$4π$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
Jonas Wiedenmann, Erwann Bocquillon, Russell S. Deacon, Simon Hartinger, Oliver Herrmann, Teun M. Klapwijk, Luis Maier, Christopher Ames, Christoph Brüne, Charl… 展开作者
Jonas Wiedenmann, Erwann Bocquillon, Russell S. Deacon, Simon Hartinger, Oliver Herrmann, Teun M. Klapwijk, Luis Maier, Christopher Ames, Christoph Brüne, Charles Gould, Akira Oiwa, Koji Ishibashi, Seigo Tarucha, Hartmut Buhmann, Laurens W. Molenkamp
备注：
revised version, main text : 15 pages, 4 figures, supplementary information : 34 pages, 17 figures
The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature however deeply influences the properties of the supercurrent. Detailed studies of Josephson junctions can reveal microscopic properties of the superconducting pairing (spin-triplet correlations, $d$-wave symmetry) or of the electronic transport (quantum dot, ballistic channels). In recent years, considerable efforts have focused on the coupling of superconductors to topological insulators, in which transport is mediated by topologically protected Dirac surface states with helical spin polarization (while the bulk remains insulating). Here, the proximity of a superconductor is predicted to give rise to unconventional induced $p$-wave superconductivity, with a doublet of topologically protected gapless Andreev bound states, whose energies varies $4π$-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction with a weak link of the 3D topological insulator HgTe. The response is understood as due to a $4π$-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet.
Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility (30,000 cm^2/Vs), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow th…
Wires made of topological insulators (TI) are a promising platform for searching for Majorana bound states. These states can be probed by analyzing the fractional ac Josephson effect in Josephson junctions with the TI wire as a weak link. An axial magnetic field can be used to tune the system from trivial to topologically nontrivial. Here we investigate the oscillations of the supercurrent in such wire Josephson junctions as a function of the axial magnetic field strength and different contact transparencies. Although the current flows on average parallel to the magnetic field we observe $h/2e…
Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enables to detect the expected presence of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency $f_J$, rather than conventional emission at $f_J$. Here we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the …
The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in wh…
We use Superconducting QUantum Interference Device (SQUID) microscopy to characterize the current-phase relation (CPR) of Josephson Junctions from 3-dimentional topological insulator HgTe (3D-HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 nm to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states …
Magnetic field-bias current interplay in HgTe-based three-terminal Josephson junctions
University of Regensburg（雷根斯堡大学）；Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）；Instituto de Ciencia de Materiales de Madrid ICMM-CSIC（马德里材料科学研究所 ICMM-CSIC）；A. V. Rzhanov Institute of Semiconductor Physics（A.V.扎哈诺夫半导体物理研究所）
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…
Control of the Josephson current by varying a gate current has recently been demonstrated in both 4-terminal and 3-terminal junctions. We show that, when the the gates are weakly coupled to the Josephson junction, the Josephson current versus gate current (or versus gate voltage) relation is the same for both the 4- and 3- terminal geometries. At low temperature, the supercurrent switches abruptly as a function of the gate voltage, but only slowly as a function of the gate current.
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 demonstrate that perfect conversion between charged supercurrents in superconductors and neutral supercurrents in electron-hole pair condensates is possible via a new Andreev-like scattering mechanism. As a result, when two superconducting circuits are coupled through a bilayer exciton condensate, the superflow in both layers is drastically modified. Depending on the phase biases the supercurrents can be completely blocked or exhibit perfect drag.
AC Josephson effect in one-dimensional Tomonaga-Luttinger liquid (TLL) adiabatically connected to superconducting electrodes is theoretically investigated. It is found that density fluctuations due to repulsive electron-electron interactions in TLL inhibit Josephson oscillations, whereas they do not affect time-independent current part. We also show that the fluctuations reduce supercurrent noise caused by multiple Andreev reflections. This indicates that the quantum fluctuations in TLL disturb the superconducting phase coherence spreading across the junction.
We demonstrate experimentally manipulation of supercurrent in Al-AlO_x-Ti Josephson tunnel junctions by injecting quasiparticles in a Ti island from two additional tunnel-coupled Al superconducting reservoirs. Both supercurrent enhancement and quenching with respect to equilibrium are achieved. We demonstrate cooling of the Ti line by quasiparticle injection from the normal state deep into the superconducting phase. A model based on heat transport and non-monotonic current-voltage characteristic of a Josephson junction satisfactorily accounts for our findings.
