Unconventional Quantum Hall Effect Research Articles

Low field hall effect for differentiating between the single- and double-layer graphenes

There is a number of powerful but costly and involved experimental techniques able to distinguish between the single- and double-layer graphene films. Here we suggest a less rigorous but easier test, which can be performed on a suspended or hexagonal boron nitride encapsulated graphene in low magnetic fields and at room temperatures. The test is based on the same physical property that is responsible for the unconventional quantum Hall effect in single-layer graphene—the cyclotron frequency dependence on the Fermi energy.

Unconventional reentrant quantum Hall effect in a HgTe/CdHgTe double quantum well

We report on observation of an unconventional structure of the quantum Hall effect (QHE) in a $ p$-type HgTe/Cd$_x$Hg$_{1-x}$Te double quantum well (DQW) consisting of two HgTe layers of critical width. The observed QHE is a reentrant function of magnetic field between two $i=2$ states (plateaus at $\rho_{xy}=h/ie^2$) separated by an intermediate $i=1$ state, which looks like some anomalous peak on the extra-long $i=2$ plateau when weakly expressed. The anomalous peak apparently separates two different regimes: a traditional QHE at relatively weak fields for a small density of mobile holes $p_s$ and a high-field QH structure with a $2-1$ plateau--plateau transition corresponding to much larger $p_s$. We show that only a part of holes, residing in an additional light hole subband in the DQW, participate in QHE at weak fields while the rest of holes is excluded into the reservoir formed in the lateral maximum of the valence subband. All the holes come into play at high fields due to a peculiar behavior of the zero-mode levels.

Integer quantum Hall effect and topological phase transitions in silicene

We numerically investigate the effects of disorder on the quantum Hall effect (QHE) and the quantum phase transitions in silicene based on a lattice model. It is shown that for a clean sample, silicene exhibits an unconventional QHE near the band center, with plateaus developing at $\nu=0,\pm2,\pm6,\ldots,$ and a conventional QHE near the band edges. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center, in which higher plateaus disappear first. However, the center $\nu=0$ Hall plateau is more sensitive to disorder and disappears at a relatively weak disorder strength. Moreover, the combination of an electric field and the intrinsic spin-orbit interaction (SOI) can lead to quantum phase transitions from a topological insulator to a band insulator at the charge neutrality point (CNP), accompanied by additional quantum Hall conductivity plateaus.

Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems

Unconventional fermions with high degeneracies in three dimensions beyond Weyl and Dirac fermions have sparked tremendous interest in condensed matter physics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D) unconventional fermion system with a pair of gapped spin-1 fermions. We find that the original unlimited number of zero energy Landau levels (LLs) in the gapless case develop into a series of bands, leading to a novel QHE phenomenon that the Hall conductance first decreases (or increases) to zero and then revives as an infinite ladder of fine staircase when the Fermi surface is moved toward zero energy, and it suddenly reverses with its sign being flipped due to a Van Hove singularity when the Fermi surface is moved across zero. We further investigate the peculiar QHEs in a dice model with a pair of spin-1 fermions, which agree well with the results of the continuous model.

Unconventional fractional quantum Hall effect in bilayer graphene

Recent experimental progress in Hall measurements in bilayer graphene in the so-called open-face configuration of boron nitride encapsulated samples, together with the earlier technique of suspended samples, allows for precise observation of the fractional quantum Hall effect (FQHE) in all 4 subbands of the Lowest Landau level (with n = 0 and n = 1) and in the next LL subbands (with n = 2) in the bilayer system. Many newly observed FQHE features do not agree with a conventional model of composite fermions and reveal a different hierarchy in comparison to monolayer graphene or GaAs 2DEG. We explain the peculiarity of the FQHE hierarchy in the bilayer system in the framework of a topological approach, which includes the composite fermion model as its special case. Inclusion of a topological effect caused by the hopping of electrons between the two sheets in the bilayer system allowed for an explanation of the FQHE hierarchy in the graphene bilayer in satisfactory accordance with the experimental observations.

