Superconductivity In Twisted Bilayer Graphene Research Articles

Moiré-enabled topological superconductivity in twisted bilayer graphene

Twisted van der Waals materials have risen as highly tunable platforms for realizing unconventional superconductivity. Here we demonstrate how a topological superconducting state can be driven in a twisted graphene multilayer at a twist angle of approximately 1.6 degrees proximitized to other 2D materials. We show that an encapsulated twisted bilayer subject to induced Rashba spin–orbit coupling, s-wave superconductivity, and exchange field generates a topological superconducting state enabled by the moiré pattern. We demonstrate the emergence of a variety of topological states with different Chern numbers, that are highly tunable through doping, strain, and bias voltage. Our proposal does not depend on fine-tuning the twist angle, but solely on the emergence of moiré minibands and is applicable for twist angles between 1.3 and 3 degrees. Our results establish the potential of twisted graphene bilayers to create topological superconductivity without requiring ultraflat dispersions.

Tuning the Flat Band in Bi2O2Se by Pressure to Induce Superconductivity.

The discovery of superconductivity in twisted bilayer graphene has reignited enthusiasm in the field of flat-band superconductivity. However, important challenges remain, such as constructing a flat-band structure and inducing a superconducting state in materials. Here, we successfully achieved superconductivity in Bi2O2Se by pressure-tuning the flat-band electronic structure. Experimental measurements combined with theoretical calculations reveal that the occurrence of pressure-induced superconductivity at 30 GPa is associated with a flat-band electronic structure near the Fermi level. Moreover, in Bi2O2Se, a van Hove singularity is observed at the Fermi level alongside pronounced Fermi surface nesting. These remarkable features play a crucial role in promoting strong electron-phonon interactions, thus potentially enhancing the superconducting properties of the material. These findings demonstrate that pressure offers a potential experimental strategy for precisely tuning the flat band and achieving superconductivity.

Interfacial magnon-mediated superconductivity in twisted bilayer graphene

The interfacial coupling between electrons and magnons in adjacent layers can mediate an attractive electron–electron interaction and induce superconductivity. We consider magic-angle twisted bilayer graphene sandwiched between two ferromagnetic insulators to optimize this effect. As a result, magnons induce an interlayer superconducting state characterized by p-wave symmetry. We investigate two candidate ferromagnets. The van der Waals ferromagnet CrI3 stands out because it allows compression to tune the superconducting state with an exponential sensitivity. This control adds a new dimension to the tunability of twisted bilayer graphene. Our results open a new path for exploring magnon-induced superconductivity.

Theoretical determination of the effect of a screening gate on plasmon-induced superconductivity in twisted bilayer graphene

Theoretical determination of the effect of a screening gate on plasmon-induced superconductivity in twisted bilayer graphene

Moiré-Assisted Realization of Octahedral MoTe2 Monolayer.

A current key challenge in 2D materials is the realization of emergent quantum phenomena in hetero structures via controlling the moiré potential created by the periodicity mismatch between adjacent layers, as highlighted by the discovery of superconductivity in twisted bilayer graphene. Generally, the lattice structure of the original host material remains unchanged even after the moiré superlattice is formed. However, much less attention is paid for the possibility that the moiré potential can also modify the original crystal structure itself. Here, it is demonstrated that octahedral MoTe2 which is unstable in bulk is stabilized in a commensurate MoTe2 /graphene hetero-bilayer due to the moiré potential created between the two layers. It is found that the reconstruction of electronic states via the moiré potential is responsible for this stabilization, as evidenced by the energy-gap opening at the Fermi level observed by angle-resolved photoemission and scanning tunneling spectroscopies. The present results provide a fresh approach to realize novel 2D quantum phases by utilizing the moiré potential.

