Steady Floquet-Andreev states in graphene Josephson junctions.

Engineering quantum states through light-matter interaction has created a paradigm in condensed-matter physics. A representative example is the Floquet-Bloch state, which is generated by time-periodically driving the Bloch wavefunctions in crystals. Previous attempts to realize such states in condensed-matter systems have been limited by the transient nature of the Floquet states produced by optical pulses1-3, which masks the universal properties of non-equilibrium physics. Here we report the generation of steady Floquet-Andreev states in graphene Josephson junctions by continuous microwave application and direct measurement of their spectra by superconducting tunnelling spectroscopy. We present quantitative analysis of the spectral characteristics of the Floquet-Andreev states while varying the phase difference of the superconductors, the temperature, the microwave frequency and the power. The oscillations of the Floquet-Andreev-state spectrum with phase difference agreed with our theoretical calculations. Moreover, we confirmed the steady nature of the Floquet-Andreev states by establishing a sum rule of tunnelling conductance4, and analysed the spectral density of Floquet states depending on Floquet interaction strength. This study provides a basis for understanding and engineering non-equilibrium quantum states in nanodevices.

Graphene-based Josephson junction microwave bolometer.

Sensitive microwave detectors are essential in radioastronomy1, dark-matter axion searches2 and superconducting quantum information science3,4. The conventional strategy to obtain higher-sensitivity bolometry is the nanofabrication of ever smaller devices to augment the thermal response5-7. However, it is difficult to obtain efficient photon coupling and to maintain the material properties in a device with a large surface-to-volume ratio owing to surface contamination. Here we present an ultimately thin bolometric sensor based on monolayer graphene. To utilize the minute electronic specific heat and thermal conductivity of graphene, we develop a superconductor-graphene-superconductor Josephson junction8-13 bolometer embedded in a microwave resonator with a resonance frequency of 7.9 gigahertz and over 99 per cent coupling efficiency. The dependence of the Josephson switching current on the operating temperature, charge density, input power and frequency shows a noise-equivalent power of 7 × 10-19 watts per square-root hertz, which corresponds to an energy resolution of a single 32-gigahertz photon14, reaching the fundamental limit imposed by intrinsic thermal fluctuations at 0.19 kelvin. Our results establish that two-dimensional materials could enable the development of bolometers with the highest sensitivity allowed by the laws of thermodynamics.

Field-Free Spin-Orbit Torque Magnetization Switching in a Single-Phase Ferromagnetic and Spin Hall Oxide.

Current-induced spin-orbit torque (SOT) offers substantial promise for the development of low-power, nonvolatile magnetic memory. Recently, a single-phase material concurrently exhibiting magnetism and the spin Hall effect has emerged as a scientifically and technologically interesting platform for realizing efficient and compact SOT systems. Here, we demonstrate external-magnetic-field-free switching of perpendicular magnetization in a single-phase ferromagnetic and spin Hall oxide SrRuO3. We delicately altered the local lattices of the top and bottom surface layers of SrRuO3, while retaining a quasi-homogeneous, single-crystalline nature of the SrRuO3 bulk. This leads to unbalanced spin Hall effects between the top and bottom layers, enabling net SOT performance within single-layer ferromagnetic SrRuO3. Notably, our SrRuO3 exhibits the highest SOT efficiency and lowest power consumption among all known single-layer systems under field-free conditions. Our method of artificially manipulating the local atomic structures will pave the way for advances in spin-orbitronics and the exploration of new SOT materials.

Controllable Andreev Bound States in Bilayer Graphene Josephson Junctions from Short to Long Junction Limits.

We demonstrate that the mode number of Andreev bound states in bilayer graphene Josephson junctions can be modulated by controlling the superconducting coherence length in situ. By exploiting the quadratic band dispersion of bilayer graphene, we control the Fermi velocity and thus the coherence length via the application of electrostatic gating. Tunneling spectroscopy of the Andreev bound states reveals a crossover from short to long Josephson junction regimes as we approach the charge neutral point of the bilayer graphene. Furthermore, analysis of different mode numbers of the Andreev energy spectrum allows us to estimate the phase-dependent Josephson current quantitatively. Our Letter provides a new way for studying multimode Andreev levels by tuning the Fermi velocity.

Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene.

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

Graphene transistor based on tunable Dirac fermion optics.

We present a quantum switch based on analogous Dirac fermion optics (DFO), in which the angle dependence of Klein tunneling is explicitly utilized to build tunable collimators and reflectors for the quantum wave function of Dirac fermions. We employ a dual-source design with a single flat reflector, which minimizes diffusive edge scattering and suppresses the background incoherent transmission. Our gate-tunable collimator-reflector device design enables the quantitative measurement of the net DFO contribution in the switching device operation. We obtain a full set of transmission coefficients between multiple leads of the device, separating the classical contribution from the coherent transport contribution. The DFO behavior demonstrated in this work requires no explicit energy gap. We demonstrate its robustness against thermal fluctuations up to 230 K and large bias current density up to 102 A/m, over a wide range of carrier densities. The characterizable and tunable optical components (collimator-reflector) coupled with the conjugated source electrodes developed in this work provide essential building blocks toward more advanced DFO circuits such as quantum interferometers. The capability of building optical circuit analogies at a microscopic scale with highly tunable electron wavelength paves a path toward highly integrated and electrically tunable electron-optical components and circuits.

Twisted van der Waals Josephson Junction Based on a High-Tc Superconductor.

Stacking two-dimensional van der Waals (vdW) materials rotated with respect to each other show versatility for studying exotic quantum phenomena. In particular, anisotropic layered materials have great potential for such twistronics applications, providing high tunability. Here, we report anisotropic superconducting order parameters in twisted Bi2Sr2CaCu2O8+x (Bi-2212) vdW junctions with an atomically clean vdW interface, achieved using the microcleave-and-stack technique. The vdW junctions with twist angles of 0° and 90° showed the maximum Josephson coupling, comparable to that of intrinsic Josephson junctions. As the twist angle approaches 45°, Josephson coupling is suppressed, and eventually disappears at 45°. The observed twist angle dependence of the Josephson coupling can be explained quantitatively by theoretical calculation with the d-wave superconducting order parameter of Bi-2212 and finite tunneling incoherence of the junction. Our results revealed the anisotropic nature of Bi-2212 and provided a novel fabrication technique for vdW-based twistronics platforms compatible with air-sensitive vdW materials.

Anisotropic Angstrom-Wide Conductive Channels in Black Phosphorus by Top-down Cu Intercalation.

Intercalation in black phosphorus (BP) can induce and modulate a variety of the properties including superconductivity like other two-dimensional (2D) materials. In this perspective, spatially controlled intercalation has the possibility to incorporate different properties into a single crystal of BP. We demonstrate anisotropic angstrom-wide (∼4.3 Å) Cu intercalation in BP, where Cu atoms are intercalated along a zigzag direction of BP because of its inherent anisotropy. With atomic structure, its microstructural effects, arising from the angstrom-wide Cu intercalation, were investigated and extended to relation with macrostructure. As the intercalation mechanism, it was revealed by in situ transmission electron microscopy and theoretical calculation that Cu atoms are intercalated through top-down direction of BP. The Cu intercalation anisotropically induces transition of angstrom-wide electronic channels from semiconductor to semimetal in BP. Our findings throw light on the fundamental relationship between microstructure changes and properties in intercalated BP, and tailoring anisotropic 2D materials at angstrom scale.

Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states.

Td-WTe2 (non-centrosymmetric and orthorhombic), a type-II Weyl semimetal, is expected to have higher-order topological phases with topologically protected, helical one-dimensional hinge states when its Weyl points are annihilated. However, the detection of these hinge states is difficult due to the semimetallic behaviour of the bulk. In this study, we have spatially resolved the hinge states by analysing the magnetic field interference of the supercurrent in Nb-WTe2-Nb proximity Josephson junctions. The Josephson current along the a axis of the WTe2 crystal, but not along the b axis, showed a sharp enhancement at the edges of the junction, and the amount of enhanced Josephson current was comparable to the upper limits of a single one-dimensional helical channel. Our experimental observations suggest a higher-order topological phase in WTe2 and its corresponding anisotropic topological hinge states, in agreement with theoretical calculations. Our work paves the way for the study of hinge states in topological transition-metal dichalcogenides and analogous phases.

