We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in table1, we conclude that long-range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions. The possibility of a universal description of the Dirac materials based on these features is also mentioned.

We study a tight-binding model on the honeycomb lattice of chiral d-wave superconductivity that breaks time-reversal symmetry. Because of its nontrivial sublattice structure, we show that it is possible to construct a gauge-invariant time-reversal-odd bilinear of the pairing potential. The existence of this bilinear reflects the sublattice polarization of the pairing state. We show that it generates persistent loop current correlations around each lattice site and opens a topological mass gap at the Dirac points, resembling Haldane's model of the anomalous quantum Hall effect. In addition to the usual chiral d-wave edge states, there also exist electronlike edge resonances due to the topological mass gap. We show that the presence of loop-current correlations directly leads to a nonzero intrinsic ac Hall conductivity, which produces the polar Kerr effect without an external magnetic field. Similar results also hold for the nearest-neighbor chiral p-wave pairing. We briefly discuss the relevance of our results to superconductivity in twisted bilayer graphene.

Hexagonal boron nitride is an ideal dielectric to form two-dimensional heterostructures due to the fact that it can be exfoliated to be just a few atoms thick and its very low density of defects. By placing graphene nanoribbons on high quality hexagonal boron nitride it is possible to create ideal quasi-one-dimensional systems with very high mobility. The availability of high quality one-dimensional electronic systems is of great interest also given that when in proximity to a superconductor they can be effectively engineered to realize Majorana bound states. In this work we study how a boron nitride substrate affects the electronic properties of graphene nanoribbons. We consider both armchair and zigzag nanoribbons. Our results show that for some stacking configurations the boron nitride can significantly affect the electronic structure of the ribbons. In particular, for zigzag nanoribbons, due to the lock between spin and sublattice degree of freedom at the edges, the hexagonal boron nitride can induce a very strong spin splitting of the spin-polarized, edge states. We find that such spin splitting can be as high as 40 meV.

Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting gapped phases of fermions is necessarily accompanied by the closing of the band gap as long as the symmetries of the system are maintained. We show that such a quantum phase transition is possible without closing the gap in the case of a three-dimensional topological band insulator. We demonstrate this by calculating the free energy of the minimal model for a topological insulator, the Bernevig-Hughes-Zhang model, and show that as the band curvature continuously varies, a jump between the band-gap minima corresponding to the topologically trivial and nontrivial insulators occurs. Therefore, this first-order phase transition is a generic feature of three-dimensional topological band insulators. For a certain parameter range we predict a reentrant topological phase transition. We discuss our findings in connection with the recent experimental observation of a discontinuous topological phase transition in a family of topological crystalline insulators.

Previously, graphene nanoribbons set in lateral heterostructures with hexagonal boron nitride were predicted to support topologically protected states at low energy. We investigate how robust the transport properties of these states are against lattice disorder. We find that forms of disorder that do not couple the two valleys of the zigzag graphene nanoribbon do not impact the transport properties at low bias, indicating that these lateral heterostructures are very promising candidates for chip-scale conducting interconnects. Forms of disorder that do couple the two valleys, such as vacancies in the graphene ribbon, or substantial inclusions of armchair edges at the graphene-hexagonal boron nitride interface will negatively affect the transport. However, these forms of disorder are not commonly seen in current experiments.

We theoretically predict that a true bilayer exciton condensate, characterized by off-diagonal long-range order and global phase coherence, can be created in one-dimensional solid state electron systems. The mechanism by which this happens is to introduce a single particle hybridization of electron and hole populations, which locks the phase of the relevant mode and hence invalidates the Mermin-Wagner theorem. Electron-hole interactions then amplify this tendency towards off-diagonal long-range order, enhancing the condensate properties by more than an order of magnitude over the noninteracting limit. We show that the temperatures below which a substantial condensate fraction would form could reach hundreds of Kelvin, a benefit of the weak screening in one-dimensional systems.

A longstanding mystery in understanding cuprate superconductors is the inconsistency between the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we reconcile the two experimental techniques by generalising a theory which was previously applied to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic superconductors. We show that the side peaks observed in tunneling conductance measurements in all these materials have a universal origin: They are formed by coherence-mediated tunneling under bias and do not directly reflect the underlying density of states (DOS) of the sample. We obtain theoretical predictions of the tunneling conductance and the density of states of the sample simultaneously and show that for cuprate and pnictide superconductors, the extracted sample DOS is consistent with the superconducting gap measured by ARPES.

Despite the now vast body of two-dimensional materials under study, bilayer graphene remains unique in two ways: it hosts a simultaneously tunable band gap and electron density; and stems from simple fabrication methods. These two advantages underscore why bilayer graphene is critical as a material for optoelectronic applications. In the work that follows, we calculate the one-and two-photon absorption coefficients for degenerate interband absorption in a graphene bilayer hosting an asymmetry gap and adjustable chemical potential-all at finite temperature. Our analysis is comprehensive, characterizing one-and two-photon absorptive behavior over wide ranges of photon energy, gap, chemical potential, and thermal broadening. The two-photon absorption coefficient for bilayer graphene displays a rich structure as a function of photon energy and band gap due to the existence of multiple absorption pathways and the nontrivial dispersion of the low energy bands. This systematic work will prove integral to the design of bilayer-graphene-based nonlinear optical devices.

We calculate the energy spectrum of a Dirac double layer, where each layer has the Dirac electronic dispersion, in the presence of a tilted magnetic field and small interlayer tunneling. We show that the energy splitting between the Landau levels has an oscillatory dependence on the in-plane magnetic field and vanishes at a series of special tilt angles of the magnetic field. Using a semiclassical analysis, we show that these special tilt angles are determined by the Berry phase of the Dirac Hamiltonian. The interlayer tunneling conductance also exhibits an oscillatory dependence on the magnetic field tilt angle, known as the angular magnetoresistance oscillations (AMRO). Our results are applicable to graphene double layers and thin films of topological insulators.

We show theoretically that excitons can form from spatially separated one-dimensional ground state populations of electrons and holes, and that the resulting excitons can form a quasicondensate. We describe a mean-field Bardeen-Cooper-Schrieffer theory in the low carrier density regime and then focus on the core-shell nanowire giving estimates of the size of the excitonic gap for InAs/GaSb wires and as a function of all the experimentally relevant parameters. We find that optimal conditions for pairing include small overlap of the electron and hole bands, large effective mass of the carriers, and low dielectric constant of the surrounding media. Therefore, one-dimensional systems provide an attractive platform for the experimental detection of excitonic quasicondensation in zero magnetic field.