechanics. Both dc Josephson effect and dc quasiparticle transport in voltage biased junctions are considered. Elastic quasiparticle scattering by the junction determines equilibrium Josephson current. We discuss the origin of Andreev bound states in tunnel junctions and their role in equilibrium Josephson transport. In contrast, quasiparticle tunneling in voltage biased junctions is determined by inelastic scattering. We derive a general expressi…
In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current-voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.
Supercurrents in Josephson junctions with chiral molecular potentials
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Universitá degli Studi di Padova（帕多瓦大学）；National Institute of Nuclear Physics (INFN), Padova Section（意大利国家核物理研究所帕多瓦分部）；Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）
When the interface of a superconductor (SC) with Weyl semimetal (WSM) supports Fermi arcs, the chirality blockade eliminates the induction of superconductivity into the bulk. This leaves the Fermi arc states as the only low-energy degrees of freedom in the proximity problem. Therefore the SC|WSM system will be a platform to probe transport properties that only involve the Fermi arcs. With a boundary condition that flips the spin at the boundary, we find a $Z_2$ protected Bogoliubov Fermi contour (BFC) around which the Bogoliubov quasi-particles disperse linearly. The resulting BFC and excitati…
The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the stron…
Quasiparticle interference (QPI) by means of scanning tunneling microscopy/spectroscopy (STM/STS), angle resolved photoemission spectroscopy (ARPES), and multi-orbital tight bind- ing calculations are used to investigate the band structure and superconducting order parameter of LiFeAs. Using this combination we identify intra- and interband scattering vectors between the hole (h) and electron (e) bands in the QPI maps. Discrepancies in the band dispersions inferred from previous ARPES and STM/STS are reconciled by recognizing a difference in the $k_z$ sensitivity for the two probes. The observ…
Since the early days of Bardeen-Cooper-Schrieffer theory, it has been predicted that a sufficiently large supercurrent can close the energy gap in a superconductor and creates gapless Bogoliubov quasiparticles through the Doppler shift of quasiparticle energy due to the Cooper pair momentum. In this gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal state Fermi surface, while its remaining part is still gapped. The finite density of states of field-induced quasiparticles, known as the Volovik effect, has been observed in tunneling and specific heat meas…
Quasiparticle interference (QPI) imaging of Bogoliubov excitations in quasi-two dimensional unconventional superconductors has become a powerful technique for measuring the superconducting gap and its symmetry. Here, we present the extension of this method to three-dimensional superconductors and analyze the expected QPI spectrum for the two-component heavy fermion superconductor UPt$_3$ whose gap structure is still controversial. Starting from a 3D electronic structure and the three proposed chiral gap models $E_{1g,u}$ or $E_{2u}$, we perform a slab calculation that determines the 2D continu…
Landau-Zener tunneling and quantum interference of Andreev states
I.E.Tamm Department of Theoretical Physics, P.N.Lebedev Physical Institute（P.N.列别杰夫物理研究所 I.E.塔姆理论物理系）；National Research University Higher School of Economics（国立研究型高等经济大学）
The effects of a non-magnetic Zn impurity substituting an in-plane Cu are studied by solving the Bogoliubov-de Gennes equation self-consistently which is derived from the \ttju Hamiltonian with all the allowed order parameters included. The Zn impurity, modeled in terms of a potential scatterer in unitary limit, induces local staggered magnetic moments around itself, and the calculated NMR shifts from the induced moments are in agreement with the experimental Cu NMR spectra. We also note that the experimentally observed negative slope of the tunneling conductance can result from the next-neare…
Focusing on a quantum-limit behavior, we study a single vortex in a clean s-wave type-II superconductor by self-consistently solving the Bogoliubov-de Gennes equation. The discrete energy levels of the vortex bound states in the quantum limit is discussed. The vortex core radius shrinks monotonically up to an atomic-scale length on lowering the temperature T, and the shrinkage stops to saturate at a lower T. The pair potential, supercurrent, and local density of states around the vortex exhibit Friedel-like oscillations. The local density of states has particle-hole asymmetry induced by the vo…
We examine a Josephson junction involving two arbitrary equal-spin-pairing unitary triplet superconductors and a ferromagnetic tunneling barrier. Using perturbation theory, we show how the interaction of the barrier moment with the spin of the tunneling triplet Cooper pairs can reverse the sign of the Josephson charge current. This also results in a Josephson spin current, which contains a phase-independent contribution due to reflection processes at the barrier. We verify our analytic predictions using a non-perturbative Bogoliubov-de Gennes method.
The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' …
Both impurity- and magnetic-field-induced quasiparticle states in chiral $p$-wave superconductors are investigated theoretically by solving the Bogoliubov--de Gennes equations self-consistently. At the strong scattering limit, we find that a universal state bound to the impurity can be induced for both a single nonmagnetic impurity and a single magnetic impurity. Furthermore, we find that different chiral order parameters and the corresponding supercurrents have uniform distributions around linear impurities. Calculations of the local density of states in the presence of an external magnetic f…
We report spatially resolved tunneling spectroscopic evidence for field-induced microscopic orders in a high-$T_c$ superconductor $\rm YBa_2Cu_3O_{7-δ}$. The spectral characteristics inside vortices reveal a pseudogap ($V_{\rm CO}$) larger than the superconducting gap ($Δ\_{\rm SC}$) as well as a subgap ($Δ\^{\prime}$) smaller than $Δ\_{\rm SC}$, and the spectral weight shifts steadily from $Δ_{\rm SC}$ to $V_{\rm CO}$ and $Δ\^{\prime}$ upon increasing magnetic field. Additionally, energy-independent conductance modulations at 3.6 and 7.1 lattice constants along the Cu-O bonding directions and…
Spin-split superconductivity in spin-orbit coupled hybrid nanowires with ferromagnetic barriers
University of Copenhagen（哥本哈根大学）；Centro de Física de Materiales Centro Mixto CSIC-UPV/EHU（CSIC-UPV/EHU联合材料物理中心）；NNF Quantum Computing Programme, Niels Bohr Institute（尼尔斯·玻尔研究所NNF量子计算项目）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
