Impurity states in the quantum spin Hall phase in graphene

Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.

Noncollinear magnetic phases and edge states in graphene quantum Hall bars

Application of a perpendicular magnetic field to charge neutral graphene is expected to result in a variety of broken symmetry phases, including antiferromagnetic, canted, and ferromagnetic. All these phases open a gap in bulk but have very different edge states and noncollinear spin order, recently confirmed experimentally. Here we provide an integrated description of both edge and bulk for the various magnetic phases of graphene Hall bars making use of a noncollinear mean field Hubbard model. Our calculations show that, at the edges, the three types of magnetic order are either enhanced (zigzag) or suppressed (armchair). Interestingly, we find that preformed local moments in zigzag edges interact with the quantum spin Hall like edge states of the ferromagnetic phase and can induce backscattering.

Single-exciton spectroscopy of single Mn doped InAs quantum dots

The optical spectroscopy of a single InAs quantum dot doped with a single Mn atom is studied using a model Hamiltonian that includes the exchange interactions between the spins of the quantum dot electron-hole pair, the Mn atom, and the acceptor hole. Our model permits linking the photoluminescence spectra to the Mn spin states after photon emission. We focus on the relation between the charge state of the Mn, A0 or A−, and the different spectra which result through either band-to-band or band-to-acceptor transitions. We consider both neutral and negatively charged dots. Our model is able to account for recent experimental results on single Mn doped InAs photoluminescence spectra and can be used to account for future experiments in GaAs quantum dots. Similarities and differences with the case of single Mn doped CdTe quantum dots are discussed.

Optical control of the spin state of two Mn atoms in a quantum dot

We report on the optical spectroscopy of the spin of two magnetic atoms (Mn) embedded in an individual quantum dot interacting with a single electron, a single exciton, or a single trion. As a result of their interaction to a common entity, the Mn spins become correlated. The dynamics of this process is probed by time-resolved spectroscopy, which permits us to determine an optical orientation time in the range of a few tens of nanoseconds. In addition, we show that the energy of the collective spin states of the two Mn atoms can be tuned through the optical Stark effect induced by a resonant laser field.

Electrical control of a single Mn atom in a quantum dot

We report on the reversible electrical control of the magnetic properties of a single Mn atom in an individual quantum dot. Our device permits us to prepare the dot in states with three different electric charges, 0, +1e, and -1e which result in dramatically different spin properties, as revealed by photoluminescence. Whereas in the neutral configuration the quantum dot is paramagnetic, the electron-doped dot spin states are spin rotationally invariant and the hole-doped dot spins states are quantized along the growth direction.

Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and backaction of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both reading and recording classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where a spin-polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom.

Exciton beats in GaAs quantum wells: bosonic representation and collective effects

We discuss light–heavy hole beats observed in transient optical experiments in GaAs quantum wells in terms of a free-boson coherent state model. This approach is compared with descriptions based on few-level representations. Results lead to an interpretation of the beats as due to classical electromagnetic interference. The boson picture correctly describes photon excitation of extended states and accounts for experiments involving coherent control of the exciton density and Rayleigh scattering beating.

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.

Mn-doped II-VI quantum dots: artificial molecular magnets

The notion of artificial atom relies on the capability to change the number of carriers one by one in semiconductor quantum dots, and the resulting changes in their electronic structure. Organic molecules with transition metal atoms that have a net magnetic moment and display hysteretic behaviour are known as single molecule magnets (SMM). The fabrication of CdTe quantum dots chemically doped with a controlled number of Mn atoms and with a number of carriers controlled either electrically or optically paves the way towards a new concept in nanomagnetism: the artificial single molecule magnet. Here we study the magnetic properties of a Mn-doped CdTe quantum dot for different charge states and show to what extent they behave like a single molecule magnet.

