Integral Quantum Hall Effect Research Articles

Gauge Nonlocality in Planar Quantum-Coherent Systems

It is shown that a system with quantum coherence can be nontrivially affected by adjacent magnetic or adjacent time-varying electric field regions, with this proximity (or remote) influence having a gauge origin. This is implicit (although overlooked) in numerous works on extended systems with inhomogeneous magnetic fields (with either conventional or Dirac materials) but is generally plagued with an apparent gauge ambiguity. The origin of this annoying feature is explained and it is shown how it can be theoretically removed, leading to macroscopic quantizations (quantized Dirac monopoles, integral quantum Hall effect, quantized magnetoelectric phenomena in topological insulators). Apart however from serving as a theoretical probe of macroscopic quantizations, there are cases (experimental conditions, clarified here) when this "gauge nonlocality" does not really suffer from any ambiguity: an apparently innocent gauge transformation corresponds to real change in physics of a companion system in higher dimensionality, that leads to physical momentum transfers to our own system. This nonlocality, together with the associated "proximity" or remote effects are then real and lead to the remarkable possibility of inducing topological phenomena from outside our system (which always remains field-free and can even reside in simply-connected space). Specific procedures are then proposed to experimentally detect such types of nonlocal effects and exploit them for novel applications. General consequences in solid state physics (such as the first violation of Bloch theorem in a field-free quantum periodic system) are pointed out, and formal analogies with certain high energy physics phenomena (axions, {\theta}-vacua and some types of Gribov ambiguities), as well as with certain largely unexplored phenomena in mechanics and in thermodynamics, are noted.

Valley-degenerate two-dimensional electrons in the lowest Landau level

We report low temperature magnetotransport measurements on a high mobility ($\ensuremath{\mu}=325\phantom{\rule{0.16em}{0ex}}000\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{V}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$) two-dimensional electron system on a H-terminated Si(111) surface. We observe the integral quantum Hall effect at all filling factors $\ensuremath{\nu}\ensuremath{\le}6$ and find that $\ensuremath{\nu}=2$ develops in an unusually narrow temperature range. An extended, exclusively even numerator, fractional quantum Hall hierarchy occurs surrounding $\ensuremath{\nu}=3/2$, consistent with twofold valley-degenerate composite fermions (CFs). We determine activation energies and estimate the CF mass.

Graphene: A Peculiar Allotrope Of Carbon

Graphene is a two dimensional one atom thick allotrope of Carbon. Electrons in grapheme behave as massless relativistic particles. It is a 2 dimensional nanomaterial with many peculiar properties. In grapheme both integral and fractional quantum Hall effects are observed. Many practical application are seen from use of Graphene material.The Himalayan PhysicsVol. 3, No. 3, July 2012Page: 87-88

Erratum: Integral quantum Hall effect in graphene: Zero and finite Hall field [Phys. Rev. B83, 075427 (2011)

Erratum: Integral quantum Hall effect in graphene: Zero and finite Hall field [Phys. Rev. B<b>83</b>, 075427 (2011)

Memristor and the integral quantum Hall effect

New equations with a fractional derivative, which relate current and voltage, are obtained for an arbitrary memristor (one of four basic passive elements of electronic circuits, along with resistor, capacitor, and inductor). The physical meaning of fractional differentiation in application to a memristor is clarified. It is shown that the integral quantum Hall effect can be the physical basis of memristor’s operational principle.

Integral quantum Hall effect in graphene: Zero and finite Hall field

We study the influence of a finite Hall field EH on the Hall conductivity σyx in graphene. Analytical expressions are derived for σyx using the Kubo-Greenwood formula. For vanishing EH, we obtain the well-known expression σyx=4(N+1/2)e2/h. The inclusion of the dispersion of the energy levels, previously not considered, and their width, due to scattering by impurities, produces the plateau of the n=0 Landau level. Further, we evaluate the longitudinal resistivity ρxx and show that it exhibits an oscillatory behavior with the electron concentration. The peak values of ρxx depend strongly on the impurity concentration and their potential. For a finite EH, the result for σyx is the same as that for EH=0, provided EH is not strong, but the values and positions of the resistivity maxima are modified due to the EH-dependent dispersion of the energy levels.

The topological structure of the integral quantum Hall effect in magnetic semiconductor-superconductor hybrids

An unconventional integer quantum Hall regime was found in magnetic semiconductor-superconductor hybrids. By making use of the decomposition of the gauge potential on a U(1) principal fibre bundle over k-space, we study the topological structure of the integral Hall conductance. It is labeled by the Hopf index β and the Brouwer degree η. The Hall conductance topological current and its evolution is discussed.

