C. de Morais Smith

Topological phases in a two-dmensional lattice: Magnetic field versus spin-orbit coupling

In this work, we explore the rich variety of two-dimensional topological phases that arise when considering the competing effects of spin-orbit couplings, Zeeman splitting, and uniform magnetic fields. We investigate minimal models, defined on a honeycomb lattice, which clarify the topological phases stemming from the intrinsic and Rashba spin-orbit couplings, and also from the Zeeman splitting. In this sense, our work provides an interesting path connecting the quantum Hall phases, generally produced by the uniform magnetic field, and the quantum spin Hall phases resulting from spin-dependent couplings. First, we analyze the properties of each coupling term individually and we point out their similarities and differences. Second, we investigate the subtle competitions that arise when these effects are combined. We finally explore the various possible experimental realizations of our model.

Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices

For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structure of several Dirac systems. In our model, the spin is conserved, which allows us to analyze the spin Chern numbers. We show that in the Lieb, kagome, and T3 lattices, variation of the amplitude of the real next-nearest-neighbor hopping term drives interesting topological phase transitions. These transitions may be experimentally realized in optical lattices under shaking, when the ratio between the nearest- and next-nearest-neighbor hopping parameters can be tuned to any possible value. Finally, we show that in the honeycomb lattice, next-nearest-neighbor hopping only drives topological phase transitions in the presence of a magnetic field, leading to the conjecture that these transitions can only occur in multigap systems.

Reentrant topological phases in Mn-doped HgTe quantum wells

Quantum wells of HgTe doped with Mn display the quantum anomalous Hall effect due to the magnetic moments of the Mn ions. In the presence of a magnetic field, these magnetic moments induce an effective nonlinear Zeeman effect, causing a nonmonotonic bending of the Landau levels. As a consequence, the quantized (spin) Hall conductivity exhibits a reentrant behavior as one increases the magnetic field. Here, we will discuss the appearance of different types of reentrant behavior as a function of Mn concentration, well thickness, and temperature, based on the qualitative form of the Landau-level spectrum in an effective four-band model.

Merging and alignment of Dirac points in a shaken honeycomb optical lattice

Inspired by the recent creation of a honeycomb optical lattice and the realization of a Mott-insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, Floquet theory may be applied to derive a time-independent Hamiltonian. In this effective description, the hopping parameters are renormalized by a Bessel function, which depends on the shaking direction, amplitude, and frequency. Consequently, the hopping parameters can vanish and even change sign, in an anisotropic manner, thus yielding different band structures. Here, we study the merging and the alignment of Dirac points and dimensional crossovers from the two-dimensional system to one-dimensional chains and zero-dimensional dimers. We also consider next-nearest-neighbor hopping, which breaks the particle-hole symmetry and leads to a metallic phase when it becomes dominant over the nearest-neighbor hopping. Furthermore, we include weak repulsive on-site interactions and find the density profiles for different values of the hopping parameters and interactions, both in a homogeneous system and in the presence of a trapping potential. Our results may be experimentally observed by use of momentum-resolved Raman spectroscopy.

Current-driven and field-driven domain walls at nonzero temperature

We present a model for the dynamics of current-driven and field-driven domain-wall lines at nonzero temperature. We compute thermally averaged drift velocities from the Fokker-Planck equation that describes the nonzero-temperature dynamics of the domain wall. As special limits of this general description, we describe rigid domain walls as well as vortex domain walls. In these limits, we also determine depinning times of the domain wall from an extrinsic pinning potential. We compare our theory with previous theoretical and experimental works.

Ferromagnetism in ABC-stacked trilayer graphene

In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electronelectroninteraction ganddopinglevel n,wedeterminewhetherthetotalenergyisminimizedforaparamagneticor ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in ABC-stacked trilayer graphene is more robust than in monolayer, in bilayer, and in ABA-stacked trilayer graphene. Although the screening reduces the ferromagnetic regime in ABC-stackedtrilayergraphene,thecriticaldopinglevelremainsoneorderofmagnitudelargerthaninunscreened bilayer graphene.

Spin-density-wave instability in graphene doped near the van Hove singularity

We study the instability of the metallic state toward the formation of a different ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and the spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value Uc(T), which depends on the temperature T, even if there are small variations in the doping. Our results can be verified by angle-resolved photoemission spectroscopy or neutron scattering experiments in highly doped graphene

Thermodynamic signatures of edge states in topological insulators

Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic description has been lacking. The challenge arises because in conventional thermodynamics the potentials are required to scale linearly with extensive variables like volume, which does not allow for a general treatment of boundary effects. In this paper, we overcome this challenge with Hill thermodynamics. In this extension of the thermodynamic formalism, the grand potential is split into an extensive, conventional contribution, and the subdivision potential, which is the central construct of Hills theory. For topologically non-trivial electronic matter, the subdivision potential captures measurable contributions to the density of states and the heat capacity: it is the thermodynamic manifestation of the topological edge structure. Furthermore, the subdivision potential reveals phase transitions of the edge even when they are not manifested in the bulk, thus opening a variety of new possibilities for investigating, manipulating, and characterizing topological quantum matter solely in terms of equilibrium boundary physics.

Supersolid phases of dipolar bosons in optical lattices with a staggered flux

We present the theoretical mean-field zero-temperature phase diagram of a Bose-Einstein condensate (BEC) with dipolar interactions loaded into an optical lattice with a staggered flux. Apart from uniform superfluid, checkerboard supersolid, and striped supersolid phases, we identify several supersolid phases with staggered vortices, which can be seen as combinations of supersolid phases found in earlier work on dipolar BECs and a staggered-vortex phase found for bosons in optical lattices with staggered flux. By allowing for different phases and densities on each of the four sites of the elementary plaquette, more complex phase patterns are found.

Spin and band ferromagnetism in trilayer graphene

We study the ground-state properties of an ABA-stacked trilayer graphene. The low-energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersion, reminiscent of monolayer and bilayer graphene, respectively. The multiband structure offers more channels for instability toward ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a subband-index 1/2 degree of freedom to the bands (parabolic and linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin- and band-ferromagnetic instabilities as a function of doping and interaction strength