Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two-dimensional material, enhance electron correlations, and give rise to novel condensed-matter phases such as
superconductors, Mott insulators, Wigner crystals and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different graphene layers. In this work, we propose a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates. We take gaphene/SiC heterostructure as a role model and demonstrate experimentally the substrate modulation leads to Dirac fermion cloning and consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Our theoretical modeling captures the cloning mechanism of Dirac states and indicates that flat bands can emerge at certain magic lattice constants of substrate when the period of modulation becomes nearly commensurate with the $(sqrt{3}timessqrt{3})R30^{circ}$ supercell of graphene. The results show that the epitaxial monolayer graphene is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.
Abrikosov vortices in Fe-based superconductors are a promising platform for hosting Majorana zero modes. Their adiabatic exchange is a key ingredient for Majorana-based quantum computing. However, the adiabatic braiding process can not be realized in
state-of-the-art experiments. We propose to replace the infinitely slow, long-path braiding by only slightly moving vortices in a special geometry without actually physically exchanging the Majoranas, like a Majorana carousel. Although the resulting finite-time gate is not topologically protected, it is robust against variations in material specific parameters and in the braiding-speed. We prove this analytically. Our results carry over to Y-junctions of Majorana wires.
Topological nodal line semimetals host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this paper, we use the Jones polynomial as a general topological invariant to capture the global knot topology o
f the nodal lines. We show that every possible change in Jones polynomial is attributed to the local evolutions around every point where two nodal lines touch. As an application of our theory, we show that nodal chain semimetals with four touching points can evolve to a Hopf-link. We extend our theory to 3D non-Hermitian multi-band exceptional line semimetals.
A vortex in an s-wave superconductor with a surface Dirac cone can trap a Majorana bound state with zero energy leading to a zero-bias peak (ZBP) of tunneling conductance. The iron-based superconductor FeTe$_x$Se$_{1-x}$ is one of the material candid
ates hosting these Majorana vortex modes. It has been observed by recent scanning tunneling spectroscopy measurement that the fraction of vortex cores possessing ZBPs decreases with increasing magnetic field on the surface of this iron-based superconductor. We construct a three-dimensional tight-binding model simulating the physics of over a hundred Majorana vortex modes in FeTe$_x$Se$_{1-x}$ with realistic physical parameters. Our simulation shows that the Majorana hybridization and disordered vortex distribution can explain the decreasing fraction of the ZBPs observed in the experiment. Furthermore, we find the statistics of the energy peaks off zero energy in our simulation with the Majorana physics in agreement with the analyzed peak statistics in the vortex cores from the experiment. This agreement and the explanation of the decreasing ZBP fraction lead to an important indication of scalable Majorana vortex modes in the iron-based superconductor. Thus, FeTe$_x$Se$_{1-x}$ can be one promising platform possessing scalable Majorana qubits for quantum computing. In addition, we further show the interplay of the ZBP presence and the vortex locations qualitatively agrees with our additional experimental observation and predict the universal spin signature of the hybridized multiple Majorana vortex modes.
Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states and unusual
magneto-transport properties. In this paper, we present a complete classification of all possible nonsymmorphic band degeneracies in hexagonal materials with strong spin-orbit coupling. This includes (i) band crossings protected by conventional nonsymmorphic symmetries, whose partial translation is within the invariant space of the mirror/rotation symmetry; and (ii) band crossings protected by off-centered mirror/rotation symmetries, whose partial translation is orthogonal to the invariant space. Our analysis is based on (i) the algebraic relations obeyed by the symmetry operators and (ii) the compatibility relations between irreducible representations at different high-symmetry points of the Brillouin zone. We identify a number of existing materials where these nonsymmorphic nodal lines are realized. Based on these example materials, we examine the surface states that are associated with the topological band crossings. Implications for experiments and device applications are briefly discussed.