Signatures of lattice geometry in quantum and topological Hall effect

The topological Hall effect (THE) of electrons in skyrmion crystals (SkXs) is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the SkX (THE) or of the corresponding Landau levels (QHE). Striking features in the energy dependence of the Hall conductivities are traced back to the band structure without magnetic field whose properties are dictated by the lattice geometry. Based on these findings, we derive an approximation that allows us to determine the energy dependence of the topological Hall conductivity on any two-dimensional lattice. The validity of this approximation is proven for the honeycomb lattice. We conclude that SkXs lend themselves for experiments to validate our findings for the THE and—indirectly—the QHE.

Valley- and spin-polarized Landau levels in monolayer WSe2

Electrons in monolayer transition metal dichalcogenides are characterized by valley and spin quantum degrees of freedom, making it possible to explore new physical phenomena and to foresee novel applications in the fields of electronics and optoelectronics. Theoretical proposals further suggest that Berry curvature effects, together with strong spin-orbit interactions, can generate unconventional Landau levels (LLs) under a perpendicular magnetic field. In particular, these would support valley- and spin-polarized chiral edge states in the quantum Hall regime. However, this unique LL structure has not been observed experimentally in transition metal dichalcogenides. Here we report the observation of fully valley- and spin-polarized LLs in high-quality WSe2 monolayers achieved by exploiting a van der Waals heterostructure device platform. We applied handedness-resolved optical reflection spectroscopy to probe the inter-LL transitions at individual valleys and derived the LL structure in turn. We also measured a sizeable doping-induced mass renormalization driven by the strong Coulomb interactions.

Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states

Numerical studies by W\'ojs, Yi and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors $\nu=$ 1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel dominates. The interaction between composite fermions in the second $\Lambda$ level (composite fermion analog of the electronic Landau level) satisfies this property, and recent studies have supported unconventional fractional quantum Hall effect of composite fermions at $\nu^*=$ 4/3 and 5/3, which manifests as fractional quantum Hall effect of electrons at $\nu=$ 4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at $\nu=$ 4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at $\nu^*=$ 4/3, 5/3 and 6/5, and find that all these fractional quantum Hall states are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman energies for the spin phase transitions between them. I calculate the excitation gaps at 4/5, 5/7, 6/7, and 6/17 and compare them against recent experiments.

Phase transitions in two tunnel-coupled HgTe quantum wells: Bilayer graphene analogy and beyond.

HgTe quantum wells possess remarkable physical properties as for instance the quantum spin Hall state and the “single-valley” analog of graphene, depending on their layer thicknesses and barrier composition. However, double HgTe quantum wells yet contain more fascinating and still unrevealed features. Here we report on the study of the quantum phase transitions in tunnel-coupled HgTe layers separated by CdTe barrier. We demonstrate that this system has a 3/2 pseudo spin degree of freedom, which features a number of particular properties associated with the spin-dependent coupling between HgTe layers. We discover a specific metal phase arising in a wide range of HgTe and CdTe layer thicknesses, in which a gapless bulk and a pair of helical edge states coexist. This phase holds some properties of bilayer graphene such as an unconventional quantum Hall effect and an electrically-tunable band gap. In this “bilayer graphene” phase, electric field opens the band gap and drives the system into the quantum spin Hall state. Furthermore, we discover a new type of quantum phase transition arising from a mutual inversion between second electron- and hole-like subbands. This work paves the way towards novel materials based on multi-layered topological insulators.

Unconventional quantum Hall effect in Floquet topological insulators

We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light’s polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity at zero Fermi energy, to a Hall insulator state with . These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at .

Unconventional fractional quantum Hall effect in monolayer and bilayer graphene

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition.

