Higher Landau Levels Research Articles

Surface-step defect in three-dimensional topological insulators: Electric manipulation of spin and quantum spin Hall effect

We study the influence of step defect on surface states in three-dimensional topological insulators subject to a perpendicular magnetic field. By calculating the energy spectrum of the surface states, we find that Landau levels (LLs) can form on flat regions of the surface and are distant from the step defect, and several subbands emerge at side surface of the step defect. The subband which connects to the two zeroth LLs is spin-polarized and chiral. In particular, when the electron transports along the side surface, the electron spin direction can be manipulated arbitrarily by gate voltage. And no reflection occurs even if the electron spin direction is changed. This provides a fascinating avenue to control the electron spin easily and coherently. In addition, regarding the subbands with high LL index, there exist spin-momentum locking helical states and the quantum spin Hall effect can appear.

Energy loss of a nonaccelerating quark moving through a strongly coupledN=4super Yang-Mills vacuum or plasma in strong magnetic field

Using AdS/CFT correspondence, we find that a massless quark moving at the speed of light $v=1$, in arbitrary direction, through a strongly coupled $\mathcal{N}=4$ super Yang-Mills (SYM) vacuum at $T=0$, in the presence of strong magnetic field $\mathcal{B}$, loses its energy at a rate linearly dependent on $\mathcal{B}$, i.e., $\frac{dE}{dt}=-\frac{\sqrt{\lambda}}{6\pi}\mathcal{B}$. We also show that a heavy quark of mass $M\neq 0$ moving at near the speed of light $v^2=v_{*}^2=1-\frac{4\pi^2 T^2}{\mathcal{B}}\simeq1$, in arbitrary direction, through a strongly coupled $\mathcal{N}=4$ SYM plasma at finite temperature $T\neq 0$, in the presence of strong magnetic field $\mathcal{B}\gg T^2$, loses its energy at a rate linearly dependent on $\mathcal{B}$, i.e., $\frac{dE}{dt}=-\frac{\sqrt{\lambda}}{6\pi}\mathcal{B}v_{*}^2\simeq-\frac{\sqrt{\lambda}}{6\pi}\mathcal{B}$. Moreover, we argue that, in the strong magnetic field $\mathcal{B}\gg T^2$ (IR) regime, $\mathcal{N}=4$ SYM and adjoint QCD theories (when the adjoint QCD theory has four flavors of Weyl fermions and is at its conformal IR fixed point $\lambda=\lambda^*$) have the same microscopic degrees of freedom (i.e., gluons and lowest Landau levels of Weyl fermions) even though they have quite different microscopic degrees of freedom in the UV when we consider higher Landau levels. Therefore, in the strong magnetic field $\mathcal{B}\gg T^2$ (IR) regime, the thermodynamic and hydrodynamic properties of $\mathcal{N}=4$ SYM and adjoint QCD plasmas, as well as the rates of energy loss of a quark moving through the plasmas, should be the same.

Positive magnetoconductivity of Weyl semimetals in the ultraquantum limit

In this paper, we numerically study the magnetic transport properties of disordered Weyl semimetals (WSM) in the ultra-quantum limit. We find a positive magnetic conductivity for the long-range disorder, although the system tends to have negative magnetic conductivity for the weak short-range disorder. Remarkably, for long-range disorder, such a positive magnetic conductivity cannot be described by the semiclassical Boltzmann transport theory even in the weak disorder limit, and the back-scattering assisted by the high Landau levels is always important. Our results have significant implications for the positive magnetic conductivity recently discovered in the WSM systems, and point out two physical mechanisms: (i) the long-range correlated disorder suppresses the back-scattering among the zeroth Landau level modes; (ii) with increasing the magnetic field, the back-scattering assisted by the high Landau levels will also be suppressed.

Reorientation of quantum Hall stripes within a partially filled Landau level

We investigate the effect of the filling factor on transport anisotropies, known as stripes, in high Landau levels of a two-dimensional electron gas. We find that at certain in-plane magnetic fields, the stripes orientation is sensitive to the filling factor within a given Landau level. This sensitivity gives rise to the emergence of stripes away from half-filling while an orthogonally-oriented, native stripes reside at half-filling. This switching of the anisotropy axes within a single Landau level can be attributed to a strong dependence of the native symmetry breaking potential on the filling factor.

