Long-Range Propagation and Interference of $d$-wave Superconducting Pairs in Graphene
D. Perconte, K. Seurre, V. Humbert, C. Ulysse, A. Sander, J. Trastoy, V. Zatko, F. Godel, P. R. Kidambi, S. Hofmann, X. P. Zhang, D. Bercioux, F. S. Bergeret, B… 展开作者
D. Perconte, K. Seurre, V. Humbert, C. Ulysse, A. Sander, J. Trastoy, V. Zatko, F. Godel, P. R. Kidambi, S. Hofmann, X. P. Zhang, D. Bercioux, F. S. Bergeret, B. Dlubak, P. Seneor, Javier E. Villegas
Recent experiments have shown that proximity with high-temperature superconductors induces unconventional superconducting correlations in graphene. Here we demonstrate that those correlations propagate hundreds of nanometer, allowing for the unique observation of $d$-wave Andreev pair interferences in YBa$_2$Cu$_3$O$_7$-graphene devices that behave as a Fabry-Pérot cavity. The interferences show as a series of pronounced conductance oscillations analogous to those originally predicted by de Gennes--Saint-James for conventional metal-superconductor junctions. The present work is pivotal to the study of exotic directional effects expected for nodal superconductivity in Dirac materials.
The problem of supercurrent in superconducting graphene is revisited and the supercurrent is calculated within the mean-field model employing the two-component wave functions on a honeycomb lattice with pairing between different valleys in the Brillouin zone. We show that the supercurrent within the linear approximation in the order-parameter-phase gradient is always finite even if the doping level is exactly zero.
Graphene is the physical realization of many fundamental concepts and phenomena in solid state-physics, but in the long list of graphene remarkable properties, a fundamental block is missing: superconductivity. Making graphene superconducting is relevant as the easy manipulation of this material by nanolytographic techniques paves the way to nanosquids, one-electron superconductor-quantum dot devices, superconducting transistors at the nano-scale and cryogenic solid-state coolers. Here we explore the doping of graphene by adatoms coverage. We show that the occurrence of superconductivity depen…
We show that effective superconducting orders generally emerge at low energy in the superconducting state of graphene with conventionally defined pairing symmetry . We study such a particular interesting example, the $d_{x^2-y^2}+id'_{xy}$ spin singlet pairing superconducting state in graphene, which can be generated by electronic correlation as well as induced through a proximity effect with a d-wave superconductor. We find that effectively the d-wave state is a state with mixed s-wave and exotic $p+ip$-wave pairing orders at low energy. This remarkable property leads to distinctive supercond…
We argue that by inducing superconductivity in graphene via the proximity effect, it is possible to observes the "quantum valley Hall effect". In the presence of magnetic field, supercurrent causes "valley pseudospin" to accumulate at the edges of the superconducting strip. This, and the structure of the superconducting vortex core, provide possibilities to experimentally observe aspects of the "deconfined quantum criticality".
We have investigated transport through graphene Andreev interferometers exhibiting reentrance of the superconducting proximity effect. We observed a crossover in the Andreev conductance oscillations as a function of gate voltage ($V_{BG}$). At high $V_{BG}$ the energy-dependent oscillation amplitude exhibits a scaling predicted for non-interacting electrons, which breaks down at low $V_{BG}$. The phenomenon is a manifestation of electron-electron interactions, whose main effect is to shorten the single-particle phase coherence time $τ_ϕ$. These results indicate that graphene provides a useful …
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…
Simultaneous transport and tunneling spectroscopy of moiré graphene: Distinct observation of the superconducting gap and signatures of nodal superconductivity
When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity1. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap2-4. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes5 suitable for topological quantum computing6. Here we report the first realization of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and wit…
Bilayer graphene has two non-equivalent sublattices and, therefore, the same adatom impurity can manifest in spectrally distinct ways-sharp versus broad resonances near the charge neutrality-depending on the sublattice it adsorbs at. Employing Green's function analytical methods and the numerical Kwant package we investigate the spectral and transport interplay between the resonances and superconducting coherence induced in bilayer graphene by proximity to an s-wave superconductor. Analyzing doping and temperature dependencies of quasi-particle spin-relaxation rates, energies of Yu-Shiba-Rusin…
We have performed photoemission studies of the electronic structure in LiC$_6$ and KC$_8$, a non-superconducting and a superconducting graphite intercalation compound, respectively. We have found that the charge transfer from the intercalant layers to graphene layers is larger in KC$_8$ than in LiC$_6$, opposite of what might be expected from their chemical composition. We have also measured the strength of the electron-phonon interaction on the graphene-derived Fermi surface to carbon derived phonons in both materials and found that it follows a universal trend where the coupling strength and…
We present here the results on superconducting properties in tantalum thin films (100nm thick) deposited on three-dimensional graphene (3DG) and carbon structures. A superconducting transition is observed in both composite thin films with a superconducting transition temperature of 1.2K and 1.0K, respectively. We have further measured the magnetoresistance at various temperatures and differential resistance dV/dI at different magnetic fields in these two composite thin films. In both samples, a much large critical magnetic field (~ 2 Tesla) is observed and this critical magnetic field shows li…
We study the effect of impurities in superconducting graphene and discuss their influence on the local electronic properties. In particular, we consider the case of magnetic and non-magnetic impurities being either strongly localized or acting as a potential averaged over one unit cell. The spin dependent local density of states is calculated and possibilities for visualizing impurities by means of scanning tunneling experiments is pointed out. A possibility of identifying magnetic scatters even by non spin-polarized scanning tunneling spectroscopy is explained.