Gapped excitations of unconventional fractional quantum Hall effect states in the second Landau level

We report the observation of low-lying collective charge and spin excitations in the second Landau level at $\ensuremath{\nu}=2+1/3$ and also for the very fragile states at $\ensuremath{\nu}=2+2/5$ and $2+3/8$ in inelastic light scattering experiments. These modes exhibit a clear dependence on filling factor and temperature substantiating the unique access to the characteristic neutral excitation spectra of the incompressible fractional quantum Hall effect (FQHE) states. A detailed mode analysis reveals low-energy modes at around 70 $\ensuremath{\mu}\mathrm{eV}$ and a sharp mode slightly below the Zeeman energy interpreted as gap and spin-wave excitation, respectively. The lowest-energy collective charge excitation spectrum at $\ensuremath{\nu}=2+1/3$ exhibits significant qualitative similarities with its cousin state in the lowest Landau level at $\ensuremath{\nu}=1/3$ suggesting similar magnetoroton minima in the neutral excitations. The mode energies differ by a scaling of 0.15 indicating different interaction physics in the $N=0$ and $N=1$ Landau levels. The striking polarization dependence in elastic and inelastic light scattering is discussed in the framework of anisotropic electron phases that allow for the stabilization of nematic FQHE states. The observed excitation spectra provide new insights by accessing quantum phases in the bulk of electron systems and facilitate comparison with different theoretical descriptions of those enigmatic FQHE states.

Magnetic crystals and helical liquids in alkaline-earth fermionic gases.

The joint action of a magnetic field and of interactions is crucial for the appearance of exotic quantum phenomena, such as the quantum Hall effect. Owing to their rich nuclear structure, equivalent to an additional synthetic dimension, one-dimensional alkaline-earth(-like) fermionic gases with synthetic gauge potential and atomic contact repulsion may display similar related properties. Here we show the existence and the features of a hierarchy of fractional insulating and conducting states by means of analytical and numerical methods. We demonstrate that the gapped states are characterized by density and magnetic order emerging solely for gases with effective nuclear spin larger than 1/2, whereas the gapless phases can support helical modes. We finally argue that these states are related to an unconventional fractional quantum Hall effect in the thin-torus limit and that their properties can be studied in state-of-the-art laboratories.

Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. We discuss possible experimental measurements of the half-integer Hall conductance $g_{xy}$ of topological insulator surface states and explain how to reconcile Laughlin's flux insertion argument with half-integer $g_{xy}$. Using a vortex state representation of Landau Level wavefunctions, we calculate current density beyond linear response, which is in particular relevant to the topological image monopole effect. As a major result, the field theory describing the localization physics of the quantum Hall effect of a single species of Dirac fermions is derived. In this connection, the issue of (absent) parity anomaly is revisited. The renormalization group flow (RG) and the resulting phase diagram are extensively discussed. Starting values of the RG flow are given by the semiclassical conductivity tensor which is obtained from the Boltzmann transport theory of the anomalous Hall effect.

Erratum: Enigmatic4/11State: A Prototype for Unconventional Fractional Quantum Hall Effect [Phys. Rev. Lett. 112, 016801 (2014)

Erratum: Enigmatic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>4</mml:mn><mml:mo>/</mml:mo><mml:mn>11</mml:mn></mml:mrow></mml:math>State: A Prototype for Unconventional Fractional Quantum Hall Effect [Phys. Rev. Lett. 112, 016801 (2014)

Quantum Hall effect of Haldane model under magnetic field

Haldane model can realize the anomalous quantum Hall effect (QHE) without Landau levels (LLs) and serves as a prototype of the quantum spin Hall effect. In this paper, we study the QHE of Haldane model under magnetic field with magnitude such that the magnetic flux in a plaquette is commensurate with the lattice structure. First, we show the origin of unconventional QHE in graphene and point out a general rule for the Hall step of Dirac fermions, which strongly depends on the valley degeneracy of each LL. Second, we study the conductance around the neutral point which lies in the gap given by continuous bands, revealing the competition between periodic magnetic flux and uniform magnetic field. Moreover, the redistribution behavior of Chern number is investigated. We find that besides the staggered magnetic flux, the next-nearest-neighbor hopping can also induce the redistribution. We also study the QHE of the extended Haldane model on a square lattice.

