Bloch's theory in periodic structures with Rashba's spin-orbit interaction

Smirnov, Sergey; Bercioux, Dario; Grifoni, Milena

doi:10.1209/0295-5075/80/27003

Cited by 18 publications

(60 citation statements)

References 13 publications

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“…It is similar to what has experimentally been observed for two-dimensional electron gazes [21]. Our conclusion is in agreement with what has been reached in [15]. To close this section let us note that when the magnetic field is switched off, we recover Bloch Hamiltonian amended by a free particle living on the z-direction.…”

Section: Total Spectrumsupporting

confidence: 90%

“…Indeed, for a strong B we analyze the corresponding spectrum and symmetries to end up with different conclusions. As an interesting consequence, we show that the polarization symmetries are preserved in such case and this generalize the obtained result in [15] to the magnetic field. More importantly, such polarizations are obtained to be B-dependent and therefore it can be controlled by different values taken by the magnetic field.…”

Section: Introductionsupporting

confidence: 86%

“…However, we will see that an analogue form to V (z) can spontaneously be created thanks to the emergence of B. Thus, one can expect that this effect will make difference with respect to the results obtained in [15]. The corresponding quasi-momentum becomes…”

Section: Gauge Field Couplingmentioning

confidence: 72%

“…This will allow us to obtain an appropriate Hamiltonian that will be used to do our task and in particular to generalize the result obtained in [15] to the case of B and offer some comments.…”

Section: Gauge Field Couplingmentioning

confidence: 99%

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Periodic structures with Rashba interaction in a magnetic field

Jellal¹,

Houça²

2008

J. Phys. A: Math. Theor.

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We analyze the behaviour of a system of particles living on a periodic crystal in the presence of a magnetic field B. This can be done by involving a periodic potential U (x) and the Rashba interaction of coupling constant k so . By resorting the corresponding spectrum, we explicitly determine the band structures and the Bloch spinors. These allow us to discuss the system symmetries in terms of the polarizations where they are shown to be broken. The dynamical spin will be studied by calculating different quantities. In the limits: k so and U (x) = 0, we analyze again the system by deriving different results. Considering the strong B case, we obtain an interesting result that is the conservation of the polarizations. Analyzing the critical point λ k,σ = ± 1 2 , we show that the Hilbert space associated to the spectrum in z-direction has a zero mode energy similar to that of massless Dirac fermions in graphene. Finally, we give the resulting energy spectrum when B = 0 and U (x) is arbitrary.

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Section: Total Spectrumsupporting

confidence: 90%

Section: Introductionsupporting

confidence: 86%

Section: Gauge Field Couplingmentioning

confidence: 72%

Section: Gauge Field Couplingmentioning

confidence: 99%

See 2 more Smart Citations

Periodic structures with Rashba interaction in a magnetic field

Jellal¹,

Houça²

2008

J. Phys. A: Math. Theor.

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“…Those studies included the effect of dimensionality and features of the band-gap structures of a gas in a superimposed periodic and arbitrary confining potentials [23], ballistic transport of electrons in periodic magnetic field [24,25], switching controlled by SO coupling [26], and quantum wire superlattices [27]. It was shown that SO coupling induced by an external periodic field leads to the appearance of new gaps, making the electronic system tunable even in the condensed matter settings.…”

mentioning

confidence: 99%

Gap Solitons in a Spin-Orbit-Coupled Bose-Einstein Condensate

2013

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We report a diversity of stable gap solitons in a spin-orbit coupled Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is shown that the solitons, can be classified by the main physical symmetries they obey, i.e. symmetries with respect to parity (P), time (T), and internal degree of freedom, i.e. spin, (C) inversions. The conventional gap and gap-stripe solitons are obtained in lattices with different parameters. It is shown that solitons of the same type but obeying different symmetries can exist in the same lattice at different spatial locations. PT and CPT symmetric solitons have anti-ferromagnetic structure and are characterized respectively by nonzero and zero total magnetizations. The progressively growing interest in the physics of mixtures of spinor Bose-Einstein condensates (BECs) and in particular in spin-orbit (SO) coupled BECs (SOBECs) [1,2], is motivated on the one hand by their fundamental importance for the atomic physics, and on the other hand by the rich possibilities they offer for emulating synthetic electric and magnetic fields in solids [3]. The last property allows one using neutral atoms to simulate numerous condensed matter phenomena [4] in a tunable way, what would be impossible in direct condensed matter experiments. In other words, a spinor BEC is a promising candidate for implementation of a quantum simulator, which due to the technologies available nowadays was already implemented using cold atoms [5], ions [6], or photonics [7]. In particular, we mention a recent experiment [8] with coupled (linear) arrays of optical waveguides simulating a discrete version of SO-coupling which in the present letter is considered for the matter waves.Meanwhile, the physics of BECs is characterized by two essential factors, which are not typical for the physics which is aimed to be simulated. First, a BEC is a nonlinear system, with the nonlinearity stemming from the twobody interactions [9]. Moreover, by changing the configuration of the system (i.e. of the laser beams) one can create effective nonlinear interactions of different types [10]. Respectively, such nonlinear objects as skyrmions [11], solitons [12,13], anti-ferromagnetic structures and symmetry breaking [14], have been recently reported for SOBECs. The second feature, is that a (quasi-) stationary state of the condensate requires the presence of the external potential. This, in particular, imposes constraints on the lower bound of the kinetic energy, what is particularly relevant for SO-BECs (see e.g. [14]). What concerns the external potentials, since the very first experiments with cold atoms loaded in optical lattices [15] it was widely recognized that lattices (i.e. periodic potentials) are particularly efficient in manipulating BECs [16]. Nowadays, the nonlinear properties of the atomic BECs held in optical lattices, described in the mean-field approximation are very well studied [17] (see also [18] for a brief review on BEC mixtures in optical lattices). It is therefore natural that studies of SO-BECs in pe...

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Quantum Dissipative Ratchets

Grifoni

2010

Nonlinear Dynamics of Nanosystems

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Bloch's theory in periodic structures with Rashba's spin-orbit interaction

Cited by 18 publications

References 13 publications

Periodic structures with Rashba interaction in a magnetic field

Periodic structures with Rashba interaction in a magnetic field

Gap Solitons in a Spin-Orbit-Coupled Bose-Einstein Condensate

Quantum Dissipative Ratchets

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