Motivated by recent scanning tunneling experiments on zigzag-terminated graphene this paper investigates an interplay of evanescent and extended quasiparticle states in the local density of states (LDOS) near a zigzag edge using the Green's function of the Dirac equation. A model system is considered where the local electronic structure near the edge influences transport of both normal and superconducting electrons via a Fano resonance. In particular, the temperature enhancement of the critical Josephson current and 0-pi transitions are predicted.
We show that a graphene pnp junction with a central superconducting electrode acts as a Veselago lens for incoming electrons by focusing them and their phase-conjugated counterpart (holes) into different points of the optical axis. This selective focusing suggested by a simple trajectory analysis is confirmed by fully microscopic calculations. Although the focusing pattern is degraded by deviations from the ideal conditions we show that it remains visible for a wide range of parameters. We discuss how this property can be useful for the detection of entangled electron pairs.
Using highly efficient simulations of the tight-binding Bogoliubov-de Gennes model we solved self-consistently for the pair correlation and the Josephson current in a Superconducting-Bilayer graphene-Superconducting Josephson junction. Different doping levels for the non-superconducting link are considered in the short and long junction regime. Self-consistent results for the pair correlation and superconducting current resemble those reported previously for single layer graphene except in the Dirac point where remarkable differences in the proximity effect are found as well as a suppression o…
We describe the formation of superconducting states in graphene in the presence of pseudo-Landau levels induced by strain, when time reversal symmetry is preserved. We show that superconductivity in strained graphene is quantum critical when the pseudo-Landau levels are completely filled, whereas at partial fillings superconductivity survives at weak coupling. In the weak coupling limit, the critical temperature scales \emph{linearly} with the coupling strength and shows a sequence of quantum critical points as a function of the filling factor that can be accessed experimentally. We argue that…
We investigate the Cooper-pair propagation and the proximity effect in graphene under conditions in which the distance L between superconducting electrodes is much larger than the width W of the contacts. In the case of undoped graphene, supercurrents may exist with a spatial decay proportional to W^2/L^3. This changes upon doping into a 1/L^2 behavior, opening the possibility to observe a supercurrent over length scales above 1 micron at suitable doping levels. We also show that there is in general a crossover temperature T ~ v_F/k_B L that marks the onset of the strong decay of the supercurr…
In their comment Calandra \textit{et al} \cite{Calandra}, assert two points: (1) the estimate of charge transfer from Li to graphene layers in LiC$_6$ in our letter \cite{Pan2011c} is incorrect because of the three dimensional (3D) character of the electronic structure in bulk LiC$_6$; (2) our main claim that the superconductivity in graphite intercalation compounds (GICs) is graphene-sheet-driven is therefore invalid.
A quantum statistical theory is presented, supporting a superconducting state of an ultrahigh critical temperature (1275 K) in the multiwalled nanotubes reported by Zhao and Beeli [Phys. Rev. B 77, 245433 (2008)].
We explore Andreev states at the interface of graphene and a superconductor for a uniform pseudo-magnetic field. Near the zeroth-pseudo Landau level, we find a topological transition as a function of applied Zeeman field, at which a gapless helical mode appears. This 1D mode is protected from backscattering as long as intervalley- and spin-flip scattering are suppressed. We discuss a possible experimental platform to detect this gapless mode based on strained suspended membranes on a superconductor, in which dynamical strain causes charge pumping
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…
The ab initio anisotropic Migdal-Eliashberg formalism has been used to examine the pairing mechanism and the nature of the superconducting gap in the recently discovered lithium-decorated monolayer graphene superconductor. Our results provide evidence that the superconducting transition in Li-decorated monolayer graphene can be explained within a standard phonon-mediated mechanism. We predict a single anisotropic superconducting gap and a critical temperature Tc = 5.1-7.6 K, in very good agreement with the experimental results.
