Magic Angle Spectroscopy (1812.08776v2)

Abstract: The electronic properties of heterostructures of atomically-thin van der Waals (vdW) crystals can be modified substantially by Moir\'e superlattice potentials arising from an interlayer twist between crystals. Moir\'e-tuning of the band structure has led to the recent discovery of superconductivity and correlated insulating phases in twisted bilayer graphene (TBLG) near the so-called "magic angle" of $\sim$1.1{\deg}, with a phase diagram reminiscent of high T$_c$ superconductors. However, lack of detailed understanding of the electronic spectrum and the atomic-scale influence of the Moir\'e pattern has so far precluded a coherent theoretical understanding of the correlated states. Here, we directly map the atomic-scale structural and electronic properties of TBLG near the magic angle using scanning tunneling microscopy and spectroscopy (STM/STS). We observe two distinct van Hove singularities (vHs) in the LDOS which decrease in separation monotonically through 1.1{\deg} with the bandwidth (t) of each vHs minimized near the magic angle. When doped near half Moir\'e band filling, the conduction vHs shifts to the Fermi level and an additional correlation-induced gap splits the vHs with a maximum size of 7.5 meV. We also find that three-fold (C$_3$) rotational symmetry of the LDOS is broken in doped TBLG with a maximum symmetry breaking observed for states near the Fermi level, suggestive of nematic electronic interactions. The main features of our doping and angle dependent spectroscopy are captured by a tight-binding model with on-site (U) and nearest neighbor Coulomb interactions. We find that the ratio U/t is of order unity, indicating that electron correlations are significant in magic angle TBLG. Rather than a simple maximization of the DOS, superconductivity arises in TBLG at angles where the ratio U/t is largest, suggesting a pairing mechanism based on electron-electron interactions.

• The paper demonstrates that van Hove singularities in TBLG converge as the twist angle approaches 1.1°, reducing bandwidth and favoring superconductivity.
• The paper finds a 7.5 meV correlation gap at half-filling, highlighting the role of strong many-body interactions.
• The paper employs STM/STS alongside tight-binding models to reveal symmetry-breaking and electron correlation phenomena in twisted bilayer graphene.

Magic Angle Spectroscopy: An Overview of Electronic and Structural Properties in Twisted Bilayer Graphene

The paper "Magic Angle Spectroscopy" explores the electronic and atomic-scale structure of twisted bilayer graphene (TBLG) near the so-called "magic angle," approximately 1.1 degrees. This investigation is prompted by the recent discovery of superconductivity and correlated insulating phases under these special conditions, which bear resemblance to the phase diagram of high-temperature superconductors. By utilizing scanning tunneling microscopy and spectroscopy (STM/STS), the authors provide a detailed atomic-scale mapping of the local density of states (LDOS) and structural properties, proffering insights into the many-body interactions and electronic phenomena at near-magic angles.

Twisted bilayer graphene has garnered significant attention due to the emergent electronic properties that arise from the Moiré superlattice—a pattern created by slight rotations between two graphene layers. Previous work indicated that at the magic angle of approximately 1.1 degrees, electron tunneling between the layers was significantly altered, leading to flat band formation where electron interactions dominated over kinetic energy. However, a comprehensive theoretical understanding of the correlated states remained elusive. The authors address this gap by analyzing van Hove singularities (vHs) in the local electronic structure and their evolution with twist angle and doping.

Key Findings

1. Van Hove Singularities: Two distinct vHs were observed in the LDOS of TBLG, moving closer together as the twist angle approached the magic angle. At the magic angle, the bandwidth of these vHs was minimized, which aligns with conditions believed to encourage superconductivity.
2. Doping and Correlated Gaps: As TBLG was doped near half-filling of the Moiré superlattice, a correlation-induced gap emerged as the conduction vHs aligned with the Fermi level, recorded as a 7.5 meV maximum gap. This indicates many-body character associated with the vHs at half-filling and resembles gap behaviors in other strongly-correlated electron systems.
3. Electron Correlations and Symmetry: The paper highlights significant electron correlation effects characterized by a ratio of on-site Coulomb interaction (U) to bandwidth (t) of about unity. Notably, a symmetry-breaking behavior was detected with doping, manifesting as a breaking of three-fold rotational symmetry, suggestive of nematic electronic interactions.
4. Theoretical Modelling: Using a tight-binding model with considerations for on-site Coulomb and nearest neighbor interactions, the authors encapsulate the observed doping and angle-dependent spectroscopies. Theoretical interpretation suggests a superconducting pairing mechanism arising from electron-electron interactions rather than a simple density of states maximization.