In recent years, Majorana physics has attracted considerable attention in both theoretical and experimental studies due to exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a two-dimensional topological insulator that exhibits the quantum spin Hall effect. The ac Josephson e…
We observe a series of discontinuities in the above gap current/voltage characteristics of highly transmissive Nb/Si superconductor/semiconductor interfaces. The bias at which each switch occurs decreases in quantized steps as a function of temperature and magnetic field. The observed step-size is the same for both dependencies. We propose that the steps correspond to supercurrent quantization through granular Josephson junctions formed near the interface.
We propose a Josephson junction setup based on a topological insulator (TI) thin film to detect Majorana states, which exploits the unique helical and extended nature of the TI surface state. When the magnetic flux through the junction is close to an integer number of flux quanta, Majorana states, present on both surfaces of the film, give rise to a narrow peak-dip structure in the current- phase relation by hybridizing at the edge of the junction. Moreover, the maximal Majorana-state contribution to Josephson current takes a (nearly) universal value, approximately equal to the supercurrent ca…
A Josephson supercurrent has been induced into the three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. We show that the transport in Bi1.5Sb0.5Te1.7Se1.3 exfoliated flakes is dominated by surface states and that the bulk conductivity can be neglected at the temperatures where we study the proximity induced superconductivity. We prepared Josephson junctions with widths in the order of 40 nm and lengths in the order of 50 to 80 nm on several Bi1.5Sb0.5Te1.7Se1.3 flakes and measured down to 30 mK. The Fraunhofer patterns unequivocally reveal that the supercurrent is a Josephson supercur…
We theoretically investigate the mapping of the supercurrent distribution in a planar superconductor-normal-superconductor junction in the presence of a perpendicular magnetic field via the scanning gate microscopy technique. We find that the distribution of counter-propagating supercurrents aligned in Josephson vortices can be mapped by the change of the critical current induced by the tip of the scanning probe, if the flux in the junction is set close to maxima of the Fraunhofer pattern. Instead, when the magnetic field drives the junction to a supercurrent minimum in the Fraunhofer pattern,…
We study the Josephson effect for a topologically nontrivial superconducting (TS) wire with Majorana fermion end states and tunnel-coupled to s-wave BCS superconducting (S) electrodes. In an S-TS junction, no supercurrent flow is possible under fairly general conditions. For the S-TS-S junction, bulk TS quasiparticles must be accessible to have a Josephson effect. In the noninteracting case, we derive the exact current-phase relation (CPR) and find π-periodic behavior with negative critical current for weak tunnel couplings. Charging effects then cause the anomalous CPR $I(φ)=I_c \cosφ$, where…
We present a theoretical study of the Josephson coupling of two s-wave superconductors which are connected through a diffusive contact consisting of noncollinear ferromagnetic domains. First, we consider a contact with two domains with magnetization vectors misoriented by an angle $θ$. Using the quantum circuit theory, we find that in addition to the charge supercurrent, a spin supercurrent, which is even in $ϕ$ and odd in $θ$, with a spin polarization normal to the magnetization vectors flows between the domains. Furthermore, with asymmetric insulating barriers at the interfaces of the juncti…
The Josephson effect is a fundamental quantum phenomenon consisting in the appearance of a dissipationless supercurrent in a weak link between two superconducting (S) electrodes. While the mechanism leading to the Josephson effect is quite general, i.e., Andreev reflections at the interface between the S electrodes and the weak link, the precise physical details and topology of the junction drastically modify the properties of the supercurrent. Specifically, a strong enhancement of the critical supercurrent $I_C$ is expected to occur when the topology of the junction allows the emergence of Ma…
It has been predicted theoretically that an unconventional odd-frequency spin-triplet component of superconducting order parameter can be induced in multilayered ferromagnetic structures with non-collinear magnetization. In this work we study experimentally nano-scale devices, in which a ferromagnetic spin valve is embedded into a Josephson junction. We demonstrate two ways of in-situ analysis of such Josephson spin valves: via magnetoresistance measurements and via in-situ magnetometry based on flux quantization in the junction. We observe that supercurrent through the device depends on the r…
