Electrical linear-response theory in an arbitrary magnetic field: A new Fermi-surface formation

Baranger, Harold U.; Stone, A. Douglas

doi:10.1103/physrevb.40.8169

Cited by 471 publications

(451 citation statements)

References 75 publications

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“…1(d) is due to only the wave functions (or Green functions) at the Fermi energy (as T → 0), in accord with the general paradigms of the Landau's Fermi liquid theory where transport quantities are expected to be expressed as the Fermi-surface property. 34,51 We recall here that similar situation appears in charge transport in an external magnetic field where equilibrium (or persistent) current density, 34 or bond charge currents in the lattice formalism, 37,41 is non-zero even in unbiased devices (all leads at the same potential) in thermal equilibrium due to breaking of time-reversal invariance by the external magnetic field. However, such circulating or diamagnetic currents carried by the Fermi sea, which in Landauer-Keldysh formalism can be subtracted by separating the integration 37 in a fashion similar to our Eq.…”

Section: Spatial Distribution Of Local Spin Currents and Spin Denmentioning

confidence: 99%

“…However, when the applied bias is low, so that linear response zero-temperature quantum transport takes place through the sample [as determined by G(E F )], the exact profile of the internal potential becomes irrelevant. 34,49 …”

Section: Local Spin Density and Its Continuity Equationmentioning

confidence: 99%

“…34 In SO coupled systemsĵ acquires extra terms since the velocity operator i v = [r,Ĥ] is modified by the presence of SO terms in the Hamiltonian H. For example, for the effective mass Rashba Hamiltonian of a finite-size 2DEG structure (in the xy-plane)…”

Section: Bond Spin Currents In Multiterminal Nanostructures: Landamentioning

confidence: 99%

“…(51), do not contribute to the net charge transport (i.e., to the total charge current measured in experiments) through any cross section of the device. 34,37 Thus, early "Fermi sea" expressions for the linear response transport coefficients in, e.g., the quantum Hall effect theory 34 or in the anomalous Hall effect theory, 51 were eventually recast in terms of the Fermi surface determined quantities. Similarly, Fig.…”

Section: Spatial Distribution Of Local Spin Currents and Spin Denmentioning

confidence: 99%

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Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

2006

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We introduce the concept of bond spin current, which describes the spin transport between two sites of the lattice model of a multiterminal spin-orbit (SO) coupled semiconductor nanostructure, and express it in terms of the spin-dependent nonequilibrium (Landauer-Keldysh) Green functions of the device. This formalism is applied to obtain the spatial distribution of microscopic spin currents in clean phase-coherent two-dimensional electron gas with the Rashba-type of SO coupling attached to four external leads. Together with the corresponding profiles of the stationary spin density, such visualization of the phase-coherent spin flow allow us to resolve several key issues for the understanding of mechanisms which generate pure spin Hall currents in the transverse leads of ballistic devices due to the flow of unpolarized charge current through their longitudinal leads: (i) while bond spin currents are non-zero locally within the SO coupled region even in equilibrium (when all leads are at the same potential), the total spin current obtained by summing the bond spin currents over an arbitrary cross section is zero so that no spin can actually be transported by such equilibrium currents; (ii) when device is brought into nonequilibrium steady current state by external voltage difference applied between the longitudinal leads, only the wave functions (or Green functions) around the Fermi energy contribute to the total spin current through a given transverse cross section; (iii) the total spin Hall current is not conserved within the SO coupled region; however, it becomes conserved and physically well-defined quantity in the ideal leads where it is, furthermore, equal to the spin current obtained within the multiprobe Landauer-Büttiker scattering formalism. The local spin current profiles crucially depend on whether the sample is smaller or greater than the spin precession length, thereby demonstrating its essential role as the characteristic mesoscale for the spin Hall effect in ballistic multiterminal semiconductor nanostructures. Although static spin-independent disorder reduces the magnitude of the total spin current in the leads, the bond spin currents continue to flow through the whole diffusive 2DEG sample, without being localized as edge spin currents around any of its boundaries. Recent experimental observation of the spin Hall effect 1,2 opens new avenues for the understanding of fundamental role which spin-orbit (SO) couplings 3,4 can play in transport and equilibrium properties of semiconductor structures. While SO coupling effects are tiny relativistic corrections for particles moving through electric fields in vacuum, they can be enhanced in solids by several orders of magnitude due to the interplay of crystal symmetry and strong crystalline potential. 3,4 Furthermore, harnessing of spin currents induced by the spin Hall effect offers new possibilities for the envisioned all-electrical manipulation of spin for semiconductor spintronics applications 5 where electrical fields can access individual spins on s...

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Section: Spatial Distribution Of Local Spin Currents and Spin Denmentioning

confidence: 99%

Section: Local Spin Density and Its Continuity Equationmentioning

confidence: 99%

Section: Bond Spin Currents In Multiterminal Nanostructures: Landamentioning

confidence: 99%

Section: Spatial Distribution Of Local Spin Currents and Spin Denmentioning

confidence: 99%

See 2 more Smart Citations

Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

2006

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“…At the end points of these "ballistic intervals" (in particular, at the fixed end points of the sample), the electrons are equilibrated (thermalized). These points of local equilibrium are theoretical constructs which may be thought to be connected via thin ideal leads (flat potentials) to large ideal reservoirs in equilibrium, with chemical potentials equal to the quasi-Fermi level at the points [17]. The current flow in a ballistic interval is assumed to result from the injection of electrons at the end points and their transmission through the interval, in line with Landauer's view of conduction as a transmission phenomenon [18][19][20][21].…”

Section: A Basic Formulationmentioning

confidence: 99%

Generalized Drude model: unification of ballistic and diffusive electron transport

Lipperheide

Weis

Wille

2001

J. Phys.: Condens. Matter

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For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean free path and arbitrary shape of the conduction band edge profile. Universal formulas are obtained for the current-voltage characteristic in the nondegenerate case and for the zero-bias conductance in the degenerate case, which describe in a transparent manner the interplay of ballistic and diffusive transport. The semiclassical approach is adopted, but quantum corrections allowing for tunneling are included. Examples are considered, in particular the case of chains of grains in polycrystalline or microcrystalline semiconductors with grain size comparable to, or smaller than, the mean free path. Substantial deviations of the results of the unified model from those of the ballistic thermionic-emission model and of the drift-diffusion model are found. The formulation of the model is one-dimensional, but it is argued that its results should not differ substantially from those of a fully three-dimensional treatment. PACS number(s): 05.60.Cd,

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Enhanced Magnetoresistance

Zahn¹,

Mertig²

2007

Handbook of Magnetism and Advanced Magnetic Materials

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The phenomenon of giant magnetoresistance (GMR) found in metallic multilayers will be discussed as an example for enhanced magnetoresistance in artificially structured systems. Theoretical formalisms based on ideas of Boltzmann, Landauer, and Kubo are capable of describing the electronic transport in layered structures and have been sketched in this chapter. The microscopic origin of GMR, the coherent band structure of the system, and the scattering at defects and imperfections are discussed by means of ab initio calculations based on density‐functional theory (DFT). Trends for the spin asymmetry of scattering will be given in comparison with the resulting resistivities and GMR ratios for the standard systems of magnetoelectronics.

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Electrical linear-response theory in an arbitrary magnetic field: A new Fermi-surface formation

Cited by 471 publications

References 75 publications

Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

Generalized Drude model: unification of ballistic and diffusive electron transport

Enhanced Magnetoresistance

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