Transport coefficients and Nernst signal of type-II superconductors under magnetic field

In this paper, we have studied the transport properties in two-dimensional superconductors in the frame of the Langevin approach to the time dependent Ginzburg–Landau equation. The electrical and thermoelectric conductivity, resulting from thermal fluctuations of the superconducting order parameter, are computed in the self-consistent Gaussian approximation for an arbitrarily strong electric field and a magnetic field. The Nernst signal, describing the Nernst effect in type-II superconductor under a magnetic field, is also calculated in linear response limit. We obtain analytical expressions for the electrical conductivity, the thermoelectric conductivity and the Nernst signal summing all Landau levels without need to cutoff higher Landau levels to treat an arbitrary magnetic field. Our results indicate that the electrical and thermoelectric conductivity are suppressed in high electric fields and the Nernst signal is in good agreement with experimental data on [Formula: see text].

Commensurability condition and hierarchy of fillings for FQHE in higher Landau levels in conventional 2DEG systems and in graphene—monolayer and bilayer

The structure of the filling rate hierarchy referred to as the fractional quantum Hall effect is studied in higher Landau levels using the commensurability condition. The hierarchy of fillings that are derived in this manner is consistent with the experimental observations of the first three Landau levels in conventional semiconductor Hall systems. The relative poverty of the fractional structure in higher Landau levels compared with the lowest Landau level is explained using commensurability topological arguments. The commensurability criterion for correlated states for higher Landau levels (with ) including the paired states at half fillings of the spin-subbands of these levels is formulated. The commensurability condition is applied to determine the hierarchy of the fractional fillings of Landau levels in the monolayer and bilayer graphene. Good agreement with current experimental observations of fractional quantum Hall effect in the graphene monolayer and bilayer is achieved. The presence of even denominator rates in the hierarchy for fractional quantum Hall effect in the bilayer graphene is also explained.

Heterostructure symmetry and the orientation of the quantum Hall nematic phases

Clean two-dimensional electron systems in GaAs/AlGaAs heterostructures exhibit anisotropic collective phases, the quantum Hall nematics, at high Landau level occupancy and low temperatures. An as yet unknown native symmetry-breaking potential consistently orients these phases relative to the crystalline axes of the host material. Here we report an extensive set of measurements examining the role of the structural symmetries of the heterostructure in determining the orientation of the nematics. In single quantum well samples we find that neither the local symmetry of the confinement potential nor the distance between the electron system and the sample surface dictates the orientation of the nematic. In remarkable contrast, for two-dimensional electrons confined at a single heterointerface between GaAs and AlGaAs, the nematic orientation depends on the depth of the two-dimensional electron system beneath the sample surface.

Quantum Hall conductance of graphene combined with charge-trap memory operation

The combination of quantum Hall conductance and charge-trap memory operation was qualitatively examined using a graphene field-effect transistor. The characteristics of two-terminal quantum Hall conductance appeared clearly on the background of a huge conductance hysteresis during a gate-voltage sweep for a device using monolayer graphene as a channel, hexagonal boron-nitride flakes as a tunneling dielectric and defective silicon oxide as the charge storage node. Even though there was a giant shift of the charge neutrality point, the deviation of quantized resistance value at the state of filling factor 2 was less than 1.6% from half of the von Klitzing constant. At high Landau level indices, the behaviors of quantum conductance oscillation between the increasing and the decreasing electron densities were identical in spite of a huge memory window exceeding 100 V. Our results indicate that the two physical phenomena, two-terminal quantum Hall conductance and charge-trap memory operation, can be integrated into one device without affecting each other.

Magnetized plasminos in cold and hot QED plasmas

The complete quasiparticle spectrum of a magnetized electromagnetic plasma is systematically explored at zero and nonzero temperatures. To this purpose, the general structure of the one-loop corrected propagator of magnetized fermions is determined, and the dispersion relations arising from the pole of this propagator are numerically solved. It turns out that in the lowest Landau level, where only one spin direction is allowed, the spectrum consists of one positively (negatively) charged fermionic mode with positive (negative) spin. In contrast, in higher Landau levels, as an indirect consequence of the double spin degeneracy of fermions, the spectrum consists of two massless collective modes with left and right chiralities. The mechanism through which these new collective excitations are created in a uniform magnetic field is similar to the production mechanism of dynamical holes (plasminos) at finite temperature and zero magnetic fields. Whereas cold magnetized plasminos appear for moderate magnetic fields and for all positive momenta of propagating fermions, hot magnetized plasminos appear only in the limit of weak magnetic fields and soft momenta.