We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair e…
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…
We investigate the effect of edges on the intrinsic electron-electron interaction driven d-wave superconducting state in graphene doped close to the van Hove singularity. While the bulk is in a chiral $d_{x^2-y^2}+id_{xy}$ state, the order parameter at any edge is enhanced and has $d_{x^2-y^2}$-symmetry, with a decay length strongly increasing with weakening superconductivity. No graphene edge is pair breaking for the $d_{x^2-y^2}$ state and we never find any localized zero-energy edge states. We find two chiral edge modes which carry a spontaneous, but not quantized, quasiparticle current rel…
We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states, s-wave and an exotic $p+ip$ that is possible because of the special structure of the honeycomb lattice. At half filling, the $p+ip$ phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.
We propose a graphene-based model for realizing a new type of gapless condensate by pairing of electron-like (n) carriers of a Dirac cone conduction band with hole-like (p) carriers of a Dirac valance band. Ferromagnetic superconductivity (FS) in monolayer graphene or pairing between oppositely (n and p) doped layers of a double layer graphene allow for the formation of this p-n superconductivity. For FS in graphene, the p-n condensate dominates the zero temperature phase diagram at low levels of doping and high exchange fields. We show that p-n pairing with p+ip-wave symmetry presents a stabl…
We report on spatial measurements of the superconducting proximity effect in epitaxial graphene induced by a graphene-superconductor interface. Superconducting aluminum films were grown on epitaxial multilayer graphene on SiC. The aluminum films were discontinuous with networks of trenches in the film morphology reaching down to exposed graphene terraces. Scanning tunneling spectra measured on the graphene terraces show a clear decay of the superconducting energy gap with increasing separation from the graphene-aluminum edges. The spectra were well described by Bardeen-Cooper-Schrieffer (BCS) …
In this paper, we propose a scheme to realize three-qubit quantum phase gate of one qubit simultaneously controlling two target qubits using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The two lowest levels |0> and |1> of each SQUID are used to represent logical states while the higher energy levels |2> and |3> are utilized for gate realization. Our scheme does not require adiabatic passage, second order detuning, and the adjustment of the level spacing during gate operation which reduce the gate time significantly. The scheme is gen…
In this work the effects of defects in the superconducting phases of the twisted bilayer graphene (TBG) are investigated. A will-accepted low energy effective model and a non-magnetic impurity potential to mimic defects are employed. Different superconducting pairing symmetries, including $s$-wave, $(d+id)$-wave and $(p+ip)$-wave pairing, are considered. In single impurity case, the local density of states (DOS) are calculated for the pairing symmetries above. For different pairing symmetries the number and property of bound states induced by defects are different. In multi-impurity case, the …
Graphene-based Josephson junctions provide a novel platform for studying the proximity effect due to graphene's unique electronic spectrum and the possibility to tune junction properties by gate voltage. Here we describe graphene junctions with a mean free path of several micrometres, low contact resistance and large supercurrents. Such devices exhibit pronounced Fabry-Pérot oscillations not only in the normal-state resistance but also in the critical current. The proximity effect is mostly suppressed in magnetic fields below 10mT, showing the conventional Fraunhofer pattern. Unexpectedly, som…
We study heat transport in normal/superconducting graphene junctions. We find that while the thermal conductance displays the usual exponential dependence on temperature, reflecting the s-wave symmetry of the superconductor, it exhibits an unusual oscillatory dependence on the potential height or the length of the barrier region. This oscillatory dependence stems from the emergent low-energy relativistic nature of fermions in graphene, essentially different from the result in conventional normal metal/superconductor junctions.
