Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1305.3180

How to construct the proper gauge-invariant density matrix in steady-state nonequilibrium: Applications to spin-transfer and spin-orbit torques

Farzad Mahfouzi·Branislav K. Nikolic
View original source ↗Read source document ↗Export metadata ↓

Abstract

Experiments observing spin density and spin currents (responsible for, e.g., spin-transfer torque) in spintronic devices measure only the nonequilibrium contributions to these quantities, typically driven by injecting unpolarized charge current or by applying external time-dependent fields. On the other hand, theoretical approaches to calculate them operate with both the nonequilibrium (carried by electrons around the Fermi surface) and the equilibrium (carried by the Fermi sea electrons) contributions. Thus, an unambiguous procedure should remove the equilibrium contributions, thereby rendering the nonequilibrium ones which are measurable and satisfy the gauge-invariant condition according to which expectation values of physical quantities should not change when electric potential everywhere is shifted by a constant amount. Using the framework of nonequilibrium Green functions, we delineate such procedure which yields the proper gauge-invariant nonequilibrium density matrix in the linear-response and elastic transport regime for current-carrying steady state of an open quantum system connected to two macroscopic reservoirs. Its usage is illustrated by computing: (i) conventional spin-transfer torque (STT) in asymmetric F/I/F magnetic tunnel junctions (MTJs); (ii) unconventional STT in asymmetric N/I/F semi-MTJs with the strong Rashba spin-orbit coupling (SOC) at the I/F interface and injected current perpendicular to that plane; and (iii) current-driven spin density within a clean ferromagnetic Rashba spin-split two-dimensional electron gas (2DEG) which generates SO torque in laterally patterned N/F/I heterostructures when such 2DEG is located at the N/F interface and injected charge current flows parallel to the plane.

Explore related subjects

cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Farzad Mahfouzi, Branislav K. Nikolic. 2013-07-11. How to construct the proper gauge-invariant density matrix in steady-state nonequilibrium: Applications to spin-transfer and spin-orbit torques. https://doi.org/10.1142/s2010324713300028

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Gapped out-of-phase plasmon modes in alternating-twist multilayer graphene

We theoretically investigate the plasmon modes of alternating-twist multilayer graphene. In multilayer systems, interlayer coupling gives rise to distinctive plasmon modes, but calculations in moiré systems remain challenging due to their complex tunneling structures. Using the Kac-Murdock-Szegő Toeplitz formalism, we derive that the in-phase mode exhibits the conventional $\sqrt{q}$ behavior, while the out-of-phase modes acquire plasmon gaps determined by specific interband transitions between Dirac cones with different velocities in the long-wavelength limit. We demonstrate that these out-of-phase modes remain undamped in the weak Coulomb-interaction limit when the twist angle exceeds a critical value ($θ\gtrsim 2.75^\circ$ for the alternating-twist trilayer case), regardless of the carrier density as long as the low-energy effective Dirac Hamiltonian remains valid. Furthermore, we consider the effect of a perpendicular electric field, and demonstrate how plasmon modes can be tuned by a gate voltage.

cond-mat.mes-hall↗
arXiv2026

Optical properties of hydrogenated graphene superlattices

We investigate with first principles theoretical methods optical response accounting for excitonic effects of quasi-one dimensional monolithic arrays of graphene nanostripes -- two-dimensional graphene superlattices, where quasi-metallic and dielectric regions alternate by selective hydrogenation of graphene. It is shown that chemical engineering of the graphene surface can lead to strong and well-isolated absorption peaks in the far-infrared and possibly even terahertz frequencies. The band gap scaling suggests no excitonic insulators.

cond-mat.mes-hall↗
arXiv2026

Long-lived Laughlin pairs in a depleted quantum Hall edge channel

On-demand sources and mesoscopic beam splitters allow individual ballistic electrons to collide in depleted quantum Hall edge channels, where their unscreened Coulomb interaction acts as a strong, controllable nonlinearity. Theory suggests a more striking possibility: in a strong magnetic field, the same repulsion can drive quantized relative circulation, allowing two electrons to propagate together as a positive-energy Laughlin pair. The relevance of such pairs to experiment depends on lifetimes in realistic guiding potentials and on whether the proposed collision pathway to pair formation survives full two-dimensional dynamics. We develop a microscopic theory of quasibound Laughlin pairs using the physical two-electron Hamiltonian. For a general local electric-field gradient, we determine the dissociation threshold, number of quasibound states, and decay rates. Complex scaling and analytic tunneling theory show that lifetimes grow exponentially with pair energy above threshold. Applied to reported GaAs parameters, the theory indicates that existing devices may already support the lowest spin-polarized pair, with a lifetime estimate roughly two orders of magnitude longer than typical propagation times. We simulate a collision with the full finite-field Hamiltonian, providing both a framework for nonlinear two-electron quantum dynamics and evidence for Laughlin-pair formation in a representative two-electron collision. We use Husimi distributions and their zeros to visualize both quasibound resonances and transient collision states in phase space. These results place the preparation, propagation, and detection of repulsively paired electrons within reach of existing single-electron circuit technology. They identify kinematic stabilization under constrained one-dimensional propagation as a pairing mechanism that may extend to anyonic quantum Hall edge excitations.

cond-mat.mes-hall↗