scholarly journals Trial Wavefunctions for the Goldstone Mode in Quantum Hall Bilayers

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Gunnar Möller ◽  
Steven H. Simon
Keyword(s):  
Ground State ◽  
Quantum Hall ◽  
Interlayer Spacing ◽  
Low Energy ◽  
The Other ◽  
Goldstone Mode ◽  
Composite Fermion ◽  
Trial Wavefunction ◽  
Wavefunction Ansatz ◽  
Nonmonotonic Behavior

Based on the known physics of the excitonic superfluid or 111 state of the quantum Hall bilayer, we create a simple trial wavefunction ansatz for constructing a low-energy branch of (Goldstone) excitations by taking the overall ground state and boosting one layer with respect to the other. This ansatz works extremely well for any interlayer spacing. For small , this is simply the physics of the Goldstone mode, whereas for large , this is a reflection of composite fermion physics. We find hints that certain aspects of composite fermion physics persist to low whereas certain aspects of Goldstone mode physics persist to high . Using these results, we show nonmonotonic behavior of the Goldstone mode velocity as a function of .

scholarly journals Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level

1997 ◽  
Vol 11 (22) ◽  
pp. 2621-2660 ◽  
Author(s):  
J. K. Jain ◽  
R. K. Kamilla
Keyword(s):  
Landau Level ◽  
Ground State ◽  
Quantum Hall ◽  
Monte Carlo Study ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Standard Manner

Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

scholarly journals Noncommutativity Parameter and Composite Fermions

2003 ◽  
Vol 18 (21) ◽  
pp. 1473-1484 ◽  
Author(s):  
Ahmed Jellal
Keyword(s):  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
The Other ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Magnetic Length

We determine some particular values of the noncommutativity parameter θ and show that the Murthy–Shankar approach is in fact a particular case of a more general one. Indeed, using the fractional quantum Hall effect (FQHE) experimental data, we give a measurement of θ. This measurement can be obtained by considering some values of the filling factor ν and other ingredients, magnetic field B and electron density ρ. Moreover, it is found that θ can be quantized either fractionally or integrally in terms of the magnetic length l0 and the quantization is exactly what Murthy and Shankar formulated recently for the FQHE. On the other hand, we show that the mapping of the FQHE in terms of the composite fermion basis has a noncommutative geometry nature and therefore there is a more general way than the Murthy–Shankar method to do this mapping.

DYNAMICAL GAPS AND QUANTUM HALL EFFECT IN GRAPHENE

2009 ◽  
Vol 23 (07) ◽  
pp. 891-902
Author(s):  
E. V. GORBAR ◽  
V. P. GUSYNIN ◽  
V. A. MIRANSKY
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Quantum Hall ◽  
Low Energy ◽  
Strong Magnetic Fields ◽  
Gap Equation ◽  
Magnetic Catalysis

We analyze the gap equation for Dirac quasiparticles in graphene in a magnetic field using a low-energy effective model with a contact interaction. It is found that the order parameters connected with the quantum Hall (QH) ferromagnetism and the magnetic catalysis scenarios necessarily coexist. The ground-state solutions of the gap equation describe all the recently discovered novel QH plateaus in graphene in strong magnetic fields.

scholarly journals Ground state and stability of the fractional plateau phase in metallic Shastry–Sutherland system TmB4

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matúš Orendáč ◽  
Slavomír Gabáni ◽  
Pavol Farkašovský ◽  
Emil Gažo ◽  
Jozef Kačmarčík ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Ground State ◽  
Constant Magnetic Field ◽  
Paramagnetic Phase ◽  
The Other ◽  
Zero Field ◽  
Plateau Phase ◽  
Low Field ◽  
Zero Field Cooling

AbstractWe present a study of the ground state and stability of the fractional plateau phase (FPP) with M/Msat = 1/8 in the metallic Shastry–Sutherland system TmB4. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/Msat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 Msat.

CHEMICAL RECONSTRUCTION OF THE TiAl(010) SURFACE

1995 ◽  
Vol 02 (02) ◽  
pp. 183-189 ◽  
Author(s):  
C.P. WANG ◽  
S.K. KIM ◽  
F. JONA ◽  
D.R. STRONGIN ◽  
B.-R. SHEU ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Atomic Structure ◽  
Atomic Layer ◽  
Interlayer Spacing ◽  
Low Energy ◽  
Intensity Analysis ◽  
Low Energy Electron Diffraction ◽  
Surface Phases ◽  
Low Energy Electron ◽  
Bulk Structure

The atomic structure of a clean (010) surface of the ordered binary alloy TiAl (with tetragonal bulk structure of the CuAu I type) is studied with quantitative low-energy electron diffraction (QLEED). Two different surface phases are found depending on the preparation procedure. After a cleaning step in vacuo by means of Ar-ion bombardments, anneals at 750−850°C produce a 2×1 surface and anneals at about 900° C produce a 1×1 surface. A QLEED intensity analysis of the 1×1 structure reveals the occurrence of chemical reconstruction, whereby the Ti atoms in the first layer exchange places with the Al atoms in the second layer. Thus, while any bulk (010) plane contains 50% Al and 50% Ti , the top atomic layer of a (010) surface contains 100% Al and the second atomic layer contains 100% Ti . Both layers are slightly buckled and the first interlayer distance is compressed about 7.1% while the second interlayer spacing is expanded about 7.4% with respect to the bulk value.

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