Magnetoelectric control of topological phases in graphene (original) (raw)
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A scheme to realize the quantum spin-valley Hall effect in monolayer graphene
Carbon, 2016
Quantum spin Hall effect was first predicted in graphene. However, the weak spin orbit interaction in graphene meant that the search for quantum spin Hall effect in graphene never fructified. In this work we show how to generate the quantum spin-valley Hall effect in graphene via quantum pumping by adiabatically modulating a magnetic impurity and an electrostatic potential in a monolayer of strained graphene. We see that not only exclusive spin polarized currents can be pumped in the two valleys in exactly opposite directions but one can have pure spin currents flowing in opposite directions in the two valleys, we call this novel phenomena the quantum spin-valley Hall effect. This means that the twin effects of quantum valley Hall and quantum spin Hall can both be probed simultaneously in the proposed device. This work will significantly advance the field of graphene spintronics, hitherto hobbled by the lack of spin-orbit interaction. We obviate the need for any spin orbit interaction and show how graphene can be manipulated to posses features exclusive to topological insulators.
Graphene-based heterojunction between two topological insulators
Arxiv preprint arXiv: …, 2012
Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. We study this phenomenon in graphene in presence of a strong perpendicular magnetic field on top of a spin-orbit (SO) induced QSH phase. We show that, below the SO gap, the QSH phase is virtually unaffected by the presence of the magnetic field. Above the SO gap, the QH phase is restored. An electrostatic gate placed on top of the system allows to create a QSH-QH junction which is characterized by the existence of a spin-polarized chiral state, propagating along the topological interface. We find that such a setup naturally provides an extremely sensitive spin-polarized current switch.
We study the electronic structures and topological properties of (M þ N)-layer twisted graphene systems. We consider the generic situation that N-layer graphene is placed on top of the other M-layer graphene and is twisted with respect to each other by an angle θ. In such twisted multilayer graphene systems, we find that there exist two low-energy flat bands for each valley emerging from the interface between the M layers and the N layers. These two low-energy bands in the twisted multilayer graphene system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities. In particular, when the stacking chiralities of the M layers and N layers are opposite, the total Chern number of the two low-energy bands for each valley equals AEðM þ N − 2Þ (per spin). If the stacking chiralities of the M layers and the N layers are the same, then the total Chern number of the two low-energy bands for each valley is AEðM − NÞ (per spin). The valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is lifted either externally by a weak magnetic field or internally by Coulomb interaction through spontaneous symmetry breaking. Such an orbital ferromagnetic state is characterized by chiral current loops circulating around the AA region of the moiré pattern, which can be experimentally detected.
Collective edge modes near the onset of a graphene quantum spin Hall state
Physical Review B, 2014
Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor ν = 0. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless and are smoothly connected to the helical edge modes of the FM state. Possible experimental consequences are discussed.
Competing topological phases in few-layer graphene
arXiv preprint arXiv: …, 2012
We investigate the effect of spin-orbit coupling on the band structure of graphene-based twodimensional Dirac fermion gases in the quantum Hall regime. Taking monolayer graphene as our first candidate, we show that a quantum phase transition between two distinct topological statesthe quantum Hall and the quantum spin Hall phases -can be driven by simply tuning the Fermi level with a gate voltage. This transition is characterized by the existence of a chiral spin-polarized edge state propagating along the interface separating the two topological phases. We then apply our analysis to the more difficult case of bilayer graphene. Unlike in monolayer graphene, spinorbit coupling by itself has indeed been predicted to be unsuccessful in driving bilayer graphene into a topological phase, due to the existence of an even number of pairs of spin-polarized edge states. While we show that this remains the case in the quantum Hall regime, we point out that by additionally breaking the layer inversion symmetry, a non-trivial quantum spin Hall phase can reemerge in bilayer graphene at low energy. We consider two different symmetry-breaking mechanisms: inducing spin-orbit coupling only in the upper layer, and applying a perpendicular electric field. In both cases, the presence at low energy of an odd number of pairs of edge states can be driven by an exchange field. The related situation in trilayer graphene is also discussed.
Proposal for the quantum spin-valley Hall effect in monolayer graphene
arXiv (Cornell University), 2016
Quantum spin Hall effect was first predicted in graphene. However, the weak spin orbit interaction in graphene meant that the search for quantum spin Hall effect in graphene never fructified. In this work we show how to generate the quantum spin-valley Hall effect in graphene via quantum pumping by adiabatically modulating a magnetic impurity and an electrostatic potential in a monolayer of strained graphene. We see that not only exclusive spin polarized currents can be pumped in the two valleys in exactly opposite directions but one can have pure spin currents flowing in opposite directions in the two valleys, we call this novel phenomena the quantum spin-valley Hall effect. This means that the twin effects of quantum valley Hall and quantum spin Hall can both be probed simultaneously in the proposed device.
Impurity states in the quantum spin Hall phase in graphene
Physical Review B, 2012
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.
Physical review letters, 2014
We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-Büttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by thallium islands, which eventually results in a minimum bulk conductivity ∼4e^{2}/h, insensitive to localization effects.
2019
The role of disorder, interactions and temperature on topological phases of matter is subtle and often presents dichotomic features. Understanding these effects is however essential to predict the topological properties and their stability in real-world materials. This is particularly relevant for 2D materials, where the low dimensionality typically enhances these effects. As an example of dichotomic behavior, topological phases are suppressed in the presence of strong local interactions [1], while some studies showed that interactions themselves could induce a topological phase on a trivial band [2,3]. The role of disorder is also subtle. For topological insulators with broken time-reversal symmetry, disorder effects localize every eigenstate except two bulk extended states that carry opposite topological numbers [4,5]. The merging of these states, for a sufficiently large disorder strength, is associated with the destruction of the topological phase. Interestingly, a disorder-induced transition into a new topologically nontrivial phase-the topological Anderson insulator-was also shown to be possible [6,7]. To unbiasedly characterize the interplay of all these ingredients we introduce a model system that combines the topological features of the Haldane model with an interaction term of the Falicov-Kimball type. The Haldane-Falicov-Kimball model can be seen as a limiting case of the Hubbard model on an hexagonal lattice, for which one of the spin species is infinitely massive and the other has the hopping matrix elements of the Haldane model. The ability to employ numerically exact methods, renders our model an excellent testbed to unveil the subtle and often contradictory role of interactions and disorder. Moreover, the model can be studied at finite temperatures, where the behavior of topological matter have been much less explored. By performing a careful numerical and analytic analysis, we obtain the phase diagram on the temperatureinteraction plane, displaying a rich set of phases. One of our main results is to show that the thermal fluctuations, that affect the spatial charge ordering, induce a temperature-driven topological phase transition into gapped and gapless topological insulators, present for a wide range of interaction strengths. We also find an insulating charge ordered state with gapless excitations where spectral regions of extended and localized states seem to coexist due to the long range nature of the interaction-induced disorder potential [8]. Recent technological advances in ultracold atoms in optical lattices, in particular, the ability of having fermionic systems with a large mass unbalance and the possibility of realizing topologically non-trivial band structures such as the one of the Haldane model, render this model easily realizable with current experimental setups.