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Register a new userGauge Potential Formulations of the Spin Hall Effect in Graphene
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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.
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We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator $H_0$ does not commute with the spin operator in view of Rashba interactions, as in the typical models for the Quantum Spin Hall effect. A gapped periodic one-particle Hamiltonian $H_0$ is perturbed by adding a constant electric field of intensity $varepsilon ll 1$ in the $j$-th direction, and the linear response in terms of a $S$-current in the $i$-th direction is computed, where $S$ is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (Unit Cell Consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper $S$-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic $S$-current as the trace per unit volume of the $S$-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models.
The formation of a superstructure - with a related Moire pattern - plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we put forward a novel, interdisciplinary approach to determine the Moire angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying Moire pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the near-infrared and visible ranges. By discovering the dependence of the frequency position of the maximal photonic spin Hall effect shift on the Moire angle, we argue that the latter could be unequivocally accessed via all-optical far-field measurements. We also disclose that, when combined with the Goos-Hanchen effect, the spin Hall effect of light enables the complete determination of the electronic conductivity of the bilayer. Altogether our findings demonstrate that sub-wavelength spin-orbit interactions of light provide a unprecedented toolset for investigating optoelectronic properties of multilayer two-dimensional van der Waals materials.
We discuss the quantum Hall effect on a single-layer graphene in the framework of noncommutative (NC) phase space. We find it induces a shift in the Hall resistivity. Furthermore, comparison with experimental data reveals an upper bound on the magnitude of the momentum NC parameter $eta$ in about $sqrt{eta}leq 2.5 , mathrm{eV}/c$.
In this letter, we investigate the anomalous Hall effect in dense QCD matter. When the dual chiral density wave which is the spatially modulated chiral condensate appears in the medium, it gives rise to two Weyl points to the single-particle energy-spectrum and then the anomalous Hall conductivity becomes nonzero. Then, dense QCD matter is analogous to the Weyl semimetal. The direct calculation of the Hall conductivity by way of Kubos linear response theory gives the term proportional to the distance between the Weyl points. Unlike the Weyl semimetal, there appears the additional contribution induced by axial anomaly.
We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square-lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field. We note connections to recent observations on the hole-doped cuprates: our theory captures the main trends, but the overall magnitude of the effect is smaller than that observed.
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