We show that a system of Josephson junctions coupled via low-resistance tunneling contacts to graphene substrate(s) may effectively operate as a current switching device. The effect is based on the dissipation-driven superconductor-to-insulator quantum phase transition, which happens due to the interplay of the Josephson effect and Coulomb blockade. Coupling to a graphene substrate with gapless excitations further enhances charge fluctuations favoring superconductivity. The effect is shown to scale exponentially with the Fermi energy in graphene, which can be controlled by the gate voltage. We develop a theory, which quantitatively describes the quantum phase transition in a two-dimensional Josephson junction array, but it is expected to provide a reliable qualitative description for one-dimensional systems as well. We argue that the local effect of dissipation-induced enhancement of superconductivity is very robust and a similar sharp crossover should be present in finite Josephson junction chains.
We have tuned in situ the proximity effect in a single graphene layer coupled to two Pt/Ta superconducting electrodes. An annealing current through the device changed the transmission coefficient of the electrode/graphene interface, increasing the probability of multiple Andreev reflections. Repeated annealing steps improved the contact sufficiently for a Josephson current to be induced in graphene.
We explore ways in which the close proximity between graphene sheets and monolayers of 2D superconductors can lead to hybridization between their collective excitations. We consider heterostructures formed by combinations of graphene sheets and 2D superconductor monolayers. The broad range of energies in which the graphene plasmon can exist, together with its tunability, makes such heterostrucutres promising platforms for probing the many-body physics of superconductors. We show that the hybridization between the graphene plasmon and the Bardasis-Schrieffer mode of a 2D superconductor results …
We investigated the electrical transport properties of superconductor-graphene-superconductor (SGS) Josephson junctions. In low voltage bias, we observed conventional proximity-coupled Josephson effect, such as the supercurrent flow through the graphene, sub-gap structure of differential conductance due to Andreev reflection, and periodic modulation of the critical current Ic with perpendicular magnetic field H to the graphene. In high bias above the superconducting gap voltage, however, we also observed an anomalous jump of the differential conductance, the voltage position of which is sensit…
Results on the superconductor to insulator transition in two-dimensional films are analyzed in terms of coupling of the system to a dissipative bath. Upon lowering the temperature the parameter that controls this coupling becomes relevant and a wide range of metallic phase is recovered.
Using the Bogoliubov de-Gennes formalism, we investigate the charge and spin-dependent thermoelectric effects in superconductor graphene junctions. Results demonstrate that despite normal-superconductor junctions, there is a temperature-dependent spin thermopower both in the graphene-based ferromagnetic-superconductor (F-S) and ferromagnetic-Rashba spin-orbit region-superconductor (F-RSO-S) junctions. It is also shown that in the presence of Rashba spin-orbit interaction, the charge and spin-dependent Seebeck coefficients can reach to their maximum up to 3.5$k_B/e$ and 2.5$k_B/e$, respectively…
We report the study of ballistic transport in normal metal/graphene/superconductor junctions in edge-contact geometry. While in the normal state, we have observed Fabry-Pérot resonances suggesting that charge carriers travel ballistically, the superconducting state shows that the Andreev reflection at the graphene/superconductor interface is affected by these interferences. Our experimental results in the superconducting state have been analyzed and explained with a modified Octavio-Tinkham-Blonder-Klapwijk model taking into account the magnetic pair-breaking effects and the two different inte…
The two-dimensional nature of graphene makes it an ideal platform to explore proximity-induced unconventional planar superconductivity and the possibility of topological superconductivity. Using Green's functions techniques, we study the transport properties of a finite size ballistic graphene layer placed between a normal state electrode and a graphene lead with proximity-induced unconventional superconductivity. Our microscopic description of such a junction allows us to consider the effect of edge states in the graphene layer and the imperfect coupling to the electrodes. The tunnel conducta…
We show that interface bound states are formed at isolated graphene-superconductor junctions. These states arise due to the interplay of virtual Andreev and normal reflections taking place at these interfaces. Simple analytical expressions for their dispersion are obtained considering interfaces formed along armchair or zig-zag edges. It is shown that the states are sensitive to a supercurrent flowing on the superconducting electrode. The states provide long range superconducting correlations on the graphene layer which may be exploited for the detection of crossed Andreev processes.
