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The unusual properties of superconductivity in magic-angle twisted bilayer graphene (MATBG) have sparked enormous research interest. However, despite the dedication of intensive experimental efforts and the proposal of several possible pairing mechanisms, the origin of its superconductivity remains elusive. Here, utilizing angle-resolved photoemission spectroscopy with micrometer spatial resolution, we have revealed flat band replicas in superconducting MATBG, where MATBG is unaligned with its hexagonal boron nitride (hBN) substrate11. These replicas exhibit uniform energy spacing, approximately 150 +- 15 meV apart, indicative of strong electron-boson coupling. Strikingly, these replicas are absent in non-superconducting twisted bilayer graphene (TBG) systems, either when MATBG is aligned to hBN or when TBG deviates from the magic angle. Calculations suggest that the formation of these flat band replicas in superconducting MATBG are attributed to the strong coupling between flat band electrons and an optical phonon mode at the graphene K point, facilitated by inter-valley scattering. These findings, although do not necessarily put electron phonon coupling as the main driving force for the superconductivity in MATBG, unravel the unique electronic structure inherent in superconducting MATBG, thereby providing crucial information for understanding the unusual electronic landscape from which the superconductivity is derived., Comment: 17 pages, 4 figures

At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample to sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductivity and correlated insulating phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned ($\theta_{Gr-hBN}$ $\approx$ 1.65$^\circ$) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap ($\Delta$ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings $\nu$ = $\pm 1/3$ and $\nu$ = $\pm 1/6$, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moir\'e superlattices. Our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements., Comment: 4 figures

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a $\sqrt{3}$ x $\sqrt{3}$ super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moir\'e superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of $\nu$ = $\pm$ 2 electrons per moir\'e unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. We also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements., Comment: 5 figures

We analytically compute the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands. After experimentally validating the strong-coupling approach at $\pm 4$ electrons/moir\'e unit cell, we consider the spatial features of the STM signal for 14 different many-body correlated states and assess the possibility of Kekul\'e distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the Kramers IVC state and its nonchiral $\mathrm{U} \left( 4 \right)$ rotations do not exhibit any KD, while the time-reversal-symmetric IVC state does. Our results, obtained over a large range of energies and model parameters, show that the STM signal and Chern number of a state can be used to uniquely determine the nature of the TBG ground state., Comment: 8+80 pages, 2+65 figures. New version matches the published version

The emergence of superconductivity with doping from correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors, as described by the Bardeen-Cooper-Schrieffer (BCS) theory. While there is now ample evidence for strong electronic correlations in MATBG, recent studies have claimed that unlike correlated insulators, superconductivity persists even when these interactions are partially screened. This suggests that the pairing in MATBG might be conventional in nature, a consequence of the large density of states of its nearly flat bands, perhaps phonon-mediated as in BCS superconductors. Here we combine tunneling and Andreev reflection spectroscopy with the scanning tunneling microscope (STM) to observe several key experimental signatures for unconventional superconductivity in MATBG. We show that the tunneling spectra below the transition temperature $T_c$ are inconsistent with that of a conventional s-wave superconductor, but rather resemble that of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunneling energy gap $\Delta_T$, which far exceeds the mean-field BCS ratio (with $2\Delta_T/k_BT_c \sim 25$) and the energy gap $\Delta_{AR}$ extracted from Andreev reflection spectroscopy ($2\Delta_{AR}/k_BT_c \sim 6$). The tunneling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase, with a suppressed density of states at the Fermi level. Moreover, the pseudogap state and superconductivity are both absent when MATBG is aligned with the hexagonal boron nitride (hBN) underneath. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.

Interactions among electrons and the topology of their energy bands can create novel quantum phases of matter. Most topological electronic phases appear in systems with weak electron-electron interactions. The instances where topological phases emerge only as a result of strong interactions are rare, and mostly limited to those realized in the presence of intense magnetic fields. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for new strongly correlated topological phases. Here we introduce a novel local spectroscopic technique using a scanning tunneling microscope (STM) to detect a sequence of topological insulators in MATBG with Chern numbers C = $\pm$ 1, $\pm$ 2, $\pm$ 3, which form near $\nu$ = $\pm$ 3, $\pm$ 2, $\pm$ 1 electrons per moir\'e unit cell respectively, and are stabilized by the application of modest magnetic fields. One of the phases detected here (C = +1) has been previously observed when the sublattice symmetry of MATBG was intentionally broken by hexagonal boron nitride (hBN) substrates, with interactions playing a secondary role. We demonstrate that strong electron-electron interactions alone can produce not only the previously observed phase, but also new and unexpected Chern insulating phases in MATBG. The full sequence of phases we observed can be understood by postulating that strong correlations favor breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moir\'e systems beyond those anticipated from weakly interacting models., Comment: 17 pages, 4 figures

Magic-angle twisted bilayer graphene (MATBG) exhibits a rich variety of electronic states, including correlated insulators, superconductors, and topological phases. Understanding the microscopic mechanisms responsible for these phases requires determining the interplay between electron-electron interactions and quantum degeneracy due to spin and valley degrees of freedom. Signatures of strong electron-electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements. Transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moir\'e unit cell. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Using high-resolution scanning tunneling microscopy (STM), we observed a cascade of transitions in the spectroscopic properties of MATBG as a function of electron filling. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moir\'e flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions we report here characterizes the correlated high-temperature parent phase from which various insulating and superconducting ground-state phases emerge at low temperatures in MATBG.

We describe the design, construction, and performance of an ultra-high vacuum (UHV) scanning tunneling microscope (STM) capable of imaging at dilution-refrigerator temperatures and equipped with a vector magnet. The primary objective of our design is to achieve a high level of modularity by partitioning the STM system into a set of easily separable, interchangeable components. This naturally segregates the UHV needs of STM instrumentation from the typically non-UHV construction of a dilution refrigerator, facilitating the usage of non-UHV materials while maintaining a fully bakeable UHV chamber that houses the STM. The modular design also permits speedy removal of the microscope head from the rest of the system, allowing for repairs, modifications, and even replacement of the entire microscope head to be made at any time without warming the cryostat or compromising the vacuum. Without using cryogenic filters, we measured an electron temperature of 184 mK on a superconducting Al(100) single crystal., Comment: 13 pages, 10 figures

The observation of surface phonon dispersion using local probes can provide important information related to local structural and thermal properties. In this study, surface phonon modes on a Cu(100) surface were measured using the inelastic tunneling spectroscopy of scanning tunneling microscopy (STM-IETS) with atomically sharp tips. Different phonon modes were selectively measured depending on the structures of the probing tips or the surfaces. Two different surface phonon modes, at 19.0 meV on a clean Cu(100) surface and at 13.5 meV on an oxygen-adsorbed Cu(100) surface, are explained by the selection rules. Additionally, the spatial variation in STM-IETS showed surface stress relaxation., Comment: 19 pages, 4 figures, supplementary material with 2 figures