Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene

Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor

Quantum simulators are ideal platforms to investigate quantum phenomena that are inaccessible through conventional means, such as the limited resources of classical computers to address large quantum systems or due to constraints imposed by fundamental laws of nature. Here, through a digitized adiabatic evolution, we report an experimental simulation of antiferromagnetic (AFM) and ferromagnetic (FM) phase formation induced by spontaneous symmetry breaking (SSB) in a three-generation Cayley tree-like superconducting lattice. We develop a digital quantum annealing algorithm to mimic the system dynamics, and observe the emergence of signatures of SSB-induced phase transition through a connected correlation function. We demonstrate that the signature of a transition from classical AFM to quantum FM-like phase state happens in systems undergoing zero-temperature adiabatic evolution with only nearest-neighbor interacting systems, the shortest range of interaction possible. By harnessing properties of the bipartite Rényi entropy as an entanglement witness, we observe the formation of entangled quantum FM and AFM phases. Our results open perspectives for new advances in condensed matter physics and digitized quantum annealing.

Programmable Electromagnetic Wave Absorption via Tailored Metal Single Atom-Support Interactions

Metal single atoms (SA)-support interactions inherently exhibit significant electrochemical activity, demonstrating potential in energy catalysis. However, leveraging these interactions to modulate electronic properties and extend application fields is a formidable challenge, demanding in-depth understanding and quantitative control of atomic-scale interactions. Herein, in situ, off-axis electron holography technique is utilized to directly visualize the interactions between SAs and the graphene surface. These interactions facilitate the formation of dispersed nanoscale regions with high charge density and are highly sensitive to external electromagnetic (EM) fields, resulting in controllable dynamic relaxation processes for charge accumulation and restoration. This leads to customized dielectric relaxation, which is difficult to achieve with current band engineering methods. Moreover, these electronic behaviors are insensitive to elevated temperatures, having characteristics distinct from those of typical metallic or semiconducting materials. Based on these results, programmable EM wave absorption properties are achieved by developing a library of SA-graphene materials and precisely controlling SA-support interactions to tailor their responses to EM waves in terms of frequency and intensity. This advancement addresses the customized anti-EM interference requirements of electronic components, greatly enhancing the development of integrated circuits and micro-nano chips. Future efforts will concentrate on manipulating atomic interactions in SA-support, potentially revolutionizing nanoelectronics and optoelectronics.

High-temperature field-free superconducting diode effect in high-Tc cuprates

The superconducting diode effect (SDE) is defined by the difference in the magnitude of critical currents applied in opposite directions. It has been observed in various superconducting systems and attracted high research interests. However, the operating temperature of the SDE is typically low and/or the sample structure is rather complex. For the potential applications in non-dissipative electronics, efficient superconducting diodes working in zero magnetic field with high operating temperatures and a simple configuration are highly desired. Here, we report the observation of a SDE under zero magnetic field with operating temperatures up to 72 K and efficiency as high as 22% at 53 K in high-transition-temperature (high-Tc) cuprate superconductor Bi2Sr2CaCu2O8+δ (BSCCO) flake devices. The rectification effect persists beyond two hundred sweeping cycles, confirming the stability of the superconducting diode. Our results offer promising developments for potential applications in non-dissipative electronics, and provide insights into the mechanism of field-free SDE and symmetry breakings in high-Tc superconductors.

Nonreciprocal superconductivity

We introduce the notion of nonreciprocal superconductors where inversion and time-reversal symmetries are broken, giving rise to an asymmetric energy dispersion. We demonstrate that nonreciprocal superconductivity can be detected by Andreev reflection. In particular, a transparent junction between a normal metal and a nonreciprocal superconductor generally exhibits an asymmetric current-voltage characteristic, which serves as a defining feature of nonreciprocal superconductivity. Unlike the superconducting diode effects, our detection scheme has the advantage of avoiding large critical currents that turn the superconducting state to normal. Last, we discuss candidates for nonreciprocal superconductivity, including graphene, UTe2, as well as engineered platforms.

