Suppression of Shubnikov–de Haas resistance oscillations due to selective population or detection of Landau levels: Absence of inter-Landau-level scattering on macroscopic length scales
B. J. van WeesE. M. M. WillemsLeo P. KouwenhovenC. J. P. M. HarmansJ. WilliamsonC. T. FoxonJ. J. Harris
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Abstract:
The Shubnikov--de Haas resistance oscillations of a wide two-dimensional electron gas are suppressed dramatically when current is injected with a quantum point contact which does not populate the upper Landau level. A similar suppression is observed when a quantum point contact is used as a voltage probe which does not detect the upper Landau level. The results are explained with a model in which the Shubnikov--de Haas oscillations arise from backscattering of electrons in the upper Landau level. It is shown that quantum ballistic transport in high magnetic fields can occur on length scales larger than 200 \ensuremath{\mu}m.Keywords:
Landau quantization
Shubnikov–de Haas effect
We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) – a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic field following the variation of the Landau bandwidth due to the commensurability effect. Notably, the decrement vanishes at the flat band conditions.
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Shubnikov–de Haas effect
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The Shubnikov--de Haas resistance oscillations of a wide two-dimensional electron gas are suppressed dramatically when current is injected with a quantum point contact which does not populate the upper Landau level. A similar suppression is observed when a quantum point contact is used as a voltage probe which does not detect the upper Landau level. The results are explained with a model in which the Shubnikov--de Haas oscillations arise from backscattering of electrons in the upper Landau level. It is shown that quantum ballistic transport in high magnetic fields can occur on length scales larger than 200 \ensuremath{\mu}m.
Landau quantization
Shubnikov–de Haas effect
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Landau quantization
Shubnikov–de Haas effect
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The pair distribution function and the static structure factor are computed for composite fermions. Clear and robust evidence for a $2k_F$ structure is seen in a range of filling factors in the vicinity of the half-filled Landau level. Surprisingly, it is found that filled Landau levels of composite fermions, i.e. incompressible FQHE states, bear a stronger resemblance to a Fermi sea than do filled Landau levels of electrons.
Landau quantization
Composite fermion
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Shubnikov–de Haas effect
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The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are successfully explained by the composite fermion (CF) model, in which an even number of magnetic flux quanta are attached to an electron and where states form the sequence of filling factors $\nu = p/(2mp \pm 1)$, with $m$ and $p$ positive integers. In the widely-studied GaAs-based system, the CF picture is thought to become unstable for the $N \geq 2$ LL, where larger residual interactions between CFs are predicted and competing many-body phases have been observed. Here we report transport measurements of FQH states in the $N=2$ LL (filling factors $4 < \nu < 8$) in bilayer graphene, a system with spin and valley degrees of freedom in all LLs, and an additional orbital degeneracy in the 8-fold degenerate $N=0$/$N=1$ LLs. In contrast with recent observations of particle-hole asymmetry in the $N=0$/$N=1$ LLs of bilayer graphene, the FQH states we observe in the $N=2$ LL are consistent with the CF model: within a LL, they form a complete sequence of particle-hole symmetric states whose relative strength is dependent on their denominators. The FQH states in the $N=2$ LL display energy gaps of a few Kelvin, comparable to and in some cases larger than those of fractional states in the $N=0$/$N=1$ LLs. The FQH states we observe form, to the best of our knowledge, the highest set of particle-hole symmetric pairs seen in any material system.
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Composite fermion
Bilayer graphene
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Shubnikov–de Haas effect
Composite fermion
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Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe5, adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.
Landau quantization
Thermal Hall effect
Shubnikov–de Haas effect
Quantum limit
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Abstract Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe 5 , adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.
Landau quantization
Thermal Hall effect
Shubnikov–de Haas effect
Quantum limit
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Oscillatory variations of the diagonal (Gxx) and Hall (G(xy)) magnetoconductances are discussed in view of topological scaling effects giving rise to the quantum Hall effect. They occur in a field range without oscillations of the density of states due to Landau quantization, and are, therefore, totally different from the Shubnikov-de Haas oscillations. Such oscillations are experimentally observed in disordered GaAs layers in the extreme quantum limit of applied magnetic field with a good description by the unified scaling theory of the integer and fractional quantum Hall effect.
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Topological insulator
Shubnikov–de Haas effect
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We have studied the fractional quantum Hall effect in higher Landau levels following Jain's composite-fermion theory. Our framework provides numerical calculations for the gaps in a range of electron densities typically used in experiments. As expected, the gaps diminish as the Landau level index increases. Surprisingly, however, they become negative in the third and higher Landau levels, indicating an absence of the fractional quantum Hall effect beyond the second Landau level.
Landau quantization
Composite fermion
Shubnikov–de Haas effect
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