Flat bands, quantum Hall effect and superconductivity in twisted bilayer graphene at magic angles

Flat band electronic modes are responsible for superconductivity in twisted bilayer graphene (TBG) rotated at magic angles. From there other magic angles can be found for any multilayered twisted graphene systems. Eventually, this lead to the discovery of the highest ever known electron-electron correlated material. Moreover, the quantum phase diagram of TBG is akin to those observed among high-Tc superconductors and thus there is a huge research effort to understand TBG in the hope of clarifying the physics behind such strong correlations. A particularity of the TBG is the coexistence of superconductivity and the fractional Quantum Hall effect, yet this relationship is not understood. In this work, a simple 2 × 2 matrix model for TBG is introduced. It contains the magic angles and due to the intrinsic chiral symmetry in TBG, a lowest energy level related to the quantum Hall effect. The non-Abelian properties of this Hamiltonian play a central role in the electronic localization to produce the flat bands and here it is proved that the squared Hamiltonian of the chiral TBG model is equivalent to a single electron Hamiltonian inside of a non-Abelian pseudo-magnetic field produced by electrons in other layers. Therefore, the basic and fundamental elements in the physics of magic angles are determined. In particular, a study is made on these fundamental energy contributions at the Γ-point due to its relation to the recurrence of magic angles and its relationship with the Quantum Hall effect.

Tuning the lattice thermal conductivity of bilayer penta-graphene by interlayer twisting

Penta-graphene (PG) is the well-known prototype of the extensively studied 2D pentagon-based materials in recent years, and twisting strategy has been widely used to tune the properties of 2D sheets since the discovery of superconductivity in twisted bilayer graphene. However, no study is reported on how twisting affects the phonon properties of such penta-sheets. In this work, for the first time, we study the effect of twisting on the phonon transport properties of PG by using density functional theory and the phonon Boltzmann transport equation combined with two-channel transport theory and machine learning method. It is found that the in-plane lattice thermal conductivity of the twisted bilayer PG with a twist angle of 36.87° is only 96.72 W/mK at 300 K, reduced by 77.16% as compared to that of untwisted bilayer PG, and the four-phonon interaction further reduces the thermal conductivity by nearly 36%, while the coherence contribution to the thermal conductivity is enhanced to 9.69 W/mK from 0.13 W/mK by twisting. These results indicate that interlayer twisting not only can enhance three- and four-phonon scattering but also can uplift phonon coherence due to the resulted complex atomic configuration and high anharmonicity in bilayer PG.

Andreev Reflection in Scanning Tunneling Spectroscopy of Unconventional Superconductors.

We evaluate the differential conductance measured in an STM setting at arbitrary electron transmission between STM tip and a 2D superconductor with arbitrary gap structure. Our analytical scattering theory accounts for Andreev reflections, which become prominent at larger transmissions. We show that this provides complementary information about the superconducting gap structure beyond the tunneling density of states, strongly facilitating the ability to extract the gap symmetry and its relation to the underlying crystalline lattice. We use the developed theory to discuss recent experimental results on superconductivity in twisted bilayer graphene.

Euler-obstructed nematic nodal superconductivity in twisted bilayer graphene

Signatures of nematic nodal superconductivity have been experimentally observed in magic angle twisted bilayer graphene (MATBG). Here, we propose a general topological mechanism explaining how a nematic pairing leads to nodal superconductivity in MATBG. By focusing on the intervalley ${C}_{2z}\mathcal{T}$-invariant Cooper pairing order parameter, we show that the pairing order parameter can always be split into a trivial channel and an Euler obstructed channel, owing to the nontrivial normal-state band topology. When the pairing is spontaneously nematic, we find that a sufficiently-dominant Euler obstructed channel with two zeros typically leads to nodal superconductivity. The mechanism is general since it is independent of the specific interaction that accounts for the required pairing. Under the approximation of exactly-flat bands, we analytically find that the mean-field zero-temperature superfluid weight is bounded from below, and thus the Berezinksii-Kosterlitz-Thouless (BKT) critical temperature can be nonzero, even if the Euler obstructed pairing is dominant. We also numerically find that a spontaneously-nematic dominant Euler obstructed pairing can arise from a local attractive interaction.

Higher-order topological superconductivity in twisted bilayer graphene

Twisted bilayer graphene, by nature of its symmetries (like the approximate particle-hole symmetry) and anomalous band structure, realizes a higher-order topological superconductor when $s$-wave pairing is introduced via proximity. Here, the authors demonstrate this exotic phase numerically and analytically, and illustrate a multitude of consequences: zero modes bound to Abrikosov vortices, the fractional Josephson effect, and much more.

