Session G56: Twisted Bilayer Graphene: Superconductivity and Symmetry Breaking

SU(4) symmetry in twisted bilayer graphene - an itinerant perspective

In our work we study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at Van Hove filling. We argue that the Landau free energy functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, however the signs of quartic terms are different for the two fillings. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong 1st-order transition to an SU(3) ⊗U(1) manifold of orders. The resulting state lifts the initial approximate four-fold degeneracy of the electronic band and induces a 3-1 splitting of fermionic excitations for small electron doping. For Van Hove filling, we find a weak 1st-order transition to an SO(4) ⊗U(1) manifold of orders that preserve the two-fold band degeneracy. We discuss the effect of particle-hole orders on superconductivity and compare our results with strong-coupling approaches.   

Spectroscopic evidence for unconventional superconductivity in twisted bilayer graphene

The pairing mechanism of superconductivity in magic-angle twisted bilayer graphene (MATBG)  is one of the most interesting questions in the study of moiré materials. Whether MATBG is a conventional BCS superconductor or an unconventional one, such as those found in other correlated materials remains unknown. We tune the carrier density of MATBG between different ground states, including the superconducting state well below its transition temperature (T_c), and probe the Bogoliubov quasiparticle excitation spectrum using scanning tunneling microscopy (STM), thereby providing key information on the nature of MATBG’s pairing state and its symmetry. We observed several spectroscopic features that support the unconventional pairing in MATBG. Our spectroscopic measurements show that the ratio of the tunneling gap to T_c far exceeds (2Δ/k_BT_c ~ 25) that of the mean-field BCS ratio. We find a V-shaped gap consistent with that of a nodal superconductor. Suppressing the zero resistance states with a magnetic field or raising the temperature above Tc, the tunneling spectra show the presence of a pseudogap phase, similar to those found in other unconventional superconductors. These spectroscopic observations are irreconcilable with a conventional BCS mechanism of superconductivity [1].   

Point-Contact Measurements of the Phase Diagram of Magic-Angle Twisted Bilayer Graphene

Due to strong interactions and flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts an incredibly complex phase diagram consisting of correlated metals, band insulators, correlated insulators, Chern and quantum Hall insulators, and superconductors. Disentangling this phase diagram though tunneling differential conductance is difficult because many phases (including insulators and superconductor) manifest as a gap in the quasiparticle energy spectrum. We use density-tuned point-contact spectroscopy (PCS) on a scanning tunneling microscope (STM) to unambiguously distinguish correlated insulators, which have strongly suppressed PCS conductance, from superconductors, which display enhanced PCS conductance around zero bias due to Andreev reflection. By comparing PCS with scanning tunneling spectroscopy (STS), we infer that the superconducting phase of MATBG has several unusual properties that are reminiscent of behavior in other unconventional superconductors [1]. Moreover, we remark that PCS is a relatively straightforward method for verifying the existence or absence of superconductivity in two-dimensional materials, as certain transport signatures can be occasionally misleading.   

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 moir\'e 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.    

Magnetic anisotropy in twisted bilayer graphene and ABC-trilayer graphene aligned with hexagonal boron nitride

We and others have previously reported ferromagnetism in both twisted bilayer graphene (tBLG) and ABC-trilayer graphene aligned with hexagonal boron nitride (hBN) evinced by a large (or even quantized) hysteretic anomalous Hall effect. These systems are composed entirely of non-magnetic elements; the magnetism arises from the strong electronic correlations of these moiré systems. Here, we report that when tilting the sample in an external magnetic field, the ferromagnetism of the two systems is highly anisotropic. In tBLG, the magnetism switches at a threshold out-of-plane component of the magnetic field down to tilt angles of about 5°. Because spin–orbit coupling is weak in graphene, such anisotropy is unlikely to come from spin but rather favors theories in which the ferromagnetism is orbital. The situation is less clear in the ABC-trilayer graphene moiré. The magnetic state at -2.3 electrons per moiré unit cell exhibits similar behavior to tBLG, switching at a threshold out-of-plane field. However, the other magnetic state observed at -1 electrons per moiré unit cell does not exhibit such a threshold, suggesting that either the spin of the electron is playing a role or the in-plane field is directly coupling to the orbital degree of freedom.   