We show that the intrinsic chiral $d_{x^2-y^2} \pm id_{xy}$-wave superconducting pairing in doped graphene is significantly strengthened in the core region of a doubly quantized s-wave superconducting vortex produced in a graphene-superconductor hybrid structure. The chiral d-wave state is induced by proximity effect, which transfers the center-of-mass angular momentum of the s-wave vortex to the orbital angular momentum of the chiral d-wave Cooper pairs. The proximity effect is enhanced by the circular geometry of the vortex and we find a $[1 + (T-T_{c,J})^2]^{-1}$ temperature dependence for …
Present study provides a comprehensive theoretical analysis of the superconducting phase in selected lithium-decorated bilayer graphene nanostructures. The numerical calculations, conducted within the Eliashberg formalism, give quantitative estimations of the most important thermodynamic properties such as the critical temperature, specific heat, critical field and others. It is shown that discussed lithium-graphene systems present enhancement of their thermodynamic properties comparing to the monolayer case e.g. the critical temperature can be raised to $\sim 15$ K. Furthermore, estimated cha…
Superconducting circuit quantum electrodynamics (QED) architecture composed of superconducting qubit and resonator is a powerful platform for exploring quantum physics and quantum information processing. By employing techniques developed for superconducting quantum computing, we experimentally investigate phase-sensitive Landau-Zener-Stückelberg (LZS) interference phenomena in a circuit QED. Our experiments cover a large range of LZS transition parameters, and demonstrate the LZS induced Rabi-like oscillation as well as phase-dependent steady-state population.
The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view graphene is special since it allows the creation of strong pseudo-magnetic fields due to strain. We show that in a Josephson junction made of strained graphene, Cooper pairs will diffuse into the strained region. The pair correlation function will be sub-lattice polarized due to the polarization of the local density of states in the zero pseudo-Landau level. We uncover …
We theoretically demonstrate the formation of a new type of unconventional superconductivity in graphene materials, which exhibits gapless property. The studied superconductivity is based on an interlayer pairing of chiral electrons in bilayer graphene, which results in an exotic s-wave spin-triplet condensate order with anomalous thermodynamic properties. These include the possibility of a temperature induced condensation causing an increase of the pairing gap with increasing temperature, and an entropy of the stable superconducting state which can be higher than its value in the normal state…
We show how the pairing symmetry of superconducting states in twisted bilayer graphene can be experimentally identified by theoretically studying effects of externally applied in-plane magnetic field and strain. In the low field regime, superconducting critical temperature $T_c$ is suppressed by in-plane magnetic field $\boldsymbol{B}_{\parallel}$ in singlet channels, but is enhanced by weak $\boldsymbol{B}_{\parallel}$ in triplet channels, providing an important distinction. The in-plane angular dependence of the critical $\boldsymbol{B}_{\parallel, c}$ has a six-fold rotational symmetry, whi…
We report electronic transport measurements of graphene contacted by NbTiN electrodes, which at low temperature remain superconducting up to at least 11 Tesla. In devices with a single superconducting contact, we find a more than twofold enhancement of the conductance at zero bias, which we interpret in terms of reflectionless tunneling. In devices with two superconducting contacts, we observe the Josephson effect, bipolar supercurrents and Fraunhofer patterns.
Graphene is a sturdy and chemically inert material exhibiting an exposed two-dimensional electron gas of high mobility. These combined properties enable the design of graphene composites either based on covalent or non- covalent coupling of adsorbates, or on multilayered structures. These systems have exhibited novel tunable electronic properties such as bandgap- engineering, reversible metal/insulating transition or supramolecular spintronics. Tunable superconductivity is expected as well, but experimental realization is lacking. Here, we show experiments based on me tal/graphene hybrid compo…
The possibility of intrinsic superconductivity in alkali-coated graphene monolayers has been recently suggested theoretically. Here, we derive the possible pairing symmetries of a carbon honeycomb lattice and discuss their phase diagram. We also evaluate the superconducting local density of states (LDOS) around an isolated impurity. This is directly related to scanning tunneling microscopy experiments, and may evidence the occurrence of unconventional superconductivity in graphene.
Vortices in the simplest superconducting state of graphene contain very low energy excitations, whose existence is connected to an index theorem that applies strictly to an approximate form of the relevant Bogoliubov-deGennes equations. When Zeeman interactions are taken into account, the zero modes required by the index theorem are (slightly) displaced. Thus the vortices acquire internal structure, that plausibly supports interesting dynamical phenomena.
