Session G57: Twisted Graphene: Electronic, Magnetic, and Topological Properties

Gate-defined wires in twisted bilayer graphene: Electrical detection of inter-valley coherence

Twisted bilayer graphene (TBG) realises a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states whose precise nature remains largely unknown. I introduce gate-defined wires in TBG with proximity-induced spin-orbit coupling as a tool for revealing the nature of correlated insulators. In particular, a class of phases possessing 'inter-valley coherent' order has been widely championed, not only as characterising the correlated insulators, but also as mediating the proximate superconductivity. Nevertheless, the symmetry breaking order in these states occurs at the level of the microscopic graphene lattice, making their experimental verification challenging - particularly in fully encapsulated samples. I demonstrate that the band structure of a gate-defined wire immersed in an inter-valley coherent correlated insulator inherits electrically detectable fingerprints of inter-valley coherence, thus promoting ultra-short-scale symmetry breaking order to a large-scale conductance signature.    

Internally engineered Majorana modes in twisted bilayer graphene

Twisted bilayer graphene (TBG) realizes an exquisitely tunable, strongly interacting system featuring superconductivity and various correlated insulating states. In this talk I will introduce gate-defined wires in TBG as an enticing platform for Majorana-based fault-tolerant qubits. Our proposal notably relies on "internally" generated superconductivity in TBG – as opposed to "external" superconducting proximity effects commonly employed in Majorana devices – and may operate even at zero magnetic field.    

TB or not TB? A comparative study of twisted bilayer and alternating twist multilayer graphene

We perform a detailed comparative analysis between twisted bilayer graphene and alternating twist multilayer systems introduced in Ref. [1]. We start by showing how the mapping from multilayer to decoupled bilayers [1] is modified in the presence of vertical displacement field and in-plane magnetic field. We then show how the effects of lattice relaxation is modified in the multilayer setting due to the increased number of layers and the different magic angle. Finally, we generalize the strong coupling theory developed for twisted bilayer graphene [2-4] to other multilayer systems making quantitative predictions about the different correlated insulating and superconducting phases and their response to vertical displacement field and in-plane magnetic field. 

[1] Khalaf, Kruchkov, Tarnopolsky, Vishwanath Phys. Rev. B 100, 085109 (2019)

[2] Bultinck, Khalaf, Liu, Chatterjee, Vishwanath, Zaletel Phys. Rev. X 10, 031034 (2020)

[3] Khalaf, Chatterjee, Bultinck, Zaletel, Vishwanath Science advances 7 (19) (2021)

[4] Ledwith, Khalaf, Vishwanath, arXiv:2105.08858, Annals of Physics, (2021)   

Imaging Commensurate Minimally Twisted Bilayer Graphene Aligned to Hexagonal Boron Nitride

Aligning magic-angle twisted bilayer graphene (TBG) with a hexagonal boron nitride (hBN)

substrate reveals the hidden non-trivial topology of the flat band through the appearance of a

quantum anomalous Hall effect (QAHE) in transport measurements. 1 The commensuration of the

two sets of Moiré patterns (graphene-graphene and graphene-hBN) is expected to occur, due to

the 1.8% difference in the lattice constants of graphene and hBN, only at a TBG twist angle of .

Surprisingly, by using low temperature scanning tunneling microscopy (STM) and spectroscopy

(STS), we find a locally stable commensurate double Moiré pattern for , suggesting strong

lattice relaxation effects that favor the alignment of the two Moiré patterns even for twist angles

that differ substantially from estimates based on rigid lattice calculations. We observe large

domains (200x200nm) of perfectly aligned double Moiré patterns separated by domain walls

where the built-up strain is released. Furthermore, STS reveals gaps at fractional fillings of the

flat band that increase in the presence of a magnetic field indicating that alignment with hBN

reveals an intrinsic non-trivial band topology even for twist angles far from the magic angle.   

A family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers

We consider a family of twisted graphene multilayers consisting of n-untwisted chirally stacked layers, e.g. AB, ABC, etc, with a single twist on top of m-untwisted {chirally stacked} layers. Upon neglecting both trigonal warping terms for the untwisted layers and the same sublattice hopping between all layers, the resulting models generalize several remarkable features of the chiral model of twisted bilayer graphene (CTBG). In particular, they exhibit a set of magic angles which are identical to those of CTBG at which a pair of bands (i) are perfectly flat, (ii) have Chern numbers in the sublattice basis given by ±(n, -m) or ±(n + m - 1, -1) depending on the stacking chirality, and (iii) satisfy the trace condition, saturating an inequality between the quantum metric and the Berry curvature, and thus realize ideal quantum geometry. We provide explicit analytic expressions for the flat band wavefunctions at the magic angle in terms of the CTBG wavefunctions. We also show that the Berry curvature distribution in these models can be continuously tuned while maintaining perfect quantum geometry. Similar to the study of fractional Chern insulators in ideal C = 1 bands, these models pave the way for investigating exotic topological phases in higher Chern bands for which no Landau level analog is available.   