Anomalous Hall effect near half-filling in twisted bilayer graphene

Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its exotic symmetry-broken phases, correlated Chern insulators, and unconventional superconductivity. Unambiguously identifying the isospin ordering of the various correlated ground states has so far been challenging owing to the large number of possible candidates, including fully spin and/or valley polarized states, intervalley coherent (IVC) states, nematics, and more. Although some devices exhibit an anomalous Hall effect (AHE) at ν = 1 or 3, so far no signatures of time-reversal symmetry (TRS) breaking have been reported in pristine tBLG devices at half-filling (ν = ±2). Here, we will discuss measurements of two tBLG devices with twist angles slightly away from the magic angle (0.95° and 1.2°) in which we observe an AHE at ν = +2 and -2, respectively. Our observations imply the existence of a TRS-broken ground state with a finite orbital magnetic moment that closely competes with the typically observed topologically trivial correlated insulating state at half-filling. Notably, we do not observe superconductivity upon doping away from half-filling in either of our devices, motivating the possibility that the ground state ordering we observe is incompatible with pairing.   

Strain-induced Kekule spiral order in magic-angle graphene: a density matrix renormalization group study

We study magic-angle graphene with a small uniaxial strain at integer fillings using density-matrix renormalization group (DMRG), in which the Hartree-Fock study has reported a new type of ground state with momentum-modulated intervalley coherence. Unlike the Kramers intervalley coherent state (K-IVC), this state is time-reversal invariant but breaks moire translation symmetry with an "incommensurate Kekule spiral" (IKS) order at the microscopic graphene scale. In this work, we confirm the presence of the IKS order in the DMRG ground state, with its properties in good agreement with the Hartree-Fock predictions. We also find that, even in the absence of strain, such order is a strong candidate in the low-energy manifold of states, which closely competes with the valley-polarized order favored by Hartree-Fock numerics. This result suggests an expanded view in the phase diagram of twisted bilayer graphene.   

Global phase diagram of twisted bilayer graphene above TC

We investigate the full doping and strain-dependent phase diagram (absent superconductivity) of magic-angle twisted bilayer graphene. Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all non-zero integer fillings of the moiré unit cell, is found to be ubiquitous for non-integer doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the 'cascade' physics and Landau fans observed experimentally.   

Charged flavour textures and skyrmion pairing in twisted bilayer graphene

We numerically study the charged spin and pseudospin textures that emerge upon doping the strong-coupling insulators in magic-angle twisted bilayer graphene [1]. Using unbiased self-consistent Hartree-Fock calculations, we show that such textures can be directly probed within the microscopic interacting Bistritzer-MacDonald model. For even integer filling, we demonstrate explicitly that singly charged skyrmions bind to form paired skyrmions, and calculate their dependence on the system parameters. By constructing beyond mean-field variational states, we analyze the effective mass and internal structure of the paired skyrmions as a function of twist angle, and comment on connections to a recently proposed theory of skyrmion superconductivity [2]. We also study spin skyrmions about the quantized anomalous Hall state, where we show the existence of spin texture lattices at finite doping.

[1] Y. H. Kwan, G. Wagner, N. Bultinck, S. H. Simon, and S. A. Parameswaran, in preparation

[2] E. Khalaf, S. Chatterjee, N. Bultinck, M. P. Zaletel, and A. Vishwanath, Charged skyrmions and topological origin of superconductivity in magic-angle graphene, Science advances 7, eabf5299 (2021)   

Symmetry-broken Chern insulators and Rashba-like Landau level crossings in magic angle twisted bilayer graphene

Flat bands in magic-angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations, superconductivity and magnetism. However, the phases of MATBG in a magnetic field and what they reveal about the zero-field phase diagram remain relatively uncharted. We report a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = ±1, ±2, ±3 and ±4, which nucleate from integer fillings of the moiré unit cell v = ±3, ±2, ±1 and 0, respectively. The exact sequence and correspondence of the Chern numbers and filling factors suggest that these states are directly driven by electronic interactions, which specifically break the time-reversal symmetry in the system. The analysis of Landau-level crossings from higher energy bands enables a parameter-free comparison to a newly derived ‘magic series’ of level crossings in a magnetic field and provides constraints on the parameters of the Bistritzer–MacDonald MATBG Hamiltonian [1]. Additionally, we observed the re-entrance of insulating states at v = +2, ±3 of the moiré unit cell of MATBG upon applying an external magnetic field close to the full flux quantum Φ/Φ₀ = 1 of the superlattice unit cell (B = 25θ² T).   

Magic-angle twisted bilayer graphene superconducting nano-calorimeter

Superconducting nano-calorimeters are currently some of the most sensitive sensors for detecting electromagnetic radiation. Two-dimensional materials, thanks to their small heat capacity are progressively evolving into a novel platform to develop a new generation of sensors that can further push the limits of detector sensitivities. Specifically, magic-angle twisted bilayer graphene (MAG) exhibits a record-small heat capacity and a sharp superconducting transition that makes it suitable for superconducting calorimetry. Here we investigate the thermal and optoelectronic properties of the MAG and provide precious insights towards applications. This study establishes MAG as a promising two-dimensional material for ultra-sensitive photodetection.   