Author Correction: Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Imaging Andreev Reflection in Graphene.

Coherent charge transport along ballistic paths can be introduced into graphene by Andreev reflection, for which an electron reflects from a superconducting contact as a hole, while a Cooper pair is transmitted. We use liquid-helium cooled scanning gate microscopy (SGM) to image Andreev reflection in graphene in the magnetic focusing regime, where carriers move along cyclotron orbits between contacts. Images of flow are obtained by deflecting carrier paths and displaying the resulting change in conductance. When electrons enter the superconductor, Andreev-reflected holes leave for the collecting contact. To test the results, we destroy Andreev reflection with a large current and by heating above the critical temperature. In both cases, the reflected carriers change from holes to electrons.

Engineering Crossed Andreev Reflection in Double-Bilayer Graphene.

Crossed Andreev reflection (CAR) is a nonlocal process that converts an incoming electron (hole) from one normal electrode to an out-going hole (electron) in another normal electrode through a superconductor (SC). CAR corresponds to the inverse process of Cooper pair splitting, which generates a quantum-entangled electron pair with spatial separation. Here, we fabricated vertically stacked double bilayer graphene (BLG) connected via a superconducting electrode and achieved a spacing between BLG sheets of ∼14 nm, which is far shorter than the superconducting coherence length. We confirm the highly efficient CAR effect by observing strong negative differential resistance in a nonlocal configuration and demonstrate that the competing processes against the CAR can be effectively suppressed by separately tuning the chemical potential of each BLG. The dependence of nonlocal signals on bias voltage, temperature, and chemical potential is consistent with the predicted CAR process. Our results provide a new pathway to a novel SC-based quantum entangler with the in situ tunability of the correlated-pair-splitting efficiency.

Edge-Limited Valley-Preserved Transport in Quasi-1D Constriction of Bilayer Graphene.

We investigated the quantization of the conductance of quasi-one-dimensional (quasi-1D) constrictions in high-mobility bilayer graphene (BLG) with different geometrical aspect ratios. Ultrashort (a few tens of nanometers long) constrictions were fabricated by applying an under-cut etching technique. Conductance was quantized in steps of ∼4 e2/ h (∼2 e2/ h) in devices with aspect ratios smaller (larger) than 1. We argue that scattering at the edges of a quasi-1D BLG constriction limits the intervalley scattering length, which causes valley-preserved (valley-broken) quantum transport in devices with aspect ratios smaller (larger) than 1. The subband energy levels, analyzed in terms of the bias-voltage and temperature dependences of the quantized conductance, indicated that they corresponded well to the effective channel width of a physically defined conducting channel with a hard-wall confining potential. Our study in ultrashort high-mobility BLG nano constrictions with physically tailored edges clearly confirms that physical edges are the major source of intervalley scattering in graphene in the ballistic limit.

Proximity coupling in superconductor-graphene heterostructures.

This review discusses the electronic properties and the prospective research directions of superconductor-graphene heterostructures. The basic electronic properties of graphene are introduced to highlight the unique possibility of combining two seemingly unrelated physics, superconductivity and relativity. We then focus on graphene-based Josephson junctions, one of the most versatile superconducting quantum devices. The various theoretical methods that have been developed to describe graphene Josephson junctions are examined, together with their advantages and limitations, followed by a discussion on the advances in device fabrication and the relevant length scales. The phase-sensitive properties and phase-particle dynamics of graphene Josephson junctions are examined to provide an understanding of the underlying mechanisms of Josephson coupling via graphene. Thereafter, microscopic transport of correlated quasiparticles produced by Andreev reflections at superconducting interfaces and their phase-coherent behaviors are discussed. Quantum phase transitions studied with graphene as an electrostatically tunable 2D platform are reviewed. The interplay between proximity-induced superconductivity and the quantum-Hall phase is discussed as a possible route to study topological superconductivity and non-Abelian physics. Finally, a brief summary on the prospective future research directions is given.

Short Ballistic Josephson Coupling in Planar Graphene Junctions with Inhomogeneous Carrier Doping.