Low-Energy Optical Sum Rule in Moiré Graphene

Few layers of graphene at small twist angles have emerged as a fascinating platform for studying the problem of strong interactions in regimes with a nearly quenched single-particle kinetic energy and nontrivial band topology. Starting from the strong-coupling limit of twisted bilayer graphene with a vanishing single-electron bandwidth and interlayer tunneling between the same sublattice sites, we present an exact analytical theory of the Coulomb interaction-induced low-energy optical spectral weight at all integer fillings. In this limit, while the interaction-induced single-particle dispersion is finite, the optical spectral weight vanishes identically at integer fillings. We study corrections to the optical spectral weight by systematically including the effects of experimentally relevant strain-induced renormalization of the single-electron bandwidth and interlayer tunnelings between the same sublattice sites. Given the relationship between the optical spectral weight and the diamagnetic response that controls superconducting T_{c}, our results highlight the relative importance of specific parent insulating phases in enhancing the tendency towards superconductivity when doped away from integer fillings.

Nonlinear edge transport in a quantum Hall system

Nonlinear transport phenomena in condensed matter reflect the geometric nature, quantum coherence, and many-body correlation of electronic states. Electric currents in solids are classified into (i) ohmic current, (ii) supercurrent, and (iii) geometric or topological current. While the nonlinear current-voltage (I-V) characteristics of the former two categories have been extensive research topics recently, those of the last category remains unexplored. Among them, the quantum Hall current is a representative example. Realized in two-dimensional electronic systems under a strong magnetic field, the topological protection quantizes the Hall conductance in the unit of e2/h (e, elementary charge; and h, Planck constant), of which the edge transport picture gives a good account. Here, we theoretically study the nonlinear I-VH characteristic of the edge transport up to third order in VH. We find that nonlinearity arises in the Hall response from electron-electron interaction between the counterpropagating edge channels with the nonlinear energy dispersions. We also discuss possible experimental observations.

Interfering Josephson diode effect in Ta2Pd3Te5 asymmetric edge interferometer

Edge states in topological systems have attracted great interest due to their robustness and linear dispersions. Here a superconducting-proximitized edge interferometer is engineered on a topological insulator Ta2Pd3Te5 with asymmetric edges to realize the interfering Josephson diode effect (JDE), which hosts many advantages, such as the high efficiency as much as 73% at tiny applied magnetic fields with an ultra-low switching power around picowatt. As an important element to induce such JDE, the second-order harmonic in the current-phase relation is also experimentally confirmed by half-integer Shapiro steps. The interfering JDE is also accompanied by the antisymmetric second harmonic transport, which indicates the corresponding asymmetry in the interferometer, as well as the polarity of JDE. This edge interferometer offers an effective method to enhance the performance of JDE, and boosts great potential applications for future superconducting quantum devices.

Microwave-Assisted Unidirectional Superconductivity in Al-InAs Nanowire-Al Junctions under Magnetic Fields

Under certain symmetry-breaking conditions, a superconducting system exhibits asymmetric critical currents, dubbed the "superconducting diode effect." Recently, systems with the ideal superconducting diode efficiency or unidirectional superconductivity have received considerable interest. In this work, we report the study of Al-InAs nanowire-Al Josephson junctions under microwave irradiation and magnetic fields. We observe an enhancement of superconducting diode effect under microwave driving, featured by a horizontal offset of the zero-voltage step in the voltage-current characteristic that increases with microwave power. Devices reach the unidirectional superconductivity regime at sufficiently high driving amplitudes. The offset changes sign with the reversal of the magnetic field direction. Meanwhile, the offset magnitude exhibits a roughly linear response to the microwave power in dBm when both the power and the magnetic field are large. The signatures observed are reminiscent of a recent theoretical proposal using the resistively shunted junction (RSJ) model. However, the experimental results are not fully explained by the RSJ model, indicating a new mechanism for unidirectional superconductivity that is possibly related to nonequilibrium dynamics or dissipation in periodically driven superconducting systems.