We present a theoretical analysis of the proximity effect at a graphene-superconductor interface. We use a tight-binding model for the electronic states in this system which allows to describe the interface at the microscopic level. Two different interface models are proposed: one in which the superconductor induces a finite pairing in the graphene regions underneath, thus maintaining the honeycomb structure at the interface and one that assumes that the graphene layer is directly coupled to a bulk superconducting electrode. We show that properties like the Andreev reflection probability and i…
Magnetic-Field-Driven Insulator-Superconductor Transition in Rhombohedral Graphene
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；National Institute for Material Sciences（国立材料研究所）；Hefei National Laboratory（合肥国家实验室）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料交叉研究所及轻元素先进材料研究中心）；Collaborative Innovation Center of Quantum Matter, Beijing（北京量子物质协同创新中心）
Based on the BTK theory, we investigate the tunneling conductance in a uniaxially strained graphene-based normal metal (NG)/ barrier (I)/superconductor (SG) junctions. In the present model, we assume that depositing the conventional superconductor on the top of the uniaxially strained graphene, normal graphene may turn to superconducting graphene with the Cooper pairs formed by the asymmetric Weyl-Dirac electrons, the massless fermions with direction-dependent velocity. The highly asymmetrical velocity, vy/vx>>1, may be created by strain in the zigzag direction near the transition point betwee…
We study the spin-polarized $ν=0$ Landau-level state of graphene. Due to the electron-hole attractive interaction, electrons and holes can bound into pairs. These pairs can then condense into a spin-triplet superfluid ground state: a spin superconductor state. In this state, a gap opens up in the edge bands as well as in the bulk bands, thus it is a charge insulator, but it can carry the spin current without dissipation. These results can well explain the insulating behavior of the spin-polarized $ν=0$ state in the recent experiments.
A ballistic strip of graphene (width W>> length L) connecting two normal metal contacts is known to have a minimum conductivity of 4e^{2}/pi h at the Dirac point of charge neutrality. We calculate what happens if one of the two contacts becomes superconducting. While the ballistic conductance away from the Dirac point is increased by Andreev reflection at the normal-superconductor (NS) interface, we find that the minimum conductivity stays the same. This is explained as a manifestation of pseudo-diffusive conduction at the Dirac point. As a generalization of our results for a ballistic system,…
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 discus…
A junction with two superconductors coupled by a normal metal hosts Andreev bound states whose energy spectrum is phase-dependent and exhibits a minigap, resulting in a periodic supercurrent. Phase-dependent dissipation also appears at finite frequency due to relaxation of Andreev bound states. While dissipation and supercurrent versus phase have previously been measured near thermal equilibrium, their behavior in nonequilibrium is still elusive. By measuring the ac susceptibility of a graphene-superconductor junction under microwave irradiation, we find supercurrent response deviates from adi…
We calculate the phase, the temperature and the junction length dependence of the supercurrent for ballistic graphene Josephson-junctions. For low temperatures we find non-sinusoidal dependence of the supercurrent on the superconductor phase difference for both short and long junctions. The skewness, which characterizes the deviation of the current-phase relation from a simple sinusoidal one, shows a linear dependence on the critical current for small currents. We discuss the similarities and differences with respect to the classical theory of Josephson junctions, where the weak link is formed…
We study spin-Hall effects in time-reversal symmetry (TRS) broken systems such as triplet chiral superconductors and TRS preserved ones such as graphene. For chiral triplet superconductors, we show that the edge states carry a quantized spin-Hall current in response to an applied Zeeman magnetic field $B$ along the ${\bf d}$ vector \cite{leggett1}, whereas the edge spin-current for ${\bf B} \perp {\bf d}$ is screened by the condensate. We also derive the bulk spin-Hall current for chiral triplet superconductors for arbitrary relative orientation of ${\bf B}$ and ${\bf d}$ and discuss its relat…
Transparent contact interfaces in superconductor-graphene hybrid systems are critical for realizing superconducting quantum applications. Here, we examine the effect of the edge-contact fabrication process on the transparency of the superconducting aluminum-graphene junction. We show significant improvement in the transparency of our superconductor-graphene junctions by promoting the chemical component of the edge contact etch process. Our results compare favorably with state-of-the-art graphene Josephson junctions. The findings of our study contribute to advancing the fabrication knowledge of…