The Josephson junction of a strong spin-orbit material under a magnetic field is a promising Majorana fermion candidate. Supercurrent enhancement by a magnetic field has been observed in the InAs nanowire Josephson junctions and assigned to a topological transition. In this work we observe a similar phenomenon but discuss the non-topological origin by considering trapping of quasiparticles by vortices that penetrate the superconductor under a finite magnetic field. This assignment is supported by the observed hysteresis of the switching current when sweeping up and down the magnetic field. Our…
The Josephson effect is a kind of macroscopic quantum phenomenon that supercurrent flows through a Josephson junction without any voltage applied. We predict a novel vortex-state-mediated Josephson effect in an SNS Josephson junction supporting vortices. The vortex-state-mediated supercurrent is enhanced or reduced significantly in magnitude depending on the junction length, and exhibits several steps with the number of effective propagating channels in current-phase evolution at zero temperature. At finite temperatures, these supercurrent steps persist in the short junction limit, and develop…
We demonstrate enhanced robustness of the supercurrent through graphene-based Josephson junctions in which strong spin-orbit interactions (SOIs) are induced. We compare the persistence of a supercurrent at high magnetic fields between Josephson junctions with graphene on hexagonal boron-nitride and graphene on WS$_2$, where strong SOIs are induced via the proximity effect. We find that in the shortest junctions both systems display signatures of induced superconductivity, characterized by a suppressed differential resistance at a low current, in magnetic fields up to 1 T. In longer junctions h…
Superconductor-graphene-superconductor (SGS) junction provides a unique platform to study relativistic electrodynamics of Dirac fermions combined with proximity-induced superconductivity. We report observation of the Josephson effect in proximity-coupled superconducting junctions of graphene in contact with Pb1-xInx (x=0.07) electrodes for temperatures as high as T = 4.8K, with a large IcRn (~ 255 microV). This demonstrates that Pb1-xInx SGS junction would facilitate the development of the superconducting quantum information devices and superconductor-enhanced phase-coherent transport of graph…
Motivated by recent experiments revealing superconductivity in MoS$_2$, we investigate the Josephson effect in the monolayer MoS$_2$ at the presence of an exchange splitting. We show that the supercurrent reversal known as $0-π$ transition can occur by varying the doping via gate voltages. This is in contrast to common superconductor/ferromagnet/superconductor junctions in which successive $0-π$ transition take place with the variation of junction length or temperature. In fact for the case of MoS$_2$ we find that both the amplitude and the period of oscillations show a dependence on the dopin…
We present a study of a graphene-based Josephson junction with dedicated side gates carved from the same sheet of graphene as the junction itself. These side gates are highly efficient, and allow us to modulate carrier density along either edge of the junction in a wide range. In particular, in magnetic fields in the $1-2$ Tesla range, we are able to populate the next Landau level, resulting in Hall plateaus with conductance that differs from the bulk filling factor. When counter-propagating quantum Hall edge states are introduced along either edge, we observe supercurrent localized along that…
We investigate superconducting quantum interference devices consisting of two highly transmissive Josephson junctions coupled by a superconducting loop, all defined in an epitaxial InAs/Al heterostructure. A novel device design allows for independent measurements of the Andreev bound state spectrum within the normal region of a junction and the resulting current-phase relation. We show that knowledge of the Andreev bound state spectrum alone is enough to derive the independently measured phase dependent supercurrent. On the other hand, the opposite relation does not generally hold true as deta…
We propose a model for resonant Josephson tunneling through quantum dots that accounts for Cooper pair-breaking processes in the superconducting leads caused by a magnetic field or spin-flip scattering. The pair-breaking effect on the critical supercurrent $I_c$ and the Josephson current-phase relation $I(ϕ)$ is largely due to the modification of the spectrum of Andreev bound states below the reduced (Abrikosov-Gorkov) quasiparticle gap. For a quantum dot formed in a quasi-one-dimensional channel, both $I_c$ and $I(ϕ)$ can show a significant magnetic field dependence induced by pair breaking d…
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The correspondin…
Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes…
We have contacted single wall carbon nanotubes grown by chemical vapor deposition to superconducting Ti/Al/Ti electrodes. The device, we here report on is in the Kondo regime exhibiting a four-fold shell structure, where a clear signature of the superconducting electrodes is observed below the critical temperature. Multiple Andreev reflections are revealed by sub-gap structure and a narrow peak in the differential conductance around zero bias is seen depending on the shell filling. We interpret the peak as a proximity induced supercurrent and examine its interplay with Kondo resonances.