We study the properties of a family of anti-pervoskite materials, which are topological crystalline insulators with an insulating bulk but a conducting surface. Using ab-initio DFT calculations, we investigate the bulk and surface topology and show t
hat these materials exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. While type-I Dirac states give rise to closed circular Fermi surfaces, type-II Dirac surface states are characterized by open electron and hole pockets that touch each other. We find that the type-II Dirac states exhibit characteristic van-Hove singularities in their dispersion, which can serve as an experimental fingerprint. In addition, we study the response of the surface states to magnetic fields.
In an ordinary three-dimensional metal the Fermi surface forms a two-dimensional closed sheet separating the filled from the empty states. Topological semimetals, on the other hand, can exhibit protected one-dimensional Fermi lines or zero-dimensiona
l Fermi points, which arise due to an intricate interplay between symmetry and topology of the electronic wavefunctions. Here, we study how reflection symmetry, time-reversal symmetry, SU(2) spin-rotation symmetry, and inversion symmetry lead to the topological protection of line nodes in three-dimensional semi-metals. We obtain the crystalline invariants that guarantee the stability of the line nodes in the bulk and show that a quantized Berry phase leads to the appearance of protected surfaces states with a nearly flat dispersion. By deriving a relation between the crystalline invariants and the Berry phase, we establish a direct connection between the stability of the line nodes and the topological surface states. As a representative example of a topological semimetal with line nodes, we consider Ca$_3$P$_2$ and discuss the topological properties of its Fermi line in terms of a low-energy effective theory and a tight-binding model, derived from ab initio DFT calculations. Due to the bulk-boundary correspondence, Ca$_3$P$_2$ displays nearly dispersionless surface states, which take the shape of a drumhead. These surface states could potentially give rise to novel topological response phenomena and provide an avenue for exotic correlation physics at the surface.
Topological phases of matter that depend for their existence on interactions are fundamentally interesting and potentially useful as platforms for future quantum computers. Despite the multitude of theoretical proposals the only interaction-enabled t
opological phase experimentally observed is the fractional quantum Hall liquid. To help identify other systems that can give rise to such phases we present in this work a detailed study of the effect of interactions on Majorana zero modes bound to vortices in a superconducting surface of a 3D topological insulator. This system is of interest because, as was recently pointed out, it can be tuned into the regime of strong interactions. We start with a 0D system suggesting an experimental realization of the interaction-induced $mathbb{Z}_8$ ground state periodicity previously discussed by Fidkowski and Kitaev. We argue that the periodicity is experimentally observable using a tunnel probe. We then focus on interaction-enabled crystalline topological phases that can be built with the Majoranas in a vortex lattice in higher dimensions. In 1D we identify an interesting exactly solvable model which is related to a previously discussed one that exhibits an interaction-enabled topological phase. We study these models using analytical techniques, exact numerical diagonalization (ED) and density matrix renormalization group (DMRG). Our results confirm the existence of the interaction-enabled topological phase and clarify the nature of the quantum phase transition that leads to it. We finish with a discussion of models in dimensions 2 and 3 that produce similar interaction-enabled topological phases.
If superconductivity is induced in the metallic surface states of topological insulators via proximity, Majorana modes will be trapped on the vortex cores. The same effects hold for doped topological insulators which become bulk s-wave superconductor
s as long as the doping does not exceed a critical values $ mu^{pm}_c.$ It is this critical chemical potential at which the material forgets it arose from a band-inverted topological insulator; it loses its topological emph{imprint.} For the most common classes of topological insulators, which can be modeled with a minimal 4-band Dirac model the values of $mu^{pm}_c$ can be easily calculated, but for materials with more complicated electronic structures such as HgTe or ScPtBi the result is unknown. We show that due to the hybridization with an additional Kramers pair of topologically trivial bands the topological imprint of HgTe-like electronic structures (which includes the ternary Heusler compounds) can be widely extended for p-doping. As a practical consequence we consider the effects of such hybridization on the range of doping over which Majorana modes will be bound to vortices in superconducting topological insulators and show that the range is strongly extended for p-doping, and reduced for n-doping. This leaves open the possibility that other topological phenomena may be stabilized over a wider range of doping.