Theory of holey twistsonic media

Rotating two overlapping lattices relative to each other produces the well known moiré interference patterns and has surprisingly led to strongly correlated superconductivity in twisted bilayer graphene. This seminal effect that is associated with electrons occupying flat dispersion bands has stimulated a surge of activities in classical wave physics such as acoustics to explore equivalent scenarios. Here, we mimic twisted bilayer physics by employing a rigorous sound wave expansion technique to conduct band engineering in holey bilayer plates, i.e., twistsonic media. Our numerical findings show how one flexibly is able to design moiré sound interference characteristics that alone are controlled by the twist angle and the interlayer air separation. More specifically, our numerical approach provides a significant advantage in both computational speed and storage size in comparison with widely used commercial finite-element-method solvers. We foresee that our findings should stimulate further studies in terms of band engineering and exotic topological twisted phases.

Pseudospin Paramagnons and the Superconducting Dome in Magic Angle Twisted Bilayer Graphene.

We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by (i)applying a sublattice polarizing field (generated by an aligned BN substrate) or (ii)changing moiré band filling to favor valley polarization. The enhanced intrasublattice attraction close to sublattice polarization instability is analogous to enhanced like-spin attraction in liquid ^{3}He near the melting curve and the enhanced valley-singlet repulsion close to valley-polarization instabilities is analogous to enhanced spin-singlet repulsion in metals that are close to a ferromagnetic instability. We comment on the relationship between our pseudospin paramagnon model and the rich phenomenology of superconductivity in twisted bilayer and multilayer graphene.

Filling- and interaction-modulated pairing symmetry in twisted bilayer graphene

Superconductivity in twisted bilayer graphene has attracted much attention in recent years. Based on the significant experimental facts, there are many theoretical investigations on its superconducting mechanism and pairing symmetry. In this paper, we study the theory of the electron-phonon coupling in magic-angle twisted bilayer graphene starting from the work of Lian et al. [Phys. Rev. Lett. 122, 257002 (2019)] and thereby develop a uniform framework for the low as well as high electron densities. From this beneficial approach, we obtain the strongest superconductivity near the moir\'e band filling factor $|\ensuremath{\nu}|\ensuremath{\approx}2$, consistent with the experimental results. By associating it with the Coulomb interaction, we find that the pairing symmetry is strongly dependent on the filling factor, with the $p$-wave, $f$-wave, and $s$-wave pairing states sequentially appearing. It can be confirmed that the superconductivity mostly exists near the half filling of the lowest flat bands with an $f$-wave pairing symmetry. We discuss the possible origin of these phenomena, the stability of the superconductivity, and also the feasible experimental verification.

Moiré engineering in van der Waals heterostructures

Isolated atomic planes can be assembled into a multilayer van der Waals (vdW) heterostructure in a precisely chosen sequence. These heterostructures feature moiré patterns if the constituent 2D material layers are stacked in an incommensurable way, due to a lattice mismatch or twist. This design-by-stacking has opened up the promising area of moiré engineering, a term that can be understood in two different perspectives, namely, (i) structural—engineering a moiré pattern by introducing twist, relative strain, or defects that affect the commensurability of the layers and (ii) functional—exploiting a moiré pattern to find and tune resulting physical properties of a vdW heterostructure. The latter meaning, referring to the application of a moiré pattern, is seen in the literature in the specific context of the observation of correlated electronic states and unconventional superconductivity in twisted bilayer graphene. The former meaning, referring to the design of the moiré pattern itself, is present in the literature but less commonly discussed or less understood. The underlying link between these two perspectives lies in the deformation field of the moiré superlattice. In this Perspective, we describe a path from designing a moiré pattern to employing the moiré pattern to tune physical properties of a vdW heterostructure. We also discuss the concept of moiré engineering in the context of twistronics, strain engineering, and defect engineering in vdW heterostructures. Although twistronics is always associated with moiré superlattices, strain and defect engineering are often not. Here, we demonstrate how strain and defect engineering can be understood within the context of moiré engineering. Adopting this perspective, we note that moiré engineering creates a compelling opportunity to design and develop multiscale electronic devices.

