Berry phases for composite fermions: Effective magnetic field and fractional statistics

This chapter focuses on the electron spin degree of freedom in semiconductor spintronics. In particular, the electrostatic control of the spin degree of freedom is an advantageous technology over metal-based spintronics. Spin–orbit interaction (SOI), which gives rise to an effective magnetic field. The essence of SOI is that the moving electrons in an electric field feel an effective magnetic field even without any external magnetic field. Rashba spin–orbit interaction is important since the strength is controlled by the gate voltage on top of the semiconductor’s two-dimensional electron gas. By utilizing the effective magnetic field induced by the SOI, spin generation and manipulation are possible by electrostatic ways. The origin of spin-orbit interactions in semiconductors and the electrical generation and manipulation of spins by electrical means are discussed. Long spin coherence is achieved by special spin helix state where both strengths of Rashba and Dresselhaus SOI are equal.

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OBSERVATION OF THE TRANSVERSE STERN–GERLACH EFFECT IN NEUTRAL POTASSIUM

Canadian Journal of Physics ◽

10.1139/p67-112 ◽

1967 ◽

Vol 45 (4) ◽

pp. 1481-1495 ◽

Cited By ~ 25

Author(s):

Myer Bloom ◽

Eric Enga ◽

Hin Lew

Keyword(s):

Magnetic Field ◽

Angular Velocity ◽

Reference Frame ◽

Inhomogeneous Magnetic Field ◽

Time Dependent ◽

Effective Magnetic Field ◽

Classical Analysis ◽

At Resonance ◽

Rotating Reference Frame

A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH0) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.

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Composite Fermions in a Long-Range Random Magnetic Field: Quantum Hall Effect versus Shubnikov–de Haas Oscillations

Physical Review Letters ◽

10.1103/physrevlett.80.2429 ◽

1998 ◽

Vol 80 (11) ◽

pp. 2429-2432 ◽

Cited By ~ 41

Author(s):

A. D. Mirlin ◽

D. G. Polyakov ◽

P. Wölfle

Keyword(s):

Magnetic Field ◽

Hall Effect ◽

Long Range ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Composite Fermions ◽

Random Magnetic Field ◽

Shubnikov De Haas Oscillations

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Spin wave interferometer employing a local nonuniformity of the effective magnetic field

Journal of Applied Physics ◽

10.1063/1.2740339 ◽

2007 ◽

Vol 101 (11) ◽

pp. 113919 ◽

Cited By ~ 63

Author(s):

S. V. Vasiliev ◽

V. V. Kruglyak ◽

M. L. Sokolovskii ◽

A. N. Kuchko

Keyword(s):

Magnetic Field ◽

Spin Wave ◽

Effective Magnetic Field

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Abrikosov vortex corrections to effective magnetic field enhancement in epitaxial graphene

Physical Review B ◽

10.1103/physrevb.104.085435 ◽

2021 ◽

Vol 104 (8) ◽

Author(s):

Luke R. St. Marie ◽

Chieh-I Liu ◽

I-Fan Hu ◽

Heather M. Hill ◽

Dipanjan Saha ◽

...

Keyword(s):

Magnetic Field ◽

Field Enhancement ◽

Epitaxial Graphene ◽

Effective Magnetic Field ◽

Abrikosov Vortex ◽

Magnetic Field Enhancement

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Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors

National Science Review ◽

10.1093/nsr/nwz117 ◽

2019 ◽

Vol 7 (1) ◽

pp. 12-20 ◽

Cited By ~ 5

Author(s):

Hongyi Yu ◽

Mingxing Chen ◽

Wang Yao

Keyword(s):

Magnetic Field ◽

Berry Phase ◽

Transition Metal Dichalcogenides ◽

Real Space ◽

Quantum Spin ◽

Moire Patterns ◽

Metal Dichalcogenides ◽

Berry Phases ◽

Different Origins ◽

Moiré Patterns

Abstract When quasiparticles move in condensed matters, the texture of their internal quantum structure as a function of position and momentum can give rise to Berry phases that have profound effects on the material’s properties. Seminal examples include the anomalous Hall and spin Hall effects from the momentum-space Berry phases in homogeneous crystals. Here, we explore a conjugate form of the electron Berry phase arising from the moiré pattern: the texture of atomic configurations in real space. In homobilayer transition metal dichalcogenides, we show that the real-space Berry phase from moiré patterns manifests as a periodic magnetic field with magnitudes of up to hundreds of Tesla. This quantity distinguishes moiré patterns from different origins, which can have an identical potential landscape, but opposite quantized magnetic flux per supercell. For low-energy carriers, the homobilayer moirés realize topological flux lattices for the quantum-spin Hall effect. An interlayer bias can continuously tune the spatial profile of the moiré magnetic field, whereas the flux per supercell is a topological quantity that can only have a quantized jump observable at a moderate bias. We also reveal the important role of the non-Abelian Berry phase in shaping the energy landscape in small moiré patterns. Our work points to new possibilities to access ultra-high magnetic fields that can be tailored to the nanoscale by electrical and mechanical controls.

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