Realising Haldane's vision for a Chern insulator in buckled lattices

The Chern insulator displays a quantum Hall effect with no net magnetic field. Proposed by Haldane over 20 years ago, it laid the foundation for the fields of topological order, unconventional quantum Hall effects, and topological insulators. Despite enormous impact over two decades, Haldane's original vision of a staggered magnetic field within a crystal lattice has been prohibitively difficult to realise. In fact, in the original paper Haldane stresses his idea is probably merely a toy model. I show that buckled lattices with only simple hopping terms, within in-plane magnetic fields, can realise these models, requiring no exotic interactions or experimental parameters. As a concrete example of this very broad, and remarkably simple principle, I consider silicene, a honeycomb lattice with out-of-plane sublattice anisotropy, in an in-plane magnetic field, and show that it is a Chern insulator, even at negligibly small magnetic fields, which is analogous to Haldane's original model.

Theory of unconventional quantum Hall effect in strained graphene

We show through both theoretical arguments and numerical calculations that graphene discerns an unconventional sequence of quantized Hall conductivity, when subject to both magnetic fields ($B$) and strain. The latter produces time-reversal symmetric pseudo/axial magnetic fields ($b$). The single-electron spectrum is composed of two interpenetrating sets of Landau levels (LLs), located at $\ifmmode\pm\else\textpm\fi{}\sqrt{2n|b\ifmmode\pm\else\textpm\fi{}B|}$, $n=0,1,2,...$. For $b&gt;B$, these two sets of LLs have opposite chiralities, resulting in oscillating Hall conductivity between 0 and $\ensuremath{\mp}2{e}^{2}/h$ in electron and hole doped systems, respectively, when the chemical potential is tuned in the vicinity of the neutrality point. The electron-electron interactions stabilize various correlated ground states, e.g., spin-polarized, quantum spin Hall insulators at and near the neutrality point, and possibly the anomalous Hall insulating phase at incommensurate filling $\ensuremath{\sim}$$B$. Such broken-symmetry ground states have similarities as well as significant differences from their counterparts in the absence of strain. For realistic strength of magnetic fields and interactions, we present scaling of the interaction-induced gap for various Hall states within the zeroth Landau level.

Berry phase and pseudospin winding number in bilayer graphene

Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of 2pi [K. S. Novoselov et al., "Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene", Nature Phys. 2, 177 (2006)], it has been widely accepted that the low-energy electronic wavefunction in this system is described by a non-trivial Berry phase of 2pi, different from the zero phase of a conventional two-dimensional electron gas. Here, we show that (i) the relevant Berry phase for bilayer graphene is not different from that for a conventional two-dimensional electron gas (as expected, given that Berry phase is only meaningful modulo 2pi) and that (ii) what is actually observed in the quantum Hall measurements is not the absolute value of the Berry phase but the pseudospin winding number.

Quantum Hall effect in kagomé lattices under staggered magnetic field

The interplay of staggered magnetic field (SMF) and uniform magnetic field (UMF) on the quantum Hall effect (QHE) in kagomé lattices is investigated in the weak UMF limit. The topological band gaps coming from SMF are robust against UMF although the extended bands split into a series of Landau levels. With SMF applied, in the unconventional QHE region, one plateau of Hall conductance becomes wider and the others are compressed. Meanwhile, one of the two series of integer Hall plateaus splits and the resulting two series of Hall plateaus still exhibit the integer behavior. The Hall conductance varies with SMF step by step with the step height being e2/h or 2e2/h according to the QHE being conventional or unconventional. In the transitional regions, redistribution of Chern numbers happens even in the weak UMF limit.