Dissipation is ubiquitous in quantum systems, and its interplay with fluctuations is critical to maintaining quantum coherence. We experimentally investigate the dissipation dynamics in single-walled carbon nanotubes coupled to superconductors. The voltage-current characteristics display gate-tunable hysteresis, with sizes that perfectly correlate with the normal state resistance RN, indicating the junction undergoes a periodic modulation between underdamped and overdamped regimes. Surprisingly, when a device's Fermi-level is tuned through a local conductance minimum, we observe a gate-control…
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…
We show that a two-dimensional topological superconductor (TSC) can be realized in a hybrid system with a conventional $s$-wave superconductor proximity-coupled to a quantum anomalous Hall (QAH) state from the Rashba and exchange effects in single layer graphene. With very low or even zero doping near the Dirac points, i.e., two inequivalent valleys, this TSC has a Chern number as large as four, which supports four Majorana edge modes. More importantly, we show that this TSC has a robust topologically nontrivial bulk excitation gap, which can be larger or even one order of magnitude larger tha…
Strongly disordered pseudogapped superconductors are expected to display arbitrary high values of kinetic inductance close to superconductor-insulator transition (SIT) that makes them attractive for the implementation of dissipationless superinductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become relevant source of dissipation and noise in the far vicinity of SIT.
We study the electron-phonon coupling in twisted bilayer graphene (TBG), which was recently experimentally observed to exhibit superconductivity around the magic twist angle $θ\approx 1.05^\circ$. We show that phonon-mediated electron electron attraction at the magic angle is strong enough to induce a conventional intervalley pairing between graphene valleys $K$ and $K'$ with a superconducting critical temperature $T_c\sim1K$, in agreement with the experiment. We predict that superconductivity can also be observed in TBG at many other angles $θ$ and higher electron densities in higher Moiré ba…
Studying the interplay between superconductivity and quantum magnetotransport in two-dimensional materials has been a topic of interest in recent years. Towards such a goal it is important to understand the impact of magnetic field on the charge transport at the superconductor-normal channel (SN) interface. Here we carried out a comprehensive study of Andreev conductance under weak magnetic fields using diffusive superconductor- graphene Josephson weak links. We observe that the Andreev conductance is suppressed even in magnetic fields far below the upper critical field of the superconductor. …
We study the interplay of Klein tunneling (= interband tunneling) between n-doped and p-doped regions in graphene and Andreev reflection (= electron-hole conversion) at a superconducting electrode. The tunneling conductance of an n-p-n junction initially increases upon lowering the temperature, while the coherence time of the electron-hole pairs is still less than their lifetime, but then drops back again when the coherence time exceeds the lifetime. This reentrance effect, known from diffusive conductors and ballistic quantum dots, provides a method to detect phase coherent Klein tunneling of…
Graphene has exhibited a wealth of fascinating properties, but is also known not to be a superconductor. Remarkably, we show that graphene can be made a conventional Bardeen-Cooper-Schrieffer superconductor by the combined effect of charge doping and tensile strain. While the effect of doping is obvious to enlarge Fermi surface, the effect of strain is profound to greatly increase the electron-phonon coupling. At the experimental accessible doping (4E+14cm-2) and strain (~16%) levels, the superconducting critical temperature Tc reaches as high as ~30 K, the highest for a single-element materia…
The response of mesoscopic superconductors to an ac magnetic field is investigated both experimentally and with numerical simulations. We study small square samples with dimensions of the order of the penetration depth. We obtain the ac susceptibitity $χ=χ'+iχ''$ at microwave frequencies as a function of the dc magnetic field $H_{dc}$. We find that the dissipation, given by $χ''$, has a non monotonous behavior in mesoscopic samples. In the numerical simulations we obtain that the dissipation increases before the penetration of vortices and then it decreases abruptly after vortices have entered…
Electronic cooling in hybrid normal metal-insulator-superconductor junctions is a promising technology for the manipulation of thermal loads in solid state nanosystems. One of the main bottlenecks for efficient electronic cooling is the electron-phonon coupling, as it represents a thermal leakage channel to the phonon bath. Graphene is a two-dimensional material that exhibits a weaker electron-phonon coupling compared to standard metals. For this reason, we study the electron cooling in graphene-based systems consisting of a graphene sheet contacted by two insulator/superconductor junctions. W…
Using the tight binding model and the non-equilibrium Green function method, we study Andreev reflection in graphene-superconductor junction, where graphene has two nonequal Dirac Cones split in energy and therefore time reversal symmetry is broken. Due to the anti-chiral edge states of the current graphene model, an incident electron travelling along the edges makes distinct contribution to Andreev reflections. In a two-terminal device, because Andreev retro-reflection is not allowed for just the anti-chiral edges, in this case the mutual scattering between edge and bulk states is necessary, …