We report on short ballistic (SB) Josephson coupling in junctions embedded in a planar heterostructure of graphene. Ballistic Josephson coupling is confirmed by the Fabry-Perot-type interference of the junction critical current I_{c}. The product of I_{c} and the normal-state junction resistance R_{N}, normalized by the zero-temperature gap energy Δ_{0} of the superconducting electrodes, turns out to be exceptionally large close to 2, an indication of strong Josephson coupling in the SB junction limit. However, I_{c} shows a temperature dependence that is inconsistent with the conventional short-junction-like behavior based on the standard Kulik-Omel'yanchuk prediction. We argue that this feature stems from the effects of inhomogeneous carrier doping in graphene near the superconducting contacts, although the junction is in fact in the short-junction limit.

New Bacterial Infection in the Prostate after Transrectal Prostate Biopsy.

BACKGROUND: The prostate is prone to infections. Hypothetically, bacteria can be inoculated into the prostate during a transrectal prostate biopsy (TRPB) and progress into chronic bacterial prostatitis. Therefore, we examined new bacterial infections in biopsied prostates after TRPB and whether they affect clinical characteristics in the biopsied patients. METHODS: Of men whose prostate cultures have been taken prior to TRPB, 105 men with bacteria-free benign prostate pathology underwent an additional repeated prostate culture within a year after TRPB. RESULTS: Twenty out of 105 men (19.05%) acquired new bacteria in their naïve prostates after TRPB. Except for one single case of Escherichia coli infection, 19 men had acquired gram-positive bacteria species. Between the culture-positive and negative groups, there were no significant differences in age, serum prostate-specific antigen (PSA) level, white blood cell (WBC) counts in expressed prostatic secretion (EPS), prostate volume, symptom severities in Korean version of the National Institutes of Health-Chronic Prostatitis Symptom Index (NIH-CPSI) questionnaire, and patient-specific risk factors for biopsy associated infectious complications. Additionally, the TRPB procedure increased the WBC counts in post-biopsy EPS (P = 0.031, McNemar test), but did not increase the serum PSA level and symptoms of NIH-CPSI in 20 men who acquired new bacteria after TRPB. CONCLUSION: The TRPB procedure was significantly associated with acquiring new bacterial infections in the biopsied prostate, but these localized bacteria did not affect patients' serum PSA level and symptoms after biopsy.

Strong Proximity Josephson Coupling in Vertically Stacked NbSe2-Graphene-NbSe2 van der Waals Junctions.

A layered two-dimensional superconducting material 2H-NbSe2 is used to build a van der Waals heterostructure, where a proximity-coupled superconducting order can be induced in the interfacing materials. Vertically stacked NbSe2-graphene-NbSe2 is fabricated using van der Waals interlayer coupling, producing defect-free contacts with a high interfacial transparency. The atomically thin graphene layer allows the formation of a highly coherent proximity Josephson coupling between the two NbSe2 flakes. The temperature dependence of the junction critical current (Ic) reveals short and ballistic Josephson coupling characteristics that agree with theoretical prediction. The strong Josephson coupling is confirmed by a large junction critical current density of 1.6 × 104 A/cm2, multiple Andreev reflections in the subgap structure of the differential conductance, and a magnetic-field modulation of Ic. This is the first demonstration of strongly proximity-coupled Josephson junctions with extremely clean interfaces in a dry-transfer-stacked van der Waals heterostructure.

Imaging Cyclotron Orbits of Electrons in Graphene.

Electrons in graphene can travel for several microns without scattering at low temperatures, and their motion becomes ballistic, following classical trajectories. When a magnetic field B is applied perpendicular to the plane, electrons follow cyclotron orbits. Magnetic focusing occurs when electrons injected from one narrow contact focus onto a second contact located an integer number of cyclotron diameters away. By tuning the magnetic field B and electron density n in the graphene layer, we observe magnetic focusing peaks. We use a cooled scanning gate microscope to image cyclotron trajectories in graphene at 4.2 K. The tip creates a local change in density that casts a shadow by deflecting electrons flowing nearby; an image of flow can be obtained by measuring the transmission between contacts as the tip is raster scanned across the sample. On the first magnetic focusing peak, we image a cyclotron orbit that extends from one contact to the other. In addition, we study the geometry of orbits deflected into the second point contact by the tip.