Commensurability condition and fractional quantum Hall effect hierarchy in higher Landau levels

The odd structure of the fractional filling hierarchy, which is referred to as the fractional quantum Hall effect, is studied in higher Landau levels using the commensurability condition. The hierarchy of fillings that are derived in this manner is consistent with the experimental observations in the first three Landau levels. The relative poverty of the fractional structure in higher Landau levels compared with the lowest Landau level is explained using commensurability topological arguments. The commensurability criterion for correlated states specific for higher Landau levels (with n ≥ 1), including also the paired states at half fillings of the spinsubbands of these levels, is formulated.

Second Landau level fractional quantum Hall effects in the Corbino geometry

For certain measurements, the Corbino geometry has a distinct advantage over the Hall and van der Pauw geometries, in that it provides a direct probe of the bulk 2DEG without complications due to edge effects. This may be important in enabling detection of the non-Abelian entropy of the 5/2 fractional quantum Hall state via bulk thermodynamic measurements. We report the successful fabrication and measurement of a Corbino-geometry sample in an ultra-high mobility GaAs heterostructure, with a focus on transport in the second and higher Landau levels. In particular, we report activation energy gaps of fractional quantum Hall states, with all edge effects ruled out, and extrapolate the conductivity prefactor from the Arrhenius fits. Our results show that activated transport in the second Landau level remains poorly understood. The development of this Corbino device opens the possibility to study the bulk of the 5/2 state using techniques not possible in other geometries.

Depinning transition of bubble phases in a high Landau level

While in the lowest Landau level the electron-electron interaction leads to the formation of the Wigner crystal, in higher Landau levels a solid phase with multiple electrons in a lattice site of crystal was predicted, which was called the bubble phase. Reentrant integer quantum Hall states are believed to be the insulating bubble phase pinned by disorder. We carry out nonlinear transport measurements on the reentrant states and study the de-pinning of the bubble phase, which is complementary to previous microwave measurements and provides unique information. In this study, conductivity is directly measured with Corbino geometry. Based on the threshold electric field of de-pinning, a phase diagram of the reentrant state is mapped. We discuss an interaction-driven topological phase transition between the integer quantum Hall state and the reentrant integer quantum Hall state.

Magnetoconductance of the Corbino disk in graphene: chiral tunneling and quantum interference in the bilayer case

Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, using the mode-matching method to give an effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Rycerz 2010 Phys. Rev. B 81 121404; Katsnelson 2010 Europhys. Lett. 89 17001), conductance at the Dirac point shows oscillations with the flux piercing the disk area ΦD characterized by the period Φ0 = 2 (h/e) ln(Ro/Ri), where Ro(Ri) is the outer (inner) disk radius. The oscillation magnitude depends either on the radii ratio or on the physical disk size, with the condition for maximal oscillations being Ro/Ri ≃ [ Rit⊥/(2ℏvF) ]4/p (for Ro/Ri ≫ 1), where t⊥ is the interlayer hopping integral, vF is the Fermi velocity in graphene, and p is an even integer. Odd-integer values of p correspond to vanishing oscillations for the normal Corbino setup, or to oscillation frequency doubling for the Andreev–Corbino setup. At higher Landau levels, magnetoconductance behaves almost identically in the monolayer and bilayer cases. A brief comparison with the Corbino disk in a two-dimensional electron gas is also provided in order to illustrate the role of chiral tunneling in graphene.

Ising quantum Hall ferromagnetism in Landau levels|N|≥1of bilayer graphene

A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG) in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,....$ While Landau level $N=0$ is eightfold degenerate, higher Landau levels $(|N|\ensuremath{\ge}1)$ are fourfold degenerate when spin and valley degrees of freedom are counted. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}=1,2,3$ of these higher Landau levels. At these filling factors, the C2DEG is a valley or spin Ising quantum Hall ferromagnet. At odd fillings, the C2DEG is spin polarized and has all its electrons in one valley or the other. There is no intervalley coherence, in contrast with most of the ground states in Landau level $N=0.$ At even filling $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}=2,$ the C2DEG is either fully spin polarized with electrons occupying both valleys or spin unpolarized with electrons occupying one of the two valleys. A finite electric field (or bias) applied perpendicularly to the plane of the C2DEG induces a series of first-order phase transitions between these different ground states. The transport gap or its slope is discontinuous at the bias where a transition occurs. Such discontinuity may result in a change in the transport properties of the C2DEG at that bias.

