Tunable Superconductivity and Möbius Fermi Surfaces in an Inversion-Symmetric Twisted van der Waals Heterostructure.

We theoretically study a moiré superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows us to switch on or off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field D_{0} and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with D_{0}; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of D_{0}, the spin-orbit-induced spin textures exhibit vortices which lead to "Möbius fermi surfaces" in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the Γ point twice, making their Möbius nature directly observable. Further, we show that the superconducting order parameter inherits the unconventional, Möbius spin textures. Our findings suggest that this system provides a promising experimental avenue for systematically studying the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.

Orderly disorder in magic-angle twisted trilayer graphene.

Magic-angle twisted trilayer graphene (TTG) has recently emerged as a platform to engineer strongly correlated flat bands. We reveal the normal-state structural and electronic properties of TTG using low-temperature scanning tunneling microscopy at twist angles for which superconductivity has been observed. Real trilayer samples undergo a strong reconstruction of the moiré lattice, which locks layers into near-magic-angle, mirror symmetric domains comparable in size with the superconducting coherence length. This relaxation introduces an array of localized twist-angle faults, termed twistons and moiré solitons, whose electronic structure deviates strongly from the background regions, leading to a doping-dependent, spatially granular electronic landscape. The Fermi-level density of states is maximally uniform at dopings for which superconductivity has been observed in transport measurements.

Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene.

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a "mechanism" for superconductivity. We present a comprehensive listing of plausible low-temperature orders and the parent flavor symmetry-breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis.

Unsupervised Machine Learning and Band Topology.

The study of topological band structures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine learning, another rising topic of interest. Specifically, we introduce an unsupervised machine learning approach that searches for and retrieves paths of adiabatic deformations between Hamiltonians, thereby clustering them according to their topological properties. The algorithm is general, as it does not rely on a specific parametrization of the Hamiltonian and is readily applicable to any symmetry class. We demonstrate the approach using several different models in both one and two spatial dimensions and for different symmetry classes with and without crystalline symmetries. Accordingly, it is also shown how trivial and topological phases can be diagnosed upon comparing with a generally designated set of trivial atomic insulators.

Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order.

Fermi surface (FS) topology is a fundamental property of metals and superconductors. In electron-doped cuprate Nd2-x Ce x CuO4 (NCCO), an unexpected FS reconstruction has been observed in optimal- and overdoped regime (x = 0.15-0.17) by quantum oscillation measurements (QOM). This is all the more puzzling because neutron scattering suggests that the antiferromagnetic (AFM) long-range order, which is believed to reconstruct the FS, vanishes before x = 0.14. To reconcile the conflict, a widely discussed external magnetic-field-induced AFM long-range order in QOM explains the FS reconstruction as an extrinsic property. Here, we report angle-resolved photoemission (ARPES) evidence of FS reconstruction in optimal- and overdoped NCCO. The observed FSs are in quantitative agreement with QOM, suggesting an intrinsic FS reconstruction without field. This reconstructed FS, despite its importance as a basis to understand electron-doped cuprates, cannot be explained under the traditional scheme. Furthermore, the energy gap of the reconstruction decreases rapidly near x = 0.17 like an order parameter, echoing the quantum critical doping in transport. The totality of the data points to a mysterious order between x = 0.14 and 0.17, whose appearance favors the FS reconstruction and disappearance defines the quantum critical doping. A recent topological proposal provides an ansatz for its origin.

Designing Morphotropic Phase Composition in BiFeO3.

In classical morphotropic piezoelectric materials, rhombohedral and tetragonal phase variants can energetically compete to form a mixed phase regime with improved functional properties. While the discovery of morphotropic-like phases in multiferroic BiFeO3 films has broadened this definition, accessing these phase spaces is still typically accomplished through isovalent substitution or heteroepitaxial strain which do not allow for continuous modification of phase composition postsynthesis. Here, we show that it is possible to use low-energy helium implantation to tailor morphotropic phases of epitaxial BiFeO3 films postsynthesis in a continuous and iterative manner. Applying this strain doping approach to morphotropic films creates a new phase space based on internal and external lattice stress that can be seen as an analogue to temperature-composition phase diagrams of classical morphotropic ferroelectric systems.

Topological order in the pseudogap metal.

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

Intertwining Topological Order and Broken Symmetry in a Theory of Fluctuating Spin-Density Waves.

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the "antinodal" region of the square lattice Brillouin zone and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin-density wave mean field theory of the square lattice Hubbard model, and in a CP^{1} theory of spinons. This theory leads to metals with an antinodal gap and topological order which intertwines with the observed broken symmetries.

Dimensional crossover and cold-atom realization of topological Mott insulators.

Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.

Topological superconductivity and unconventional pairing in oxide interfaces.

Pinpointing the microscopic mechanism for superconductivity has proven to be one of the most outstanding challenges in the physics of correlated quantum matter. Thus far, the most direct evidence for an electronic pairing mechanism is the observation of a new symmetry of the order parameter, as done in the cuprate high-temperature superconductors. Alternatively, global, topological invariants allow for a sharp discrimination between states of matter that cannot be transformed into each other adiabatically. Here we propose an unconventional pairing state for the electron fluid in two-dimensional oxide interfaces and establish a direct link to the emergence of non-trivial topological invariants. Topological signatures, in particular Majorana edge states, can then be used to detect the microscopic origin of superconductivity. In addition, we show that also the density wave states that compete with superconductivity sensitively depend on the nature of the pairing interaction.