A chiral time-reversal symmetry breaking (d+id)-wave superconducting state is likely to emerge in graphene doped close to the Van Hove singularity. As heavy doping procedures are expected to introduce defects, we here investigate the effects of microscopic defects on the (d+id)-wave superconducting state at the Van Hove singularity. We find that, while the superconducting order is reduced near a defect, the (d+id)-wave state remains intact and recovers in an exponential manner away from the defect. The recovery length is found to be on the order of one lattice constant for weak couplings. This…
Using the {\it ab initio} anisotropic Eliashberg theory including Coulomb interactions, we investigate the electron-phonon interaction and the pairing mechanism in the recently-reported superconducting Ca-intercalated bilayer graphene. We find that C$_6$CaC$_6$ can support phonon-mediated superconductivity with a critical temperature $T_{\rm c}=$6.8-8.1~K, in good agreement with experimental data. Our calculations indicate that the low-energy Ca$_{xy}$ vibrations are critical to the pairing, and that it should be possible to resolve two distinct superconducting gaps on the electron and hole Fe…
We analyze various possible superconducting pairing states and their relative stabilities in lightly doped graphene. We show that, when inter-sublattice electron-electron attractive interaction dominates and Fermi level is close to Dirac points, the system will favor intra-valley spin-triplet $p+\mathrm{i}p$ pairing state. Based on the novel pairing state, we further propose a scheme for doing topological quantum computation in graphene by engineering local strain fields and external magnetic fields.
We experimentally investigate electrical transport properties of graphene, which is a two dimensional (2D) conductor with relativistic energy dispersion relation. By investigating single- and bi-layer graphene devices with different aspect ratios, we confirm experimentally that the minimum conductivity in wide and short graphene strips approaches the theoretical value of 4e^2/π\h. At low temperatures, quantum interference of multiply-reflected waves of electrons and holes in graphene give rise to periodic conductance oscillations with bias and gate voltages. Thus graphene acts as a quantum bil…
Graphene is known to be non-superconducting. However, surprising superconductivity is recently discovered in a flat-band in a twisted bi-layer graphene. Here we show that superconductivity can be more easily realized in topological flat-bands induced by strain in graphene through periodic ripples. Specifically, it is shown that by including correlation effects, the chiral d-wave superconductivity can be stabilized under strain even for slightly doped graphene. The chiral d-wave superconductivity generally coexists with charge density waves (CDW) and pair density waves (PDW) of the same period.…
The coexistence of superconducting and correlated insulating states in magic-angle twisted bilayer graphene prompts fascinating questions about the relationship of these orders. Independent control of the microscopic mechanisms governing these phases could help uncover their individual roles and shed light on their intricate interplay. Here we report on direct tuning of electronic interactions in this system by changing its separation from a metallic screening layer. We observe quenching of correlated insula-tors in devices with screening layer separations that are smaller than a typical Wanni…
The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible order parameters forming the algebra U(1) X Cl(3), where Cl(3) is the three dimensional Clifford algebra. A sufficiently strong Zeeman coupling of the magnetic field of the vortex to the electron spin breaks the degeneracy in the core in favor of the anomalous quantum Hall state. I consider a variety of superconducting condensates on the honeycomb lattice and demonstrate the surprising universality of this result. A way to experimentally determine the outcome of the possib…
Using a Green's function approach, we study phonon-mediated superconducting pairing symmetries that may arise in bilayer graphene where the monolayers are displaced in-plane with respect to each other. We consider a generic coupling potential between the displaced graphene monolayers, which is applicable to both shifted and commensurate twisted graphene layers; study intralayer and interlayer phonon-mediated BCS pairings; and investigate AA and AB(AC) stacking orders. Our findings demonstrate that at the charge neutrality point, the dominant pairings in both AA and AB stackings with intralayer…
The distinctive features of the electronic structure of vortex states in superconducting graphene are studied within the Bogolubov-de Gennes theory applied to excitations near the Dirac point. We suggest a scenario describing the subgap spectrum transformation which occurs with a change in the doping level. For an arbitrary vorticity and doping level we investigate the problem of existence of zero energy modes. The crossover to a Caroli - de Gennes - Matricon type of spectrum is studied.
We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $eΔ_{0}/\hbar$ for the armchair edges. At…
We develop a theory for interlayer pairing of chiral electrons in graphene materials which results in an unconventional superconducting (S) state with s-wave spin-triplet order parameter. In a pure bilayer graphene, this superconductivity exhibits a gapless property with an exotic effect of temperature-induced condensation causing an increase of the pairing amplitude (PA) with increasing temperature. We find that a finite doping opens a gap in the excitation spectrum and weakens this anomalous temperature-dependence. We further explore the possibility of realizing variety of pairing patterns w…
In a recent experiment [Lin et al., arXiv:2112.07841], the superconducting phase hosted by a heterostructure of mirror-symmetric twisted trilayer graphene and WSe$_2$ was shown to exhibit significantly different critical currents in opposite directions in the absence of external magnetic fields. We here develop a microscopic theory and analyze necessary conditions for this zero-field superconducting diode effect. Taking into account the spin-orbit coupling induced in trilayer graphene via the proximity effect, we classify the pairing instabilities and normal-state orders and derive which combi…