Quantized escape and formation of edge channels at high Landau levels and edge transport mediated zero-differential resistance states

We present nonlocal resistance measurements in an ultrahigh-mobility two-dimensional electron gas. Our experiments show that even at weak magnetic fields, classical guiding along edges leads to a strong nonlocal resistance on macroscopic distances. In this high Landau level regime, the transport along edges is dissipative and can be controlled by the amplitude of the voltage drop along the edge. We report resonances in the nonlocal transport as a function of this voltage that are interpreted as escape and formation of edge channels, and the formation of zero-differential resistance states when the nonlocal voltage is measured on length scales much larger than the mean free path.

Plateaus in the Hall Resistance Curve at Filling Factors 2

The fractional quantum Hall (FQH) states with higher Landau levels have new characters different from those with 0<ν<2. The FQH states at 2<ν<3 are examined by developing the Tao-Thouless theory. We can find a unique configuration of electrons with the minimum Coulomb energy in the Landau orbitals. Therein the electron (or hole) pairs placed in the first and second nearest Landau orbitals can transfer to all the empty (or filled) orbitals at ν0=8/3, 14/5, 7/3, 11/5, and 5/2 via the Coulomb interaction. More distant electron (or hole) pairs with the same centre position have the same total momentum. Therefore, these pairs can also transfer to all the empty (or filled) orbitals. The sum of the pair energies from these quantum transitions yields a minimum at ν=ν0. The spectrum of the pair energy takes the lowest value at ν0 and a higher value with a gap in the neighbourhood of ν0 because many transitions are forbidden at a deviated filling factor from ν0. From the theoretical result, the FQH states with ν=ν0 are stable and the plateaus appear at the specific filling factors ν0.

Landau levels in lattices with long-range hopping

In the presence of a periodic potential Landau levels (LLs) are broadened, forming a barrier for accurate simulation of fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight binding lattice, if a particular form of long range hopping is introduced [E. Kapit and E. J. Mueller, Phys. Rev. Lett. 105, 215303 (2010)]. In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are infinitely many long range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wavefunctions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restore the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wavefunctions is as large as the space spanned by continuum wavefunctions and find the constraints on magnetic field for this condition to be satisfied. Finally, using these constraints and first Chern numbers, we identify the bands of the Hofstadter butterfly that correspond to continuum LLs.

The Polyanalytic Ginibre Ensembles

We consider a polyanalytic generalization of the Ginibre ensemble. This models allowing higher Landau levels (the Ginibre ensemble corresponds to the lowest Landau level). We study the local behavior of this point process under blow-ups.

Role of crystal anisotropy on the vortex state in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase

We demonstrate that the vortex state in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase may be very different depending on the field orientation relative to the crystalline axes. We calculate numerically the upper critical field near the tricritical point taking into account the modulation of the order parameter along the magnetic field as well as the higher Landau levels. For s-wave superconductors with the anisotropy described by an elliptical Fermi surface we propose a general scheme of the analysis of the angular dependence of upper critical field at all temperatures on the basis of the exact solution for the order parameter. Our results show that the transitions (with tilting magnetic field) between different types of mixed states may be a salient feature of the FFLO phase. Moreover we discuss the reasons for the first-order phase transition into the FFLO state in the case of CeCoIn5 compound.

Anisotropy in a high Landau level due to effective electron-electron interactions

Quantization of Hall resistivity in strongly correlated two-dimensional electronic systems at high magnetic fields generally indicates the stabilization of novel electronic quantum liquid phases of matter. This is the nature of the integer and fractional quantum Hall states that stabilize at integer and fractional odd-denominator (not always, though) filling factors of the Landau level. Away from certain filling factors that represent quantum Hall liquid states, different phases, some of them with unusually high magneto-transport anisotropy have been known to stabilize specially in high Landau levels. In this work, we try to understand this anisotropic behaviour in terms of effective electron-electron interaction potentials. To this effect, we implement a full projection of the original Coulomb interaction potential in the suitable Landau level. We find out that, in high Landau levels, thus for relatively weak magnetic fields, a semi-classical description of the interaction potential between electrons appear to be an adequate choice. The features of this semi-classical interaction potential in this limit suggest ways how the energetic balance between density waves and/or liquid crystalline phases might be sensitively affected.