MBE deserves a place in the history books

McCray, W. Patrick

doi:10.1038/nnano.2007.121

Cited by 83 publications

(46 citation statements)

References 6 publications

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“…First let us look at the equilibrium conditions. Toward this end we note that physically the the leads are equivalent two potential wells which contains two liquids as shown in figure (2). The scattering region is equivalent to a spin-dependent potential step or barrier.…”

Section: The Incident Density Matrix In the Leadsmentioning

confidence: 97%

“…This experimental land was prepared through the painstaking efforts and research of eminent experimentalist and engineers over next 15 years and brought in existence the nano-fabrication or micro-fabrication technology, commonly know as MBE, for a beautiful account of such efforts see Ref. [2]. Availability of fertile land made the seed to sprout and in its early days the name, 'Mesoscopic' was give by Van Kampen [3].…”

Section: Introductionmentioning

confidence: 99%

“…This amounts to replacing the V z by V z → V z + B ext,z ≈ V z as is done in eq. (2). Further if one assumes ǫ 0 = ǫ z that would imply that both spin-independent and spin-dependent potential along the chosen quantization axis can be switched on adiabatically simultaneously.…”

Section: Introductionmentioning

confidence: 99%

“…(1) instead of the approximate potential given in eq. (2). This means that one should use a formulation which allows to treat all spin-quantization axis at equal footing which is possible only in density matrix formulation.…”

Section: Introductionmentioning

confidence: 99%

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Quantum non-Abelian hydrodynamics: Anyonic or spin–orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

Pareek

2014

Int. J. Mod. Phys. B

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In this article we develop an exact(non-adiabatic,non-perturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential.The generic spin dependent quantum potential[eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated non-adiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix ,̺sc [eq.(30)]. We find that the number or charge density in scattered fluid,Tr(̺sc), expressions in eqs. (32) depends on non-trivial quantum interference coefficients, Q αβ 0ijk which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr(̺sc) can be expressed in a compact form [eq.(39)] where the effect of quantum interference coefficients can be include using a vector Q αβ which allows us to define a vector order parameter Q. Since the number density is obtained using and exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However for sake of completeness we make detailed mathematical analysis for the conditions under which the vector order parameter Q would be zero or non-zero.We find that in presence of spin-dependent interaction the vector order parameter Q is necessarily non-zero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S † [eq. (78)]. It is further shown that Q = 0, implies four physically equivalent conditions,i.e, spin-orbital entanglement is non-zero, NonAbelian scattering phase ,i.e, matrices, scattering matrix is NonUnitary and the broken time reversal symmetry for scattered density matrix. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a natural consequence. This aspect has also been discussed from the perspective of number or charge density conservation, which implies i.e, Tr(̺sc) = Tr(̺in). On the other hand Q = 0 turns out to be a mathematically forced unphysical solution in presence of spin-dependent potential or scattering which is equivalent 1 to Abelian hydrodynamics ,Unitary scattering matrix, absence of spinspace entanglement, and preserved time reversal symmetry.We have formulated the theory using mesoscopic language, specifically, we have considered two terminal systems connected to spin-dependent scattering region, which is equivalent to having two potential wells separated by a generic spin-dependent potential barrier. The formulation using mesoscopic language is practically useful because it leads directly to the measured quantities such as conductance and spin-polarization density in the leads, however, the presented formulation is not limited to the mesoscopic system only, its generality has been stressed at various places in this article.

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Section: The Incident Density Matrix In the Leadsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum non-Abelian hydrodynamics: Anyonic or spin–orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

Pareek

2014

Int. J. Mod. Phys. B

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show abstract

“…Like molecular beam epitaxy 1 , for instance, they have had a much lower profile than the carbon nanotube and various forms of scanning probe microscopy 2 . However, quantum dots have been around for at least as long as either of these stalwarts of nanotech, and have been the focus of just as much research.…”

Section: Editorialmentioning

confidence: 99%