In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here show solid state systems this classification is incomplete find several additional types of crystal symmetry-protected free fermionic excitations . We exhaustively classify linear quadratic 3-, 6- 8- band crossings stabilized by space group symmetries with spin-orbit coupling time-reversal symmetry. Several distinct arise, differentiated their degeneracies at along high symmetry points,...

The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed Zak several decades ago for spinless systems with without time-reversal his theory "elementary" representations. In Nature 547, 298-305 (2017), we introduced the generalization this to experimentally relevant situation spin-orbit coupled symmetry proved that all bands do not transform as representations are topological. Here, give full details...

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the Fermi arcs in are topological consequences of points themselves, not directly related to bulk points, raising question whether there exists a bulk-boundary correspondence for semimetals. In this work, we discover that strong fragile 1D higher-order hinge (HOFAs) as universal, direct their 3D points. To predict HOFAs coexisting with states solid-state semimetals, introduce layer spinful model an...

We show that bilayer graphene in the presence of a 2D superlattice potential provides highly tunable setup can realize variety flat band phenomena. focus on two regimes: (i) topological bands with nonzero Chern numbers, C, including higher numbers |C|>1 and (ii) an unprecedented phase consisting stack nearly perfect C=0. For realistic values periodicity, this span 100 meV, encompassing all low-energy spectrum. further regime, has favorable geometry for realizing fractional insulator (FCI)...

The effect of applied pressure on fractional Chern insulators (FCIs) in moir\'e TMDs is numerically studied, indicating that can enhance the many-body gap these topologically ordered phases. This supported by showing that, within region stability FCI, quantum geometry topmost flat band almost satisfies ideal condition.

We propose heterostructures that realize first and second order topological superconductivity with vanishing net magnetization by utilizing altermagnetism. Such platforms may offer a significant improvement over conventional uniform since the latter suppresses superconducting gap. introduce 1D semiconductor-superconductor structure in proximity to an altermagnet realizes end Majorana zero modes (MZMs) magnetization. Additionally, coexisting Zeeman term provides tuning knob distinguish...

Quantum geometry plays a pivotal role in the second-order response of PT-symmetric antiferromagnets. Here we study nonlinear 2D altermagnets protected by C_{n}T symmetry and show that their leading is third order. Furthermore, contributions from quantum metric Berry curvature enter separately: longitudinal for all planar only has contribution quadrupole (QMQ), while transverse responses general have both (BCQ) QMQ. We well-known example d-wave Hall dominated BCQ. Both are strongly dependent...

Two-dimensional materials subject to long-wavelength modulations have emerged as novel platforms study topological and correlated quantum phases. In this article, we develop a versatile computationally inexpensive method predict the properties of subjected superlattice potential by combining degenerate perturbation theory with symmetry indicators. absence electronic interactions, our analysis provides systematic rule find Chern number superlattice-induced miniband starting from harmonics...

Elementary band representations are the fundamental building blocks of atomic limit structures. They have defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples—one each in a symmorphic nonsymmorphic space group—of elementary realized with an energy gap. In doing so, explicitly construct counterexample to claim by Michel Zak single-valued groups time-reversal symmetry connected. For example, topological invariant demonstrate valence bands...

In this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these may be "fragile" respect to addition of extra bands, their properties are manifest certain nontrivial holonomies (Wilson loops) space bands. introduce an eigenvalue index for fragile topology, and how a value manifests as winding hexagonal Wilson loop; remains true even absence time-reversal or sixfold rotational symmetry....

Weyl fermions can be created in materials with both time reversal and inversion symmetry by applying a magnetic field, as evidenced recent measurements of anomalous negative magnetoresistance. Here, we do thorough analysis the points these materials: enforcing crystal symmetries, classify location monopole charges fields aligned high-symmetry axes. The applies generally to band $T_d$, $D_{4h}$ $D_{6h}$ point groups. For $T_d$ group, find that nodes persist for all directions field. Further,...

