2008
Leurs, B. W. A.; Nazario, Z.; Santiago, D. I.; Zaanen, J.
Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances Tijdschriftartikel
In: ANNALS OF PHYSICS, vol. 323, nr. 4, pp. 907-945, 2008, ISSN: 0003-4916.
Abstract | Links | BibTeX | Tags: spin-orbit coupling; spintronics; non-Abelian flow; superfluidity; Aharonov-Casher effect
@article{WOS:000255216300008,
title = {Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled
substances},
author = {B. W. A. Leurs and Z. Nazario and D. I. Santiago and J. Zaanen},
doi = {10.1016/j.aop.2007.06.012},
issn = {0003-4916},
year = {2008},
date = {2008-04-01},
journal = {ANNALS OF PHYSICS},
volume = {323},
number = {4},
pages = {907-945},
publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE},
address = {525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA},
abstract = {Motivated by the heavy ion collision experiments there is much activity
in studying the hydrodynamical properties of non-Abelian (quark-gluon)
plasmas. A major question is how to deal with color currents. Although
not widely appreciated, quite similar issues arise in condensed matter
physics in the context of the transport of spins in the presence of
spin-orbit coupling. The key insight is that the Pauli Hamiltonian
governing the leading relativistic corrections in condensed matter
systems can be rewritten in a language of SU(2) covariant derivatives
where the role of the non-Abelian gauge fields is taken by the physical
electromagnetic fields: the Pauli system can be viewed as Yang-Mills
quantum-mechanics in a `fixed frame', and it can be viewed as an
`analogous system' for non-Abelian transport in the same spirit as
Volovik's identification of the He superfluids as analogies for quantum
fields in curved space time. We take a similar perspective as Jackiw and
coworkers in their recent study of non-Abelian hydrodynamics, twisting
the interpretation into the `fixed frame' context, to find out what this
means for spin transport in condensed matter systems. We present an
extension of Jackiw's scheme: non-Abelian hydrodynamical currents can be
factored in a `noncoherent' classical part, and a coherent part
requiring macroscopic non-Abelian quantum entanglement. Hereby it
becomes particularly manifest that non-Abelian fluid flow is a much
richer affair than familiar hydrodynamics, and this permits us to
classify the various spin transport phenomena in condensed matter
physics in an unifying framework. The ``particle based hydrodynamics''
of Jackiw et al. is recognized as the high temperature spin transport
associated with semiconductor spintronics. In this context the absence
of faithful hydrodynamics is well known, but in our formulation it is
directly associated with the fact that the covariant conservation of
non-Abelian currents turns into a disastrous non-conservation of the
incoherent spin currents of the high temperature limit. We analyze the
quantum-mechanical single particle currents of relevance to mesoscopic
transport with as highlight the Ahronov-Casher effect, where we
demonstrate that the intricacies of the non-Abelian transport render
this effect to be much more fragile than its abelian analog, the
Ahronov-Bohm effect. We subsequently focus on spin flows protected by
order parameters. At present there is much interest in multiferroics
where non-collinear magnetic order triggers macroscopic electric
polarization via the spin-orbit coupling. We identify this to be a
peculiarity of coherent non-Abelian hydrodynamics: although there is no
net particle transport, the spin entanglement is transported in these
magnets and the coherent spin `super' current in turn translates into
electric fields with the bonus that due to the requirement of single
valuedness of the magnetic order parameter a true hydrodynamics is
restored. Finally, `fixed-frame' coherent non-Abelian transport comes to
its full glory in spin-orbit coupled `spin superfluids', and we
demonstrate a new effect: the trapping of electrical line charge being a
fixed frame, non-Abelian analog of the familiar magnetic flux trapping
by normal superconductors. The only known physical examples of such spin
superfluids are the He-3 A- and B-phase where unfortunately the
spin-orbit coupling is so weak that it appears impossible to observe
these effects. (C) 2007 Elsevier Inc. All rights reserved.},
keywords = {spin-orbit coupling; spintronics; non-Abelian flow; superfluidity; Aharonov-Casher effect},
pubstate = {published},
tppubtype = {article}
}
Motivated by the heavy ion collision experiments there is much activity
in studying the hydrodynamical properties of non-Abelian (quark-gluon)
plasmas. A major question is how to deal with color currents. Although
not widely appreciated, quite similar issues arise in condensed matter
physics in the context of the transport of spins in the presence of
spin-orbit coupling. The key insight is that the Pauli Hamiltonian
governing the leading relativistic corrections in condensed matter
systems can be rewritten in a language of SU(2) covariant derivatives
where the role of the non-Abelian gauge fields is taken by the physical
electromagnetic fields: the Pauli system can be viewed as Yang-Mills
quantum-mechanics in a `fixed frame', and it can be viewed as an
`analogous system' for non-Abelian transport in the same spirit as
Volovik's identification of the He superfluids as analogies for quantum
fields in curved space time. We take a similar perspective as Jackiw and
coworkers in their recent study of non-Abelian hydrodynamics, twisting
the interpretation into the `fixed frame' context, to find out what this
means for spin transport in condensed matter systems. We present an
extension of Jackiw's scheme: non-Abelian hydrodynamical currents can be