Emergent phases in graphene flat bands

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

Anomalous h/2e Periodicity and Majorana Zero Modes in Chiral Josephson Junctions

Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either h/e [Vignaud et al., Nature (London) 624, 545 (2023)NATUAS0028-083610.1038/s41586-023-06764-4] or h/2e [Amet et al., Science 352, 966 (2016)SCIEAS0036-807510.1126/science.aad6203]. While the h/e-periodic component of the supercurrent had been anticipated theoretically before, the emergence of the h/2e periodicity is still not fully understood. In this Letter, we systematically study the Fraunhofer oscillations of chiral Josephson junctions. In chiral Josephson junctions, the chiral edge states coupled to the superconductors become chiral Andreev edge states. We find that in short junctions, the coupling of the chiral Andreev edge states can trigger the h/2e-magnetic flux periodicity. Our theory resolves the important puzzle concerning the appearance of the h/2e periodicity in chiral Josephson junctions. Furthermore, we explain that when the chiral Andreev edge states couple, a pair of localized Majorana zero modes appear at the ends of the Josephson junction, which are robust and independent of the phase difference between the two superconductors. As the h/2e periodicity and the Majorana zero modes have the same physical origin in the wide junction limit, the Fraunhofer oscillation period could be useful in identifying the regime with Majorana zero modes.

Unconventional superconductivity in chiral molecule-TaS2 hybrid superlattices

Chiral superconductors, a unique class of unconventional superconductors in which the complex superconducting order parameter winds clockwise or anticlockwise in the momentum space1, represent a topologically non-trivial system with intrinsic time-reversal symmetry breaking (TRSB) and direct implications for topological quantum computing2,3. Intrinsic chiral superconductors are extremely rare, with only a few arguable examples, including UTe2, UPt3 and Sr2RuO4 (refs. 4-7). It has been suggested that chiral superconductivity may exist in non-centrosymmetric superconductors8,9, although such non-centrosymmetry is uncommon in typical solid-state superconductors. Alternatively, chiral molecules with neither mirror nor inversion symmetry have been widely investigated. We suggest that an incorporation of chiral molecules into conventional superconductor lattices could introduce non-centrosymmetry and help realize chiral superconductivity10. Here we explore unconventional superconductivity in chiral molecule intercalated TaS2 hybrid superlattices. Our studies reveal an exceptionally large in-plane upper critical field Bc2,|| well beyond the Pauli paramagnetic limit, a robust π-phase shift in Little-Parks measurements and a field-free superconducting diode effect (SDE). These experimental signatures of unconventional superconductivity suggest that the intriguing interplay between crystalline atomic layers and the self-assembled chiral molecular layers may lead to exotic topological materials. Our study highlights that the hybrid superlattices could lay a versatile path to artificial quantum materials by combining a vast library of layered crystals of rich physical properties with the nearly infinite variations of molecules of designable structural motifs and functional groups11.

Link between supercurrent diode and anomalous Josephson effect revealed by gate-controlled interferometry

In Josephson diodes the asymmetry between positive and negative current branch of the current-phase relation leads to a polarity-dependent critical current and Josephson inductance. The supercurrent nonreciprocity can be described as a consequence of the anomalous Josephson effect -a φ0-shift of the current-phase relation- in multichannel ballistic junctions with strong spin-orbit interaction. In this work, we simultaneously investigate φ0-shift and supercurrent diode efficiency on the same Josephson junction by means of a superconducting quantum interferometer. By electrostatic gating, we reveal a direct link between φ0-shift and diode effect. Our findings show that spin-orbit interaction in combination with a Zeeman field plays an important role in determining the magnetochiral anisotropy and the supercurrent diode effect.

Chirality Probe of Twisted Bilayer Graphene in the Linear Transport Regime

We propose minimal transport experiments in the coherent regime that can probe the chirality of twisted moiré structures. We show that only with a third contact and in the presence of an in-plane magnetic field (or another time-reversal symmetry breaking effect) a chiral system may display nonreciprocal transport in the linear regime. We then propose to use the third lead as a voltage probe and show that opposite enantiomers give rise to different voltage drops on the third lead. Additionally, in the scenario of layer-discriminating contacts, the third lead can serve as a current probe capable of detecting different handedness even in the absence of a magnetic field. In a complementary configuration, applying opposite voltages on the two layers of the third lead gives rise to a chiral (super)current in the absence of a source-drain voltage whose direction is determined by its chirality.

Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction

We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.

Stacking Order Engineering of Two-Dimensional Materials and Device Applications

Stacking orders in 2D van der Waals (vdW) materials dictate the relative sliding (lateral displacement) and twisting (rotation) between atomically thin layers. By altering the stacking order, many new ferroic, strongly correlated and topological orderings emerge with exotic electrical, optical and magnetic properties. Thanks to the weak vdW interlayer bonding, such highly flexible and energy-efficient stacking order engineering has transformed the design of quantum properties in 2D vdW materials, unleashing the potential for miniaturized high-performance device applications in electronics, spintronics, photonics, and surface chemistry. This Review provides a comprehensive overview of stacking order engineering in 2D vdW materials and their device applications, ranging from the typical fabrication and characterization methods to the novel physical properties and the emergent slidetronics and twistronics device prototyping. The main emphasis is on the critical role of stacking orders affecting the interlayer charge transfer, orbital coupling and flat band formation for the design of innovative materials with on-demand quantum properties and surface potentials. By demonstrating a correlation between the stacking configurations and device functionality, we highlight their implications for next-generation electronic, photonic and chemical energy conversion devices. We conclude with our perspective of this exciting field including challenges and opportunities for future stacking order engineering research.

Functional nanoporous graphene superlattice

Two-dimensional (2D) superlattices, formed by stacking sublattices of 2D materials, have emerged as a powerful platform for tailoring and enhancing material properties beyond their intrinsic characteristics. However, conventional synthesis methods are limited to pristine 2D material sublattices, posing a significant practical challenge when it comes to stacking chemically modified sublattices. Here we report a chemical synthesis method that overcomes this challenge by creating a unique 2D graphene superlattice, stacking graphene sublattices with monodisperse, nanometer-sized, square-shaped pores and strategically doped elements at the pore edges. The resulting graphene superlattice exhibits remarkable correlations between quantum phases at both the electron and phonon levels, leading to diverse functionalities, such as electromagnetic shielding, energy harvesting, optoelectronics, and thermoelectrics. Overall, our findings not only provide chemical design principles for synthesizing and understanding functional 2D superlattices but also expand their enhanced functionality and extensive application potential compared to their pristine counterparts.

Ultrafast Umklapp-assisted electron-phonon cooling in magic-angle twisted bilayer graphene

Understanding electron-phonon interactions is fundamentally important and has crucial implications for device applications. However, in twisted bilayer graphene near the magic angle, this understanding is currently lacking. Here, we study electron-phonon coupling using time- and frequency-resolved photovoltage measurements as direct and complementary probes of phonon-mediated hot-electron cooling. We find a remarkable speedup in cooling of twisted bilayer graphene near the magic angle: The cooling time is a few picoseconds from room temperature down to 5 kelvin, whereas in pristine bilayer graphene, cooling to phonons becomes much slower for lower temperatures. Our experimental and theoretical analysis indicates that this ultrafast cooling is a combined effect of superlattice formation with low-energy moiré phonons, spatially compressed electronic Wannier orbitals, and a reduced superlattice Brillouin zone. This enables efficient electron-phonon Umklapp scattering that overcomes electron-phonon momentum mismatch. These results establish twist angle as an effective way to control energy relaxation and electronic heat flow.

Intrinsic supercurrent non-reciprocity coupled to the crystal structure of a van der Waals Josephson barrier

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 that clearly reflects the intrinsic crystal structure of Td-WTe2. The Josephson diode efficiency increases with the Td-WTe2 thickness up to critical thickness, and all junctions, irrespective of the barrier thickness, reveal magneto-chiral characteristics with respect to a mirror plane of Td-WTe2. Our results, together with the twist-angle-tuned magneto-chirality of a Td-WTe2 double-barrier junction, show that two-dimensional materials promise vertical Josephson diodes with high efficiency and tunability.