In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional pseudo-diffusive charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to th…
In this work we study the ac dissipation of mesoscopic superconductors at microwave frequencies using the time dependent Ginzburg-Landau equations. Our numerical simulations show that the ac dissipation is strongly dependent on the orientation of the ac magnetic field ($h_{ac}$) relative to the dc magnetic field ($H_{dc}$). When $h_{ac}$ is parallel to $H_{dc}$ we observe that each vortex penetration event produces a significant supression of the ac losses because the imaginary part of the ac susceptibility as a function of $H_{dc}$ increases before the penetration of vortices, and then it dec…
We show that Andreev reflection in a junction between ferromagnetic (F) and superconducting (S) graphene regions is fundamentally different from the common FS junctions. For a weakly doped F graphene with an exchange field $h$ larger than its Fermi energy $E_{\rm F}$, Andreev reflection of massless Dirac fermions is associated with a Klein tunneling through an exchange field p-n barrier between two spin-split conduction and valence subbands. We find that this Andreev-Klein process results in an enhancement of the subgap conductance of a graphene FS junction by $h$ up to the point at which the …
Abrikosov vortex melting in high-temperature superconductors of ErBa2Cu3O7-δ system is investigated using mechanical contactless method of energy dissipation.
We investigate quantum transport in a normal/superconductor graphene heterostructure, including the possibility of an anisotropic pairing potential in the superconducting region. We find that under certain circumstances, the conductance displays an undamped, oscillatory behaviour as a function of applied bias voltage. Also, we investigate how the conductance spectra are affected by a d-wave pairing symmetry. These results combine unusual features of the electronic structure of graphene with the unconventional pairing symmetry found for instance in high-T_c superconductors.
We investigate the crossed Andreev reflections between two graphene leads connected by a narrow superconductor. When the leads are respectively of the n-and p- type, we find that electron elastic cotunneling and local Andreev reflection are both eliminated even in the absence of any valley-isospin or spin polarizations. We further predict oscillations of both diagonal and cross conductances as a function of the distance between the graphene-superconductor interfaces.
We fabricate superconductor-graphene-superconductor Josephson junctions with superconducting regions made of lead (Pb). The critical current through grapehene may be modulated by external magnetic field; the resulting Fraunhofer interference pattern shows several periods of oscillations, indicating that the junction is uniform. Deviations from the perfect Fraunhofer pattern are observed, and their cause is explained by a simulation that takes into account the sample design.
We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is…
A graphene superlattice is formed by a one-dimensional periodic potential and is characterized by the emergence of new Dirac points in the electronic structure. The group velocity of graphene's massless Dirac fermions at the new points is drastically reduced, resulting in a measurable effect in the conductance spectroscopy. We show here that tunnel spectroscopy using a superconducting hybrid junction is more sensitive to the formation of Dirac points in the spectrum of graphene superlattices due to the additional contribution of Andreev processes. We examine the transport properties of a graph…
Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. In this paper we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems --- a broad regime of $T-$linear resistivity above a small, density dependent, crossover temperature--- for a range of fillings near the correlated insulator. We also extract a transport "scattering rate", which satisfies a near Planckian form that is universally related to the ratio of $(k_BT/\hbar)$. Our…
We investigate the conductance spectra of a normal/superconductor graphene junction using the extended Blonder-Tinkham-Klapwijk formalism, considering pairing potentials that are both conventional (isotropic s-wave) and unconventional (anisotropic d-wave). In particular, we study the full crossover from normal to specular Andreev reflection without restricting ourselves to special limits and approximations, thus expanding results obtained in previous work. In addition, we investigate in detail how the conductance spectra are affected if it is possible to induce an unconventional pairing symmet…
Recent phase sensitive experiments on high Tc superconductors, e.g., YBa_2Cu_3O_7 single crystals, have established the d-wave nature of the cuprate materials. Here we discuss how to make use of d-wave Josephson junctions in the construction of a phase qubit. We especially focus on the effect of quasiparticle dissipation on the macroscopic quantum tunneling which corresponds to the measurement process for the d-wave phase qubit.