The GW approximation in magic-angle twisted bilayer graphene

A generalized form of ferromagnetism in which spin is replaced by spin×valley flavor degrees of freedom is a prominent part of the physics of magic-angle twisted bilayer graphene (MATBG). The MATBG flat band octet consists of a single valence band and a single conduction band for four different flavors.  We report on a semi-quantitative theory of flavor ferromagnetism in MATBG based on a realistic band structure model and a one-shot GW approximation for the dependence of the exchange-correlation energy on flavor-dependent filling factors ν∈(-1,1).  We find that the exchange-correlation energy tends to be minimized when ν_f is close to zero for as many flavors as possible, explaining the cascade flavor-symmetry-breaking pattern identified experimentally, and that the correlation energy favors metallic states over insulating states.   

Imaging broken inversion symmetry state in magic angle twisted bilayer graphene.

Magic angle twisted bilayer graphene has been realized as a new platform to study strongly correlated quantum states of matter such as superconductors, correlated insulators and topological orders hosted by its native flat bands. Recent observations of anomalous Hall effect in MATBG revealed a non-zero Berry-curvature-induced orbital ferromagnetism and has been followed by extensive experimental and theoretical studies of its origin  [1,2]. Initial electronic transport works demonstrated anomalous Hall effect at ν=+3 electrons per moiré unit cell in the samples aligned with the adjacent insulating hBN layer, which breaks MATBG moiré inversion symmetry thus assisting in opening non-trivial insulating gaps with finite Chern numbers. Here we report on photovoltage scanning near-field imaging at cryogenic temperatures (10 K) of a MATBG device structurally aligned with hBN layer. We reveal a complex pattern of the quasi-local photothermoelectric effect (PTE) fringes attributed to the second-order superlattice (supermoiré) potential variation through the sample bulk. We assume that predominantly the photocurrent originates from PTE induced by the proximity of a hot spot formed on the metallic atomic force microscopy tip radiated by mid-infrared photons. Strikingly, we find a clear change of the PTE fringe real-space orientation when the sample doping changes between the valence and conductance flat bands which may signal a detection of a nematic ordered state in a highly doping-dependent low-energy spectrum of MATBG. Our observation sheds a new light on the microscopic mechanisms of the inversion symmetry breaking on a mesoscale length.

[1]  M. Serlin, et. al. Intrinsic Quantized Anomalous Hall Effect in a Moiré Heterostructure, Science 367, 900 (2020).

[2]  A. Sharpe, et. al. Emergent Ferromagnetism near Three-Quarters Filling in Twisted Bilayer Graphene, Science 365, 605 (2019).   

Four Flat Bands in Twisted Bilayer Graphene with an alternative magnetic field

The Moiré energy flat bands in twisted bilayer graphene serve as a fruitful playground for strong correlations and topological phases. We introduce a magnetic field that spatially alternates directions in the graphene layers so that the Dirac cones possess additional magnetic phases. By properly adjusting the phase and the twisted angle, in this twisted bilayer system, the energy spectrum for each valley can form FOUR moiré flat bands. In contrast, the conventional twisted bilayer graphene has only TWO moiré energy flat bands at magic angles. The doubled number of the flat bands in this magnetic platform might bring more rich correlation physics.   

Proximity Induced Density Wave and Long-range Coulomb Correlation in twisted trilayer graphene

The realization of Magic Angle Twisted Trilayer Graphene (MATTG) offers a new platform for studying strongly correlated, highly-tunable, two-dimensional electrons. In this work, we explore the influence of graphene/tungsten diselenide interface on the band structure and quantum ground state of twisted trilayer graphene. We show that flavor symmetry breaking and the associated Fermi surface reconstruction are absent due to the tTLG/WSe2 interface. Instead, the ground state is dominated by an abundance of density waves appearing at every half and quarter moire band filling, in both the Moire flat band and the remote energy band. The density wave instability likely arises from the dominance of long-range Coulomb interaction. We will also examine the temperature and magnetic field dependence in order to characterize properties of the sub-energy band associated with density wave states.