Phase study of oscillatory resistances in microwave-irradiated- and dark-GaAs/AlGaAs devices: Indications of an unfamiliar class of the integral quantum Hall effect

We report the experimental results from a dark study and a photoexcited study of the high-mobility GaAs/AlGaAs system at large filling factors, $\ensuremath{\nu}$. At large $\ensuremath{\nu}$, the dark study indicates several distinct phase relations (``type 1,'' ``type 2,'' and ``type 3'') between the oscillatory diagonal and Hall resistances, as the canonical integral quantum Hall effect (IQHE) is manifested in the type 1 case of approximately orthogonal diagonal and Hall resistance oscillations. Surprisingly, the investigation indicates quantum Hall plateaus also in the type 3 case characterized by approximately ``antiphase'' Hall and diagonal resistance oscillations, suggesting an unfamiliar and distinct class of IQHE. Transport studies under microwave photoexcitation exhibit radiation-induced magnetoresistance oscillations in both the diagonal, ${R}_{xx}$, and off-diagonal, ${R}_{xy}$, resistances. Further, when the radiation-induced magnetoresistance oscillations extend into the quantum Hall regime, there occurs a radiation-induced nonmonotonic variation in the amplitude of Shubnikov--de Haas (SdH) oscillations in ${R}_{xx}$ vs $B$, and a nonmonotonic variation in the width of the quantum Hall plateaus in ${R}_{xy}$. The latter effect leads into the vanishing of IQHE at the minima of the radiation-induced ${R}_{xx}$ oscillations with increased photoexcitation. We reason that the mechanism which is responsible for producing the nonmonotonic variation in the amplitude of SdH oscillations in ${R}_{xx}$ under photoexcitation is also responsible for eliminating, under photoexcitation, the type 3 associated IQHE in the high-mobility specimen.

Topological Anderson Insulator

Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal-insulator transition and the integral and fractional quantum Hall effects. In this Letter, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions and exhibits the phenomenon of quantum spin Hall effect. We predict an unexpected and nontrivial quantum phase termed "topological Anderson insulator," which is obtained by introducing impurities in a two-dimensional metal; here disorder not only causes metal-insulator transition, as anticipated, but is fundamentally responsible for creating extended edge states. We determine the phase diagram of the topological Anderson insulator and outline its experimental consequences.

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity ρxx near the critical filling factor νc ≈ 0.5 follows the universal scaling law ρxx(ν, T) ∝ exp(-Δν/(T/T0)κ), where Δν = ν-νc. The critical exponent κ equals 0.56 ± 0.02, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class.

Hierarchy of composite fermions in the Hamiltonian theory

Most states of the fractional quantum Hall effect may be interpreted in terms of an integral quantum Hall effect of weakly-interacting quasiparticles (composite fermions). The recently discovered 4 11 state does not belong to these states because its formation is due to the residual interactions between composite fermions, which become relevant when the composite-fermion levels are only partially filled. We have derived a model of interacting composite fermions, which reveals the self-similarity of the fractional quantum Hall effect and which allows for a systematic study of higher generations of composite fermions. Here, we derive the form of the interaction potential between these hierarchical composite fermions and provide some stability criteria for such states.

Quantum electronic phases in partially filled Landau levels

On the basis of energy calculations, we investigate the competition between quantum-liquid and electron-solid phases in intermediate Landau levels as a function of their partial filling factor. An alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains an observed reentrance of the integral quantum Hall effect. The phase transitions are identified as first-order. Recent transport measurements under micro-wave irradiation reveal the crystalline origin of the reentrant points, and a mixed phase of a coexisting Wigner crystal and a 2-electron bubble phase is found in a Landau-level filling-factor range 4,15? ν? 4.26, as expected from our calculations.

Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu = 4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu = 4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.

Microscopic origin of the next-generation fractional quantum Hall effect.

Most of the fractions observed to date belong to the sequences nu=n/(2pn+/-1) and nu=1-n/(2pn+/-1), n and p integers, understood as the familiar integral quantum Hall effect of composite fermions. These sequences fail to accommodate, however, many fractions such as nu=4/11 and 5/13, discovered recently in ultrahigh mobility samples at very low temperatures. We show that these "next generation" fractional quantum Hall states are accurately described as the fractional quantum Hall effect of composite fermions.

