We study electronic ordering instabilities of twisted bilayer graphene with n = 2 electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find d/p-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at n = 2 and yields a single doubly-degenerate pocket upon doping to n > 2. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations. arXiv:1805.06449v2 [cond-mat.str-el]

Vortices in topological superconductors host Majorana zero modes (MZMs), which are proposed to be building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform for realizing MZM has been discovered in iron-based superconductors, without involving hybrid semiconductor-superconductor structures. Here we report on a detailed scanning tunneling spectroscopy study of a FeTe 0.55 Se 0.45 single crystal, revealing two distinct classes of vortices present in this system which differ by a half-integer level shift in the energy spectra of the vortex bound states. This level shift is directly tied with the presence or absence of zero-bias peak and also alters the ratios of higher energy levels from integer to half-odd-integer. Our model calculations fully reproduce the spectra of these two types of vortex bound states, suggesting the presence of topological and conventional superconducting regions that coexist within the same crystal. Our findings provide strong evidence for the topological nature of superconductivity in FeTe 0.55 Se 0.45 and establish it as an excellent platform for further studies on MZMs.Majorana zero modes (MZMs) are proposed to be building blocks of fault-tolerant topological quantum computation 1 due to their non-Abelian statistics. Several systems are predicted to host MZMs, such as intrinsic p-wave superconductors 2,3 , and multiple heterostructures combining strong spin-orbital coupling (SOC) and superconductivity 4-12 .Recently, a new single-material platform of iron-based superconductors (FeSC) has been discovered 13-15 , in which topological nontrivial bands and high-T c superconductivity coexist naturally 16 without the need of proximity effect common to other proposals. This has led to the observation of a pronounced zero-bias conductance peak (ZBCP) in vortices of FeTe 0.55 Se 0.45 17 and a related compound 18 .While a ZBCP that does not split across the vortex core is regarded as a strong indication of MZM and topological nature of the superconducting vortex 4,17-19 , the observation of ZBCP alone is not enough to prove it. Although several pieces of evidence including spatial profile, tunneling barrier dependence, magnetic field dependence and temperature evolution are fully consistent with MZM in FeTe 0.55 Se 0.45 17 , more convincing verification requires demonstration of the nontrivial topology of the superconducting vortex and underlying band structure. The single crystal of FeTe 0.55 Se 0.45 is a unique platform to demonstrate the fundamental distinction between the trivial and topological vortices. Its large ratio 17,20 of Δ /E F enables realization of the quantum limit 21 , where the low-lying quasiparticle bound states, the so-called Caroli-de Gennes-Matricon bound states (CBSs) 22 , become discrete levels observable separately within the hard superconducting gap. These bound states are the eigenstates of the vortex planar angular momentum 21-23 with the eigenvalue determined by topological phase of the host superconductor 4,24 . Even thou...

The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space. We introduce a new type of van Hove singularity in two dimensions, resulting from high-order saddle points and exhibiting power-law divergent density of states. We show that high-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. Correlation effects from high-order van Hove singularity near Fermi level are also discussed.

We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multivalley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group Z 8 . In particular, we explicitly construct a microscopic interaction Hamiltonian to gap eight flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of U (1) × Z 2 symmetry-protected topological phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between three-dimensional topological phases protected by spatial symmetries and two-dimensional topological phases protected by internal symmetries. The prediction and observation of topological crystalline insulators (TCIs) in the SnTe material class has expanded the scope of topological matter and gained wide interest [1][2][3][4][5]. These TCIs possess topological surface states that are protected by mirror symmetry of the rocksalt crystal and become gapped under symmetry-breaking structural distortions [6][7][8][9]. These surface states are predicted to exhibit a plethora of novel phenomena ranging from large quantum anomalous Hall conductance [1,10,11] to strain-induced pseudo-Landau levels and superconductivity [12], which are currently under intensive study [13][14][15].According to band theory, TCIs protected by mirror symmetry are classified by an integer topological invariant, the mirror Chern number [16]. However, recent theoretical breakthroughs [17][18][19][20][21][22][23][24] have found that the classifications of interacting systems are markedly different from noninteracting systems in various classes of topological insulators and superconductors protected by internal symmetries [25]. This raises the open question about the classification of interacting TCIs protected by spatial symmetries. On the experimental side, a growing body of interaction-driven phenomena has been found in existing TCI materials, including spontaneous surface structural transition and gap generation [6][7][8] and anomalous bulk band inversion [26]. Moreover, new TCI materials have been predicted in transition-metal oxides [27,28] and heavy fermion compounds [29,30], where strong electron interactions are expected.Motivated by these theoretical and experimental developments, in this work we study the effect of electron interactions in mirror-symmetric TCIs. Our main result is that interactions reduce the classification of three-dimensional (3D) TCIs from Z in the noninteracting case to Z 8 . We obtain this result by introducing a "domain wall" construction of interacting surface states of 3D TCIs, which exploits the nonlocal nature of mirror symmetry. This construction builds on interacting edge states of two-dimensional (2D) TCIs or U (1) × Z 2 symmetryprotected topological (SPT) phases, which...

No abstract