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We study the current-phase relation in Josephson junctions of twisted bilayer graphene [1-3], computing Green’s functions with a decimation technique based on a real space description [4]. Due to the narrow bands, the critical current near the magic angle is four orders of magnitude higher than in monolayer graphene. We find a highly non-sinusoidal current-phase relation, with two maxima for certain angles, which implies that increasing the current could lead to spontaneous jumps of the phase difference across the junction. There is strong electron-hole asymmetry, which diminishes near the magic angle. We argue that the superconducting gap to bandwidth ratio is the main quantity governing the current-phase relation and the local density of states at the junction.

[1] F. K. de Vries et. al. Nature Nanotechnology pp. 1-4 (2021).

[2] D. Rodan-Legrain et. al., Nature Nanotechnology pp. 1-7 (2021).

[3] J. Diez-Merida, et. al. (2021). arXiv preprint arXiv:2110.01067.

[4] H. Sainz-Cruz, T. Cea, P. A. Pantaleon, and F. Guinea, Phys. Rev. B 104, 075144 (2021).

The authors acknowledge funding from the European Commision Graphene Flagship, Core 3, grant number 881603, and from grants NMAT2D (Comunidad de Madrid, Spain), SprQuMat and SEV-2016-0686, (Ministerio de Ciencia e Innovación, Spain).   

Highly tunable junctions in magic-angle graphene tunnelling devices

Magic-angle twisted bilayer graphene (MATBG) and related systems have recently emerged as highly tunable two-dimensional material platforms exhibiting a wide range of phases, such as metal, insulator and superconductor states. Local electrostatic control over these phases may enable the creation of versatile quantum devices that were previously not achievable in other single-material platforms. In this talk, I will expand on our recent results in MATBG [1], where we show Josephson junctions and tunnelling transistors in twisted graphene devices, solely defined by electrostatic gates. Our multi-gated device geometry offers independent control of the weak link, barriers and tunnelling electrodes. Utilizing the intrinsic bandgaps of MATBG, we also demonstrate monolithic edge tunnelling spectroscopy within the same MATBG devices and measure the energy spectrum of MATBG in the superconducting phase. Furthermore, by inducing a double-barrier geometry, the devices can be operated as a single-electron transistor, exhibiting Coulomb blockade. With versatile functionality encompassed within a single material, these tunnelling devices may find applications in graphene-based tunable superconducting qubits, on-chip superconducting circuits and electromagnetic sensing. 

 

[1] Rodan-Legrain, D. et al. Highly tunable junctions and non-local Josephson effect in magic-angle graphene tunnelling devices. Nature Nanotechnology 16, 769–775 (2021).    

Magnetic Josephson Junctions and Superconducting Diodes in Magic Angle Twisted Bilayer Graphene

The simultaneous co-existence and gate-tunability of the superconducting,magnetic and topological orders in magic angle twisted bilayer graphene (MATBG) open up entirely new possibilities for the creation of complex hybrid Josephson junctions (JJ). Here we report on the creation of gate-defined, magnetic Josephson junctions in MATBG, where the weak link is gate-tuned close to the correlated state at a moiré filling factor of ν = −2. A highly unconventional Fraunhofer pattern emerges, which is phase-shifted and asymmetric with respect to the current and magnetic field directions, and shows a pronounced magnetic hysteresis. We demonstrate how the combination of magnetization and its current induced magnetization switching in the MATBG JJ allows us to realize a programmable zero field superconducting diode, which represents a major building block for a new generation of superconducting quantum electronics.   

Superconducting Quantum Interference Devices in Magic-Angle Twisted Bilayer Graphene

Magic-Angle Twisted Bilayer Graphene hosts a range of physical phenomena that can be tuned by electrostatic doping [1]. We have realized Josephson junctions on this material by combining gate-defined regions tuned to superconducting or insulating phases [2]. This has shown the potential of the material to become a platform for versatile superconducting devices [2, 3]. Here we take the next step in terms of device complexity and show data from a Superconducting Quantum Interference Device (SQUID) defined in Magic-Angle Twisted Bilayer Graphene. We characterize the device and use it to directly measure the current-phase relation of one of the junctions in the ring, a measurement impossible to realize with a single junction.

[1] Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018)

[2] de Vries, F.K. et al. Gate-defined Josephson junctions in magic-angle twisted bilayer graphene. Nat. Nanotechnol. 16, 760–763 (2021)

[3] Rodan-Legrain, et al. Highly tunable junctions and non-local Josephson effect in magic-angle graphene tunnelling devices. Nat. Nanotechnol. 16, 769–775 (2021)