Quantum Hall effect in gapped graphene heterojunctions

We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, Δ1 and Δ2. We consider two main situations, Δ1=0,Δ2≠0, and Δ1=−Δ2. They are different in a fundamental aspect: only the latter features kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two-terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we quantify the robustness of kink states with respect to backscattering. Transport perpendicular to the boundary shows how interface states open a backscattering channel for the conducting edge states, spoiling the perfect conductance quantization featured by the homogeneously gapped graphene Hall bars. Our results can be relevant for the study of graphene deposited on hexagonal boron-nitride, as well as to model graphene with an interaction-driven gapped phase with two equivalent phases separated by a domain wall.

Consequences of Kondo exchange on quantum spins

When individual quantum spins are placed in close proximity to conducting substrates, the localized spin is coupled to the nearby itinerant conduction electrons via Kondo exchange. In the strong coupling limit this can result in the Kondo effect — the formation of a correlated, many body singlet state — and a resulting renormalization of the density of states near the Fermi energy. However, even when Kondo screening does not occur, Kondo exchange can give rise to a wide variety of other phenomena. In addition to the well known renormalization of the g factor and the finite spin decoherence and relaxation times, Kondo exchange has recently been found to give rise to a newly discovered effect: the renormalization of the single ion magnetic anisotropy. Here we put these apparently different phenomena on equal footing by treating the effect of Kondo exchange perturbatively. In this formalism, the central quantity is ρJ, the product of the density of states at the Fermi energy ρ and the Kondo exchange constant J. We show that perturbation theory correctly describes the experimentally observed exchange induced shifts of the single spin excitation energies, demonstrating that Kondo exchange can be used to tune the effective magnetic anisotropy of a single spin.

Quantum spin Hall phase in multilayer graphene

The so-called quantum spin Hall phase is a topologically nontrivial insulating phase that is predicted to appear in graphene and graphenelike systems. In this paper we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four-orbital tight-binding model that includes full atomic spin-orbit coupling and we calculate the Z2 topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all possible stackings, only those with an odd number of layers host gapless edge states while those with an even number of layers are trivial insulators. For heterostructures where graphene is encapsulated by trivial insulators, it turns out that interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.

Quantum anomalous Hall effect in graphene coupled to skyrmions

Skyrmions are topologically protected spin textures, characterized by a topological winding number N, that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a system that exhibits a two-dimensional skyrmion lattice. Here we show that a weak exchange coupling between the Dirac electrons in graphene and a two-dimensional skyrmion lattice withN = ±1 drives graphene into a quantum anomalous Hall phase, with a band gap in bulk, a Chern number C = 2N, and chiral edge states with perfect quantization of conductance G = 2N e2 h . Our findings imply that the topological properties of the skyrmion lattice can be imprinted in the Dirac electrons of graphene.

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.

Transport across two interacting quantum dots: Bulk Kondo, Kondo box, and molecular regimes

We analyze the transport properties of a double quantum dot device with both dots coupled to perfect conducting leads and to a finite chain of N noninteracting sites connecting both of them. The interdot chain strongly influences the transport across the system and the local density of states of the dots. We study the case of a small number of sites, so that Kondo box effects are present, varying the coupling between the dots and the chain. For odd N and small coupling between the interdot chain and the dots, a state with two coexisting Kondo regimes develops: the bulk Kondo due to the quantum dots connected to leads and the one produced by the screening of the quantum dot spins by the spin in the finite chain at the Fermi level. As the coupling to the interdot chain increases, there is a crossover to a molecular Kondo effect, due to the screening of the molecule (formed by the finite chain and the quantum dots) spin by the leads. For even N the two Kondo temperatures regime does not develop and the physics is dominated by the usual competition between Kondo and antiferromagnetism between the quantum dots. We finally study how the transport properties are affected as N is increased. For the study we used exact multiconfigurational Lanczos calculations and finite-U slave-boson mean-field theory at T=0. The results obtained with both methods describe qualitatively and also quantitatively the same physics.