The same bulk two-dimensional topological phase can have multiple distinct, fully chiral edge phases. We show that this occur in the integer quantum Hall states at $\ensuremath{\nu}=8$ and 12, with experimentally testable consequences. Abelian fractional as well, simplest examples being $\ensuremath{\nu}=\frac{8}{7},\frac{12}{11},\frac{8}{15},\frac{16}{5}$. give a general criterion for existence of distinct phases discuss experimental Edge correspond to lattices while genera lattices. Since...

A new section of databases and programs devoted to double crystallographic groups (point space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The are required study physical systems whose Hamiltonian includes spin-dependent terms. In symmetry analysis such systems, instead irreducible representations groups, it is necessary consider single- double-valued groups. operations (DGENPOS) space) (REPRESENTATIONS DPG REPRESENTATIONS DSG). tool...

Topological phases of noninteracting particles are distinguished by the global properties their band structure and eigenfunctions in momentum space. On other hand, group theory as conventionally applied to solid-state physics focuses only on that local (at high-symmetry points, lines, planes) Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268] mapped problem constructing structures out data a graph...

Twisted bilayer transition metal dichalcogenides have emerged as important model systems for the investigation of correlated electron physics because their interaction strength, carrier concentration, band structure, and inversion symmetry breaking are controllable by device fabrication, twist angle, most importantly, gate voltage, which can be varied in situ. The low energy some these materials has been shown to described a "moir\'e Hubbard model" generalized from usual addition strong,...

Exotic topology on the surface Analyzing spatial symmetries of three-dimensional (3D) crystal structures has led to discovery exotic types quasiparticles and topologically nontrivial materials. Wieder et al. focus symmetry groups 2D surfaces 3D materials—the so-called wallpaper groups—and find that some them allow for an additional topological class. This class hosts a single fourfold-degenerate Dirac fermion material and, basis authors' calculations, is expected occur in compound Sr 2 Pb 3...

A quantitative description of the excited electronic states point defects and impurities is crucial for understanding materials properties, possible applications in quantum technologies. This a considerable challenge computational methods, since Kohn-Sham density-functional theory (DFT) inherently ground state theory, while higher-level methods are often too computationally expensive defect systems. Recently, embedding approaches have been applied that treat with many-body using DFT to...

We theoretically study the interplay between magnetism and a heavy Fermi liquid in AB stacked transition metal dichalcogenide bilayer system MoTe$_2$/WSe$_2$ regime which Mo layer supports localized magnetic moments coupled by interlayer electron tunnelling to weakly correlated band of itinerant electrons W layer. show that transfer leads chiral Kondo exchange, with consequences including strong dependence temperature on carrier concentration, topological hybridization gap an anomalous Hall...

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state the topmost valence moir\'e band. The effective attraction between charge carriers is generated by electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tuanble strength, which be large. Together with low carrier densities reachable gating, this robust enables access to long-sought BEC-BCS transition....

The topological classification of electronic band structures is based on symmetry properties Bloch eigenstates single-particle Hamiltonians. In parallel, field theory has opened the doors to formulation and characterization non-trivial phases matter driven by strong electron-electron interaction. Even though important examples Mott insulators have been constructed, relevance underlying non-interacting topology physics phase remained unexplored. Here, we show that momentum structure Green's...

Superlattice potential modulation can produce flat minibands in Bernal-stacked bilayer graphene.In this work we study how band topology and interaction-induced symmetry-broken phases system are controlled by tuning the displacement field shape strength of superlattice potential.We use an analytic perturbative analysis to demonstrate that topological bands favored a honeycomb-lattice-shaped potential, numerics show robustness depends on both periodicity potential.At integer fillings bands,...

Shorter time-to-antibiotics improves survival from sepsis, particularly among patients in shock. There may be other subgroups for whom faster antibiotics are beneficial.