Spectrum of the bloch electron in a magnetic field in a two-dimensional lattice

1984 ◽  
Vol 58 (3) ◽  
pp. 302-310 ◽  
Author(s):  
V. A. Geiler ◽  
V. A. Margulis
Keyword(s):  
Magnetic Field ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Bloch Electron

scholarly journals Fractionally Charged Anyon Generated by Topological Path Fusion in Magnetic Flux Lattice

2020 ◽  
Author(s):  
Tieyan Si
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Collective Excitation ◽  
Quantum Hall ◽  
Experimental System ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Topological Quantum ◽  
Fusion Theory

Anyon usually exists as collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. Fractional quantum Hall effect (FQHE) is the only experimental system showing solid evidence of anyon and a serial of fractional charges so far. Searching for new serial of fractional charges in FQHE or other physical system is still a challenge for both theoretical and experimental study. Here a topological fusion theory of propagating paths winding around a pair of fluxes is proposed to explore the physical origin of fractional charges. This topological path fusion theory not only generated all of the existed serial of fractional charges in FQHE and found the exact correspondence between FQHE and integral quantum Hall effect (IQHE), but also predicted new serial of fractional charges in FQHE. Further more, serial irrational charges like $2/(3+\sqrt{2})$ in one dimensional lattice of magnetic fluxes as well as that in two dimensional lattice of magnetic fluxes, such as $(1+\sqrt{2})$, are predicted. Even in three dimensional network of magnetic fluxes, a serial of fractionally charged anyon is predicted by this topological path fusion theory, which has exactly correspondence with the knot lattice model of anyon. In fact, in a multi-connected space time without magnetic field, this topological path fusion theory still holds, revealing an universal existence of fractional charge and mass in quantum material with strong confinement of particles (such as photonic crystal with porous nano-structures) and paving a new way for topological quantum computation.

ORBITAL PARAMAGNETISM IN TWO-DIMENSIONAL LATTICES

1991 ◽  
Vol 05 (08) ◽  
pp. 571-579 ◽  
Author(s):  
F.V. KUSMARTSEV
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Phase State ◽  
Two Dimensional ◽  
Absolute Minimum ◽  
Dimensional Lattice ◽  
The Absolute

We calculate the ground state energy and the magnetization of spinless fermions on a two-dimensional lattice in an external magnetic field. We prove that the absolute minimum of the energy corresponds to a flux value equal to the filling, i.e. the “commensurate flux phase” state is preferable. The magnetization of these fermions has a paramagnetic character of special orbital type.

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