Relation between the spin Hall conductivity and the spin Chern number for Dirac-like systems (original) (raw)
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Gauge potential formulations of the spin Hall effect in graphene
Physics Letters A, 2011
Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.
Physical Review B, 2007
For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z2 topological order and the spin Chern number proposed by Kane and Mele and by Sheng et al., respectively, in the quantum spin Hall effect. It turns out that a global gauge transformation connects different spin Chern numbers (even integers) modulo 4, which implies that the spin Chern number and the Z2 topological order yield the same classification. We present a method of computing spin Chern numbers and demonstrate it in single and double plane of graphene.
Charge and Spin Hall Conductivity in Metallic Graphene
Physical Review Letters, 2006
Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity σ SH xy. In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to σ SH xy values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.
Unified Model of Intrinsic Spin-Hall Effect in Spintronic, Optical, and Graphene Systems
Journal of the Physical Society of Japan, 2009
A semi-classical description of the intrinsic spin-Hall effect (SHE) is presented which is relevant for a wide class of systems. A heuristic model for the SHE is developed, starting with a fully quantum mechanical treatment, from which we construct an intuitive expression for the spin-Hall current and conductivity. Our method makes transparent the physical mechanism which drives the effect, and unifies the SHE across several spintronic and optical systems. Finally, we propose an analogous effect in bilayer graphene.
Physical Review B, 2009
We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account -the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.
U(1)×SU(2)gauge invariance leading to charge and spin conductivity of Dirac fermions in graphene
Physical Review B, 2013
Gauge symmetries have been identified in graphene and associated with specific physical properties. For instance, the U (1) gauge group is related to electrodynamics in (1 + 2)-dimensional [(1 + 2)D] space-time and non-Abelian gauge groups can describe curvature and torsion. Here we demonstrate that the Dirac Lagrangian for massless electrons near the Dirac points is also invariant under the group SU (2) related to local spin rotations, leading to the correct spin-orbit interactions and a rigorous definition for the spin-current density. Furthermore, we computed the charge and spin conductivity within the framework of Kubo linear response theory, using the algebra of relativistic Dirac spinors in (1 + 2)D space-time. The minimal value of electrical conductivity is predicted to be πq 2 /h, in agreement with typical experimental findings.
Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
Physical Review B, 2006
The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical potential and applied field which is caused by the fact that the quasiparticle excitations in graphene are Dirac-like. One of the most striking effects observed in graphene is the odd integer quantum Hall effect. We argue that it is caused by the anomalous properties of the Dirac quasiparticles from the lowest Landau level. Other quantities such as Hall angle and Nernst signal also exhibit rather unusual behavior, in particular when there is an excitonic gap in the spectrum of the Dirac quasiparticle excitations.
Spintronics and pseudospintronics in graphene and topological insulators
Nature Materials, 2012
The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topologicalinsulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analog of giant magnetoresistance in bilayer graphene.
2016
We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic singularity appears in the Hall conductivity when the frequency of the external field agrees with the width of the gap.
Optical Hall conductivity in bulk and nanostructured graphene beyond the Dirac approximation
Physical Review B, 2012
We present a perturbative method for calculating the optical Hall conductivity in a tight-binding framework based on the Kubo formalism. The method involves diagonalization only of the Hamiltonian in absence of the magnetic field, and thus avoids the computational problems usually arising due to the huge magnetic unit cells required to maintain translational invariance in presence of a Peierls phase. A recipe for applying the method to numerical calculations of the magneto-optical response is presented. We apply the formalism to the case of ordinary and gapped graphene in a next-nearest neighbour tight-binding model as well as graphene antidot lattices. In both case, we find unique signatures in the Hall response, that are not captured in continuum (Dirac) approximations. These include a non-zero optical Hall conductivity even when the chemical potential is at the Dirac point energy. Numerical results suggest that this effect should be measurable in experiments.