Nonreciprocal Josephson Linear Response

We consider the finite-frequency response of multiterminal Josephson junctions and show how nonreciprocity in them can show up at linear response, in contrast to the static Josephson diodes featuring nonlinear nonreciprocity. At finite frequencies, the response contains dynamic contributions to the Josephson admittance, featuring the effects of Andreev bound state transitions along with Berry phase effects, and reflecting the breaking of the same symmetries as in Josephson diodes. We show that outside exact Andreev resonances, the junctions feature nonreciprocal reactive response. As a result, the microwave transmission through those systems is nondissipative, and the electromagnetic scattering can approach complete nonreciprocity. Besides providing information about the nature of the weak link energy levels, the nonreciprocity can be utilized to create nondissipative and small-scale on-chip circulators whose operation requires only rather small magnetic fields.

Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors

Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi2Sr2CaCu2O8+x crystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Our results open a path to engineering topological devices at higher temperatures.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe_{2} revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe_{2} as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe_{2} is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for "internally engineered" topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.

Gate-Defined Josephson Weak-Links in Monolayer WTe2

Systems combining superconductors with topological insulators offer a platform for the study of Majorana bound states and a possible route to realize fault tolerant topological quantum computation. Among the systems being considered in this field, monolayers of tungsten ditelluride (WTe2 ) have a rare combination of properties. Notably, it has been demonstrated to be a quantum spin Hall insulator (QSHI) and can easily be gated into a superconducting state. Measurements on gate-defined Josephson weak-link devices fabricated using monolayer WTe2 are reported. It is found that consideration of the 2D superconducting leads are critical in the interpretation of magnetic interference in the resulting junctions. The reported fabrication procedures suggest a facile way to produce further devices from this technically challenging material and the results mark the first step toward realizing versatile all-in-one topological Josephson weak-links using monolayer WTe2 .

Josephson Diode Effect Induced by Valley Polarization in Twisted Bilayer Graphene

Recently, the Josephson diode effect (JDE), in which the superconducting critical current magnitudes differ when the currents flow in opposite directions, has attracted great interest. In particular, it was demonstrated that gate-defined Josephson junctions based on magic-angle twisted bilayer graphene showed a strong nonreciprocal effect when the weak-link region is gated to a correlated insulating state at half filling (two holes per moiré cell). However, the mechanism behind such a phenomenon is not yet understood. In this Letter, we show that the interaction-driven valley polarization, together with the trigonal warping of the Fermi surface, induce the JDE. The valley polarization, which lifts the degeneracy of the states in the two valleys, induces a relative phase difference between the first and the second harmonics of the supercurrent and results in the JDE. We further show that the nontrivial current phase relation, which is responsible for the JDE, also generates the asymmetric Shapiro steps.

Gate-tunable superconducting diode effect in a three-terminal Josephson device

The phenomenon of non-reciprocal critical current in a Josephson device, termed the Josephson diode effect, has garnered much recent interest. Realization of the diode effect requires inversion symmetry breaking, typically obtained by spin-orbit interactions. Here we report observation of the Josephson diode effect in a three-terminal Josephson device based upon an InAs quantum well two-dimensional electron gas proximitized by an epitaxial aluminum superconducting layer. We demonstrate that the diode efficiency in our devices can be tuned by a small out-of-plane magnetic field or by electrostatic gating. We show that the Josephson diode effect in these devices is a consequence of the artificial realization of a current-phase relation that contains higher harmonics. We also show nonlinear DC intermodulation and simultaneous two-signal rectification, enabled by the multi-terminal nature of the devices. Furthermore, we show that the diode effect is an inherent property of multi-terminal Josephson devices, establishing an immediately scalable approach by which potential applications of the Josephson diode effect can be realized, agnostic to the underlying material platform. These Josephson devices may also serve as gate-tunable building blocks in designing topologically protected qubits.