We report an experimental study of Cooper pair splitting in an encapsulated graphene based multiterminal junction in the ballistic transport regime. Our device consists of two transverse junctions, namely the superconductor/graphene/superconductor and the normal metal/graphene/normal metal junctions. In this case, the electronic transport through one junction can be tuned by an applied bias along the other. We observe clear signatures of Cooper pair splitting in the local as well as nonlocal electronic transport measurements. Our experimental data can be very well described by using a modified…
Within the tunneling Hamiltonian formulation for the eight-component spinors,the Josephson critical super-current has been calculated in a planar superconductor-normal graphene-superconductor junction. Coupling between superconductor regions and graphene is taken into account by a tunneling Hamiltonian which contains two types of tunneling, intra-valley and inter-valley tunneling. Within the present tunneling approach, we find that the contributions of two kinds of tunneling to the critical super-current, are completely separable. Therefore, it is possible to consider the effect of the inter-v…
The ground states of bosons have been classified into superfluid, Mott insulator, and bose glass. Recent experiments in two-dimensional superconductors strongly suggest the existence of the fourth quantum state of Cooper pairs, i.e., bose metal or quantum metal, where the resistivity remains constant at lowest temperature. However, its theoretical understanding remains unsettled. In this paper, we show theoretically that the bosons in the dilute limit subject to dissipation can lose the superfluidity and remain metallic, utilizing the Feynman's picture of superfluidity in the first quantized f…
We examine the macroscopic quantum tunneling (MQT) in high-Tc superconductor Josephson junctions with a d-wave order parameter. Using microscopic Hamiltonian and the functional integral method, we analytically obtain the MQT rate (the inverse lifetime of the metastable state) for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is strongly suppressed in compared with the finite twist angle cases.
We report on Andreev reflections at clean NbSe2-bilayer graphene junctions. The high transparency of the junction, which manifests as a large conductance enhancement of up to 1.8, enables us to see clear evidence of a proximity-induced superconducting gap in bilayer graphene and two Andreev reflections through a vertical NbSe2-graphene and a lateral graphene-graphene junction respectively. Quantum transport simulations capture the complexity of the experimental data and illuminate the impact of various microscopic parameters on the transmission of the junction. Our work establishes the practic…
A normal conductor placed in good contact with a superconductor can inherit its remarkable electronic properties. This proximity effect microscopically originates from the formation in the conductor of entangled electron-hole states, called Andreev states. Spectroscopic studies of Andreev states have been performed in just a handful of systems. The unique geometry, electronic structure and high mobility of graphene make it a novel platform for studying Andreev physics in two dimensions. Here we use a full van der Waals heterostructure to perform tunnelling spectroscopy measurements of the prox…
We present a detailed theoretical study of chiral topological superconductor phases in proximity-superconducting graphene systems based on an effective model inspired by DFT simulations. Inducing s-wave superconductivity to quantum anomalous Hall effect systems leads to chiral topological superconductors. For out-of-plane magnetization we find topological superconducting phases with even numbers of chiral Majorana fermions per edge which is correlated to the opening of a nontrivial gap in the bulk system in the $\mathrm{ K}$-points and their connection under particle-hole symmetry. We show tha…
The dissipation process in two dimensional BCS superconductor due to the quasiparticles in the core of moving vortex is studied from a quantum mechanical point of view, especially paying attention to the spectral flow of the bound state energies in the vortex core. In order to clarify the nature of the spectral flow, we performed a numerical study of a finite system and, by extending the analysis to include the effect of impurities, we discuss the quantum mechanical origin of the dissipation in the vortex core.
