scholarly journals Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry

2005 ◽  
Vol 71 (15) ◽  
Author(s):  
Shun-Qing Shen ◽  
Yun-Juan Bao ◽  
Michael Ma ◽  
X. C. Xie ◽  
Fu Chun Zhang
Keyword(s):  
Quantum Hall ◽  
Inversion Symmetry ◽  
Hall Conductance ◽  
Quantum Hall Systems ◽  
Structural Inversion

Superfluidity of the Lattice Anyon Gas

1989 ◽  
Vol 03 (12) ◽  
pp. 1965-1995 ◽  
Author(s):  
Eduardo Fradkin
Keyword(s):  
Quantum Hall ◽  
Goldstone Mode ◽  
Two Dimensional ◽  
Hall Conductance ◽  
Dimensional Lattice ◽  
Quantum Hall Systems ◽  
Wigner Transformation ◽  
Topological Invariance ◽  
Quantum Hall System ◽  
Chern Simons

I consider a gas of “free” anyons with statistical paremeter δ on a two dimensional lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on a lattice coupled to a Chern-Simons gauge theory with coupling [Formula: see text]. I show that if [Formula: see text] and the density [Formula: see text], with r and q integers, the system is a superfluid. If q is even and the system is half filled the state may be either a superfluid or a Quantum Hall System depending on the dynamics. Similar conclusions apply for other values of ρ and δ. The dynamical stability of the Fetter-Hanna-Laughlin goldstone mode is insured by the topological invariance of the quantized Hall conductance of the fermion problem. This leads to the conclusion that anyon gases are generally superfluids or quantum Hall systems.

scholarly journals REVISITING THE CHARGE TRANSPORT IN QUANTUM HALL SYSTEMS

2004 ◽  
Vol 16 (09) ◽  
pp. 1115-1189 ◽  
Author(s):  
TOHRU KOMA
Keyword(s):  
Electric Field ◽  
Charge Transport ◽  
Spectral Gap ◽  
Quantum Hall ◽  
Electrostatic Potentials ◽  
Weak Electric Field ◽  
Hall Conductance ◽  
Independent Term ◽  
Quantum Hall Systems ◽  
Volume Limit

We re-examine the charge transport induced by a weak electric field in two-dimensional quantum Hall systems in a finite, periodic box at very low temperatures. Our model covers random vector and electrostatic potentials and electron–electron interactions. The resulting linear response coefficients consist of the time-independent term σxy corresponding to the Hall conductance and the linearly time-dependent term γsy · t in the transverse and longitudinal directions s=x,y in a slow switching limit for adiabatically applying the initial electric field. The latter terms γsy · t are due to the acceleration of the electrons by the uniform electric field in the finite and isolated system, and so the time-independent term σyy corresponding to the diagonal conductance which generates dissipation of heat always vanishes. The well-known topological argument yields the integral and fractional quantization of the averaged Hall conductance [Formula: see text] over gauge parameters under the assumption that there exists a spectral gap above the ground state. In addition to this fact, we show that the averaged acceleration coefficients [Formula: see text] vanish under the same assumption. In the non-interacting case, the spectral gap between the neighboring Landau levels persists if the vector and the electrostatic potentials together satisfy a certain condition, and then the Hall conductance σxy without averaging exhibits the exact integral quantization with the vanishing acceleration coefficients in the infinite volume limit. We also estimate their finite size corrections. In the interacting case, the averaged Hall conductance [Formula: see text] for a non-integer filling of the electrons is quantized to a fraction not equal to an integer under the assumption that the potentials satisfy certain conditions in addition to the gap assumption. We also discuss the relation between the fractional quantum Hall effect and the Atiyah–Singer index theorem for non-Abelian gauge fields.

scholarly journals Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nicodemos Varnava ◽  
Justin H. Wilson ◽  
J. H. Pixley ◽  
David Vanderbilt
Keyword(s):  
Topological Insulator ◽  
Information Science ◽  
Domain Walls ◽  
Quantum Hall ◽  
Edge State ◽  
Wave Functions ◽  
Quantum Hall Systems ◽  
Electron Quantum ◽  
Quantum Point ◽  
Higher Temperature

AbstractEngineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

scholarly journals The quantum Hall effect in the absence of disorder

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Kyung-Su Kim ◽  
Steven A. Kivelson
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Finite Interval ◽  
Quantum Hall ◽  
Wigner Crystal ◽  
Quasi Particle ◽  
Hall Conductance ◽  
Finite Extent

AbstractIt is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e., for the existence of “plateaus” in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal (QPWC) results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are also explored.

Anisotropic multicomponent terahertz photoconductivity in quantum Hall systems

JETP Letters ◽  
2002 ◽  
Vol 76 (10) ◽  
pp. 625-627 ◽  
Author(s):  
N. G. Kalugin ◽  
Yu. B. Vasil’ev ◽  
S. D. Suchalkin ◽  
G. Nachtwei ◽  
B. E. Sagol ◽  
...  
Keyword(s):  
Quantum Hall ◽  
Quantum Hall Systems
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