Competition between quantum-liquid and electron-solid phases in intermediate Landau levels

On the basis of energy calculations we investigate the competition between quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a function of their partial filling factor. Whereas the quantum-liquid phases are stable only in the vicinity of quantized values 1/(2s+1) of the partial filling factor, an electron solid in the form of a triangular lattice of clusters with a few number of electrons (bubble phase) is energetically favorable between these fillings. This alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains a recently observed reentrance of the integral quantum Hall effect in the Landau levels n=1 and 2. Around half-filling of the last Landau level, a uni-directional charge density wave (stripe phase) has a lower energy than the bubble phase.

New Results of Ultra-Low Temperature Experiments in the Second Landau Level in a Two-Dimensional Electron System

In the second Landau level around v = 5/2 filling of an extremely high quality 2D electron system and at temperatures T down to 9 mK we observe a very strong even-denominator fractional quantum Hall effect at Landau level filling v = 5/2 and its energy gap is large and Δ ∼ 0.45K. A clear FQHE state is seen at v = 2 + 2/5, with well-quantized R xy . A novel, even-denominator FQHE state at v = 2 + 3/8 seems to develop, as deduced from the T-dependence of dR xy /dB. In addition, four fully developed re-entrant integral quantum Hall effect (RIQHE) states are also observed. At low temperatures, the wide RIQHE plateau around at v = 2 + 2/7 is interrupted by a dip, indicating an additional reentrance. Finally, the tilted magnetic field experiment at an ultra-low temperature of 10 mK was carried out to examine the spin-polarization of the v = 5/2 FQHE state.

Microscopic theory of the reentrant integer quantum Hall effect in the first and second excited Landau levels

We present a microscopic theory for the recently observed reentrant integral quantum Hall effect in the n=1 and n=2 Landau levels. Our energy investigations indicate an alternating sequence of M-electron-bubble and quantum-liquid ground states in a certain range of the partial filling factor of the n-th level. Whereas the quantum-liquid states display the fractional quantum Hall effect, the bubble phases are insulating, and the Hall resistance is thus quantized at integral values of the total filling factor.

The role of analogy in unraveling the fractional quantum Hall effect mystery

This introductory article, intended for non-experts, explains how the analogy to the integral quantum Hall effect provided the key to understanding the fractional quantum Hall effect, at the same time leading to a new class of topological fermions called composite fermions. It is shown how the enormous ambiguity of the original electron problem is eliminated as a result of the formation of composite fermions, and a unique solution is obtained that is extremely accurate and consistent with dramatic experimental observations.

Effective potentials in the integral quantum Hall effect

The exact n-body distribution functions are calculated for a two-dimensional, noninteracting quantum electron gas in an external magnetic field for any temperature and density. At low temperature and filled lowest Landau level, these functions are identical to the exact distribution functions obtained by Jancovici [Phys. Rev. Lett. 46, 386 (1981)] for the classical two-dimensional one-component plasma (2DOCP) at the special plasma parameter $\ensuremath{\Gamma}=2.$ This establishes that the quantum state with filling factor $\ensuremath{\nu}=1,$ associated with the integral quantum Hall effect, is precisely described by an effective classical potential $\ensuremath{\varphi}(r)=\ensuremath{-}2\mathrm{ln}r,$ so that a classical Boltzmann factor of 2DOCP form can replace the quantum Slater sum. Further, this Boltzmann factor exactly matches that constructed by Laughlin [Phys. Rev. Lett. 50, 1395 (1983)] to account for the fractional quantum Hall effect. Additional effective potentials for higher filling factors $\ensuremath{\nu}=2,3,\dots{}$ are obtained semianalytically from the exact Yvon-Born-Green integral equation and numerically from the approximate hypernetted-chain integral equation. They have the asymptotic form $\ensuremath{\varphi}(r)\ensuremath{\sim}\ensuremath{-}(2/\ensuremath{\nu})\mathrm{ln}r.$

Distribution functions for a two-dimensional non-interacting quantum electron gas in an external magnetic field

The exact n-body distribution functions are calculated for a two-dimensional, non-interacting quantum electron gas in an external magnetic field for any temperature and density. At low tempertures and filled lowest Landau level (LLL), these functions are identical to the exact distribution functions obtained by Jancovici [1981, Phys. Rev. Lett., 46, 386] for the classical two-dimensional one-component plasma (2DOCP) at the special plasma parameter Γ = 2, thus establishing that the 2DOCP provides an exact classical Boltzmann factor which describes the ideal LLL quantum state associated with the integral quantum Hall effect.