Implications and Future Directions

The detailed mapping of atomic and electronic properties in twisted bilayer graphene underscores the significance of the magic angle for investigating new emergent behaviors, particularly in electron correlation regimes akin to strongly correlated materials such as cuprates. The results present a deeper understanding of the superconducting and insulating behaviors in TBLG, highlighting the role of electron interactions in driving these states.

Practically, insights from this paper may pave the way for novel applications in quantum materials and devices by exploiting the-title-field input?","\n", "content": "## Overview of the Study on Magic Angle Spectroscopy\n\nThe research presented in the paper titled \"Magic Angle Spectroscopy\" offers a comprehensive examination of the unique electronic properties that emerge in twisted bilayer graphene (TBLG) near the magic angle of approximately 1.1 degrees. This work is pivotal for understanding the superconductivity and correlated insulating phases that the TBLG system exhibits, resembling the properties of high-temperature superconductors. The paper delineates the outcomes of precise atomic-scale mapping using scanning tunneling microscopy and spectroscopy (STM/STS) to evaluate the local density ofmarkdown files, you're correct.

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## Magic Angle Spectroscopy: An Overview of Electronic and Structural Properties in Twisted Bilayer Graphene The paper "Magic Angle Spectroscopy" explores the electronic and atomic-scale structure of twisted bilayer graphene (TBLG) near the so-called "magic angle," approximately 1.1 degrees. This investigation is prompted by the recent discovery of superconductivity and correlated insulating phases under these special conditions, which bear resemblance to the phase diagram of high-temperature superconductors. By utilizing scanning tunneling microscopy and spectroscopy (STM} can directly address the challenges posed by disentangling the individual contributions of interactions and atomic rearrangements in TBLG, and provide the necessary resolution to disentangle these competing mechanisms at work. \section*{Implications and Future Directions} This paper provides key insights into the electronic structure of TBLG near the magic angle, establishing the presence of significant vHs splitting and superconductivity tied to electronic correlations. This suggests that interactions rather than the density of states are paramount in giving rise to the observed phenomena. The paper provides evidence for nematic electronic order in TBLG, which would be an exciting avenue for future research in understanding}[Methodological Approach] The authors employed scanning tunneling microscopy and spectroscopy (STM/STS) to achieve atomic-scale mapping of TBLG. This methodology was significant as it allowed direct observation of the electronic structure changes with varying twist angles and doping concentrations. The approach provided high-resolution images of the Moiré patterns and their influence on LDOS, revealing key insights into the electronic and structural behavior of TBLG. The tight-binding model with Coulomb interactions supported these findings, identifying a crucial <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>U</mi><mi mathvariant="normal">/</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">U/t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mord">/</span><span class="mord mathnormal">t</span></span></span></span> ratio and its role in the observed electronic phenomena. ### Implications and Future Directions The research presented provides a robust foundational understanding. The paper delivers significant insights into the electronic properties of TBLG at the magic angle, revealing a non-trivial interplay of electronic correlations, symmetry-breaking, and electronic order that resemble certain aspects of high-Tc superconductor systems. The detailed spectroscopic evidence presented in this paper is pivotal to unraveling the mechanisms underpinning the exotic phases in TBLG, which may inform future developments in the field. The demonstration that superconductivity in TBLG at near-magic angles likely arises from electron-electron interaction dynamics is notable. Contrary to the simple maximization of density of states (DOS), the findings suggest that superconductivity occurs at angles where the ratio of the on-site Coulomb interaction <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>U</mi></mrow><annotation encoding="application/x-tex">U</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span></span></span></span> to the bandwidth <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span></span></span></span> is maximized, implying that mechanisms such as spin fluctuations might play a primary role in pairing. Moreover, the evidence supporting the existence of interaction-induced gaps at half-filling positions, correlated with vHs peaks, points toward density wave orders. This underlines the necessity of supporting unconventional electronic order considerations, such as the emergent nematicity as indicated by broken C3 symmetry in the doped state, to fully comprehend the superconducting and insulating phases. ### Implications and Future Directions The findings in this paper bolster the view of TBLG at the magic angle as a model system for studying strongly correlated electron systems, offering a tunable platform to explore unconventional high-Tc superconductivity mechanisms. The observed relationship between electron correlation parameters and the emergence of superconductivity suggests avenues for engineering correlation strength through structural adjustments of the TBLG. Future developments could further leverage the tuning of twist angles, explore the effects of additional Moiré potential modifications, and focus on low-temperature and high-resolution measurements to capture the intricate details of the electron interactions and symmetry breaking phenomena—insights that are crucial for developing next-generation quantum materials and devices. As the field progresses, understanding the balance between phase stability, electronic correlations, and structural perfectness in such nanoscale systems will be vital in steering discoveries in quantum materials towards significant technological applications.