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 be…
In the past year, several groups have observed evidence for long-range spin-triplet supercurrent in Josephson junctions containing ferromagnetic (F) materials. In our work, the spin-triplet pair correlations are created by non-collinear magnetizations between a central Co/Ru/Co "synthetic antiferromagnet" (SAF) and two outer thin F layers. Here we present data showing that the spin-triplet supercurrent is enhanced up to 20 times after our samples are subject to a large in-plane magnetizing field. This surprising result can be explained if the Co/Ru/Co SAF undergoes a "spin-flop" transition, wh…
The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density and, therefore the overall current distribution could be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five mini-gates. We demonstrate that not only can the junction width be electrostatically defined but also we can locally adjust the current profi…
Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this work, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demons…
Josephson junctions containing multiple ferromagnetic layers can carry spin-triplet supercurrent under certain conditions. Large-area junctions containing multiple domains are expected to have a random distribution of 0 or pi coupling across the junction surface, whereas magnetized samples should have uniquely pi coupling everywhere. We have measured the area dependence of the critical current in such junctions, and confirm that the critical current scales linearly with area in magnetized junctions. For as-grown (multi-domain) samples, the results are mixed. Samples grown on a thick Nb base ex…
Recent experiments have demonstrated the nonequilibrium control of the supercurrent through diffusive phase-coherent normal-metal weak links. The experimental results have been accurately described by the quasiclassical Green's function technique in the Keldysh formalism. Taking into account the geometry of the structure, different energy scales and the nonidealities at the interfaces allows us to obtain a quantitative agreement between the theory and the experimental results in both the amplitude and the phase dependence of the supercurrent, with no or very few fitting parameters. Here we dis…
A strained and undoped HgTe layer is a three-dimensional topological insulator, in which electronic transport occurs dominantly through its surface states. In this Letter, we present transport measurements on HgTe-based Josephson junctions with Nb as superconductor. Although the Nb-HgTe interfaces have a low transparency, we observe a strong zero-bias anomaly in the differential resistance measurements. This anomaly originates from proximity-induced superconductivity in the HgTe surface states. In the most transparent junction, we observe periodic oscillations of the differential resistance as…
We investigate theoretical aspects of the detection of Majorana bound states in Josephson junctions using the semiclassical RCSJ model of junction dynamics. The influence of a 4$π$-periodic supercurrent contribution can be detected through its effect on the width of the Shapiro steps and the Fourier spectrum of the voltage signal. We explain how the inclusion of a capacitance term results in a strong quenching of the odd steps when the junction is underdamped, and hence may be used to effectively detect Majorana bound states. Furthermore, in presence of capacitance the first and third steps ar…
Scanning Gate Microscopy Modulation of Supercurrent in Graphene Josephson Junctions
Istituto Nanoscienze–CNR, NEST-Scuola Normale Superiore（意大利国家研究委员会纳米科学研究所，NEST-比萨高等师范学校）；Dipartimento di Fisica, Università di Genova（热那亚大学物理系）；CNR-SPIN（意大利国家研究委员会自旋物理学研究所）；Center for Nanotechnology Innovation, Laboratorio NEST, Istituto Italiano di Tecnologia（意大利理工大学NEST纳米技术创新中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（日本物质材料研究机构电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（日本物质材料研究机构材料纳米构造研究中心）
A Josephson diode is a non-reciprocal circuit element that supports a larger dissipationless supercurrent in one direction than in the other. In this work, we propose and theoretically study a class of Josephson diodes based on supercurrent interferometers containing mesoscopic Josephson junctions, such as point contacts or quantum dots, which are not diodes themselves but possess non-sinusoidal current-phase relations. We show that such Josephson diodes have several important advantages, like being electrically tunable and requiring neither Zeeman splitting nor spin-orbit coupling, only time-…
In 2010, several experimental groups obtained compelling evidence for spin-triplet supercurrent in Josephson junctions containing strong ferromagnetic materials. Our own best results were obtained from large-area junctions containing a thick central Co/Ru/Co "synthetic antiferromagnet" and two thin outer layers made of Ni or PdNi alloy. Because the ferromagnetic layers in our samples are multi-domain, one would expect the sign of the local current-phase relation inside the junctions to vary randomly as a function of lateral position. Here we report measurements of the area dependence of the cr…
We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference …
We report on the fabrication and measurements of planar mesoscopic Josephson junctions formed by InAs nanowires coupled to superconducting Nb terminals. The use of Si-doped InAs-nanowires with different bulk carrier concentrations allowed to tune the properties of the junctions. We have studied the junction characteristics as a function of temperature, gate voltage, and magnetic field. In junctions with high doping concentrations in the nanowire Josephson supercurrent values up to 100\,nA are found. Owing to the use of Nb as superconductor the Josephson coupling persists at temperatures up to …
We fabricate Josephson field-effect-transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a tra…
We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollin…