factored in a `noncoherent' classical part, and a coherent part
requiring macroscopic non-Abelian quantum entanglement. Hereby it
becomes particularly manifest that non-Abelian fluid flow is a much
richer affair than familiar hydrodynamics, and this permits us to
classify the various spin transport phenomena in condensed matter
physics in an unifying framework. The ``particle based hydrodynamics''
of Jackiw et al. is recognized as the high temperature spin transport
associated with semiconductor spintronics. In this context the absence
of faithful hydrodynamics is well known, but in our formulation it is
directly associated with the fact that the covariant conservation of
non-Abelian currents turns into a disastrous non-conservation of the
incoherent spin currents of the high temperature limit. We analyze the
quantum-mechanical single particle currents of relevance to mesoscopic
transport with as highlight the Ahronov-Casher effect, where we
demonstrate that the intricacies of the non-Abelian transport render
this effect to be much more fragile than its abelian analog, the
Ahronov-Bohm effect. We subsequently focus on spin flows protected by
order parameters. At present there is much interest in multiferroics
where non-collinear magnetic order triggers macroscopic electric
polarization via the spin-orbit coupling. We identify this to be a
peculiarity of coherent non-Abelian hydrodynamics: although there is no
net particle transport, the spin entanglement is transported in these
magnets and the coherent spin `super' current in turn translates into
electric fields with the bonus that due to the requirement of single
valuedness of the magnetic order parameter a true hydrodynamics is
restored. Finally, `fixed-frame' coherent non-Abelian transport comes to
its full glory in spin-orbit coupled `spin superfluids', and we
demonstrate a new effect: the trapping of electrical line charge being a
fixed frame, non-Abelian analog of the familiar magnetic flux trapping
by normal superconductors. The only known physical examples of such spin
superfluids are the He-3 A- and B-phase where unfortunately the
spin-orbit coupling is so weak that it appears impossible to observe
these effects. (C) 2007 Elsevier Inc. All rights reserved.
in studying the hydrodynamical properties of non-Abelian (quark-gluon)
plasmas. A major question is how to deal with color currents. Although
not widely appreciated, quite similar issues arise in condensed matter
physics in the context of the transport of spins in the presence of
spin-orbit coupling. The key insight is that the Pauli Hamiltonian
governing the leading relativistic corrections in condensed matter
systems can be rewritten in a language of SU(2) covariant derivatives
where the role of the non-Abelian gauge fields is taken by the physical
electromagnetic fields: the Pauli system can be viewed as Yang-Mills
quantum-mechanics in a `fixed frame', and it can be viewed as an
`analogous system' for non-Abelian transport in the same spirit as
Volovik's identification of the He superfluids as analogies for quantum
fields in curved space time. We take a similar perspective as Jackiw and
coworkers in their recent study of non-Abelian hydrodynamics, twisting
the interpretation into the `fixed frame' context, to find out what this
means for spin transport in condensed matter systems. We present an
extension of Jackiw's scheme: non-Abelian hydrodynamical currents can be
factored in a `noncoherent' classical part, and a coherent part
requiring macroscopic non-Abelian quantum entanglement. Hereby it
becomes particularly manifest that non-Abelian fluid flow is a much
richer affair than familiar hydrodynamics, and this permits us to
classify the various spin transport phenomena in condensed matter
physics in an unifying framework. The ``particle based hydrodynamics''
of Jackiw et al. is recognized as the high temperature spin transport
associated with semiconductor spintronics. In this context the absence
of faithful hydrodynamics is well known, but in our formulation it is
directly associated with the fact that the covariant conservation of
non-Abelian currents turns into a disastrous non-conservation of the
incoherent spin currents of the high temperature limit. We analyze the
quantum-mechanical single particle currents of relevance to mesoscopic
transport with as highlight the Ahronov-Casher effect, where we
demonstrate that the intricacies of the non-Abelian transport render
this effect to be much more fragile than its abelian analog, the
Ahronov-Bohm effect. We subsequently focus on spin flows protected by
order parameters. At present there is much interest in multiferroics
where non-collinear magnetic order triggers macroscopic electric
polarization via the spin-orbit coupling. We identify this to be a
peculiarity of coherent non-Abelian hydrodynamics: although there is no
net particle transport, the spin entanglement is transported in these
magnets and the coherent spin `super' current in turn translates into
electric fields with the bonus that due to the requirement of single
valuedness of the magnetic order parameter a true hydrodynamics is
restored. Finally, `fixed-frame' coherent non-Abelian transport comes to
its full glory in spin-orbit coupled `spin superfluids', and we
demonstrate a new effect: the trapping of electrical line charge being a
fixed frame, non-Abelian analog of the familiar magnetic flux trapping
by normal superconductors. The only known physical examples of such spin
superfluids are the He-3 A- and B-phase where unfortunately the
spin-orbit coupling is so weak that it appears impossible to observe
these effects. (C) 2007 Elsevier Inc. All rights reserved.