Symmetry constraints on superconductivity in twisted bilayer graphene: Fractional vortices, 4e condensates, or nonunitary pairing

Twisted bilayer graphene has recently emerged as an exciting platform to study interaction-driven phases. Among these, superconductivity has received intense theoretical effort to understand its underlying mechanism. In this work, the authors establish general symmetry constraints on the nature of superconductivity in twisted bilayer graphene that are independent of its mechanism. These constraints are sufficient to limit the nature of superconductivity to one of three unconventional possibilities: nonunitary pairing, unitary pairing with fractional vortices, or higher-charge condensates. They identify parameter regimes where each possibility is likely to occur.

Stacking-Dependent Interlayer Ferroelectric Coupling and Moiré Domains in a Twisted AgBiP2Se6 Bilayer.

Rotation/twisting of bilayers could induce unprecedented new physics due to stacking-dependent electronic properties and interlayer coupling, such as the superconductivity in twisted bilayer graphene, which can find applications in electronics. However, deep understanding at the atomic/electronic levels is limited by the capability of accurate theoretical simulations. Here, from first-principles simulations, we found that the AgBiP2Se6 bilayer has stacking-dependent ferroelectric ground states due to interlayer polarization coupling. Interlayer ferroelectric coupling is preferred in an AA-stacked AgBiP2Se6 bilayer, but antiferroelectric coupling is preferred in AB- or AC-stacked configurations. The ferroelectric Moiré patterns are thus observed in a twisted AgBiP2Se6 bilayer with ferroelectric (antiferroelectric) interlayer couplings in the AA (AB/AC)-stacked areas. Our work for the first time unveils the effects of twisting/rotation on interlayer polarization coupling and provides a real example of ferroelectric Moiré patterns.

Theory of Correlated Insulators and Superconductivity in Twisted Bilayer Graphene.

We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at noninteger fillings. Adding a phonon-mediated intervalley retarded attractive interaction, we obtain strong-coupling superconducting domes, whose structure is in qualitative agreement with experiments. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic structure determine the phase diagram. It also explains how subtle differences between devices may lead to the different behaviors observed experimentally. A similar model can be applied with minor modifications to other moiré systems, such as twisted trilayer graphene.

Evidence for unconventional superconductivity in twisted bilayer graphene.

The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors1-4, as described by the Bardeen-Cooper-Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened5,6. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. Here we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature Tc are inconsistent with those of a conventional s-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap ΔT, which far exceeds the mean-field BCS ratio (with 2ΔT/kBTc ~ 25), and the gap ΔAR extracted from Andreev reflection spectroscopy (2ΔAR/kBTc ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.

Superconductivity in the twisted bilayer graphene: emergent mystery in the magic angle, the topological bosons and the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover

ABSTRACT Theory of superconductivity in twisted bilayer graphene (tBLG) is presented, based on the fact that Dirac fermions are pairing creating the topological bosons as consequence of topologically protected Lifshitz topological transition (TPLTT). We have shown that multiple TPLTTs are realised at low twisting angles in tBLG. At TPLTT the Berry phase changes from 2π in bilayer graphene to π in tBLG. It is favourable to form the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover (BCS-BEUC) when the attractive interaction for pairing dominates the repulsive screened Coulomb interaction. The theory yields a second-order phase transition for BCS-BEUC, and values of specific heat and the Ginzburg−Landau coherence length are calculated. The problem has been solved of emergent mystery in the magic angles at which there exists possibility for observation of BCS-BEUC. The solution is connected with the Umklapp processes when the quasiwave vector of the superconducting carriers is shifted from the Brillouin zone to other cell of the reciprocal space. The table is given of the allowed magic angles which include the corresponding effective masses of the pairing Dirac fermions.

Coulomb interaction, phonons, and superconductivity in twisted bilayer graphene

The polarizability of twisted bilayer graphene, due to the combined effect of electron-hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron-hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.