Hole Landau Levels Research Articles

Next-generation even-denominator fractional quantum Hall states of interacting composite fermions.

The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors are of particular interest as they may host quasiparticles obeying non-Abelian statistics and be of potential use in topological quantum computing. The even-denominator FQHSs, however, are scarce and have been observed predominantly in low-disorder two-dimensional (2D) systems when an excited electron Landau level is half filled. An example is the well-studied FQHS at filling factor [Formula: see text] 5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at [Formula: see text] 3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahigh-quality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as even-denominator FQHSs of CFs, emerging from pairing of higher-order CFs when a CF Landau level, rather than an electron or a hole Landau level, is half-filled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for even-denominator FQHSs, and suggest the realization of FQHSs with non-Abelian anyons.

ВЫЧИСЛЕНИЕ ТЕМПЕРАТУРНОЙ ЗАВИСИМОСТИ ЭНЕРГЕТИЧЕСКОГО СПЕКТРА НОСИТЕЛЕЙ ЗАРЯДОВ В ПОЛУПРОВОДНИКАХ ПРИ ВОЗДЕЙСТВИИ СИЛЬНОГО МАГНИТНОГО ПОЛЯ

The energy spectrum of free holes in a st rong magnetic field is calculated for a non- quadratic dispersion law. The temperature dependen ce of the broadening of the Landau levels of holes in crystals with the Kane dispersion law has been studied. A new method for calculating the discrete energy spectrum in a quantizing magnetic field is proposed

Optical radiation induced chaotic dynamics of electrons in a uniform magnetic field

We investigate the effects of linearly polarized optical radiation on the cyclotron motion of an electron wave packet, considering the full quantum dynamics of the system. Analysis of the Landau-level (LL) spectrum reveals that only intra band cyclotron oscillation frequencies contribute to the effective oscillation frequency of the motion, whereas scattering between electron and hole Landau levels are forbidden. We find that the wave packet dynamics is significantly affected by varying the polarization direction of the electromagnetic radiation. The optical radiation is also affected by its interaction with electrons. Interestingly, we find that chaotic effects are induced by radiation in the dynamics of electron wave packet in an applied uniform magnetic field. Chaotic signatures in the dynamics are diagnosed by computing the relevant out-of-time-order correlation function and analyzed by using Poincaré maps. We attribute the appearance of such chaotic transport of electron wave packet to the nonlinear interaction between the optical radiation and internal cooperative oscillating mode produced by the interplay of relativistic (zitterbewegung) and cyclotron oscillations.

Orientation of hole quantum Hall nematic phases in an out-of-plane electric field

We present observations of an anisotropic resistance state at Landau level filling factor $\nu=5/2$ in a two-dimensional hole system (2DHS), which occurs for certain values of hole density $p$ and average out-of-plane electric field $E_\perp$. The 2DHS is induced by electric field effect in an undoped GaAs/AlGaAs quantum well, where front and back gates allow independent tuning of $p$ and $E_\perp$, and hence the symmetry of the confining potential. For $p\approx2\times10^{11}$~cm$^{-2}$ and $E_\perp \approx -2 \times10^{5}$~V/m, the magnetoresistance along $\langle01\bar1\rangle$ greatly exceeds that along $\langle011\rangle$, suggesting the formation of a quantum Hall nematic or `stripe' phase. Reversing the sign of $E_\perp$ rotates the stripes by $90^{\circ}$. We suggest this behavior may arise from the mixing of the hole Landau levels and a combination of the Rashba and Dresselhaus spin-orbit coupling effects.

Thermopower and Unconventional Nernst Effect in the Predicted Type-II Weyl Semimetal WTe2.

WTe2 is one of a series of recently discovered high mobility semimetals, some of whose properties are characteristic of topological Dirac or Weyl metals. One of its most interesting properties is the unsaturated giant magnetoresistance that it exhibits at low temperatures. An important question is the degree to which this property can be ascribed to a conventional semimetallic model in which a highly compensated, high mobility metal exhibits large magnetoresistance. Here, we show that the longitudinal thermopower (Seebeck effect) of semimetallic WTe2 exfoliated flakes exhibits periodic sign changes about zero with increasing magnetic field that indicates distinct electron and hole Landau levels and nearly fully compensated electron and hole carrier densities. However, inconsistent with a conventional semimetallic picture, we find a rapid enhancement of the Nernst effect at low temperatures that is nonlinear in magnetic field, which is consistent with Weyl points in proximity to the Fermi energy. Hence, we demonstrate the role played by the Weyl character of WTe2 in its transport properties.

Landau-Level Quantization of the Yellow Excitons in Cuprous Oxide

Lately, the yellow series of P-excitons in cuprous oxide could be resolved up to the principal quantum number n = 25. Adding a magnetic field, leads to additional confinement normal to the field. Thereby, the transition associated with the exciton n is transformed into the transition between the electron and hole Landau levels with quantum number n, once the associated magnetic length becomes smaller than the related exciton Bohr radius. The magnetic field of this transition scales roughly as n–3. As a consequence of the extended exciton series, we are able to observe Landau level transitions with unprecedented high quantum numbers of more than 75.

Landau-level quantization of the yellow excitons in cuprous oxide

AbstractLately, the yellow series of P -excitons in cuprous oxide could be resolved up to the principal quantum number n = 25. Adding a magnetic field, leads to additional confinement normal to the field. Thereby, the transition associated with the exciton n is transformed into the transition between the electron and hole Landau levels with quantum number n , once the associated magnetic length becomes smaller than the related exciton Bohr radius. The magnetic field of this transition scales roughly as n ^–3. As a consequence of the extended exciton series, we are able to observe Landau level transitions with unprecedented high quantum numbers of more than 75.

Scaling laws of Rydberg excitons

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number $n$ for features such as the magnetic field for level crossing. While bearing striking similarities to Rydberg atoms, fundamentally new insights may be obtained for Rydberg excitons, as the crystal environment gives easy optical access to many states within an exciton multiplet. Here we study experimentally and theoretically the scaling of several characteristic parameters of Rydberg excitons with $n$. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a $B_r \propto n^{-4}$ dependence of the resonance field strength, $B_r$, due to the dominant paramagnetic term unlike in the atomic case where the diamagnetic contribution is decisive. By contrast, in electric field we find scaling laws just like for Rydberg atoms. The resonance electric field strength scales as $E_r \propto n^{-5}$. We observe anticrossings of the states belonging to multiplets with different principal quantum numbers. The energy splittings at the avoided crossings scale as $n^{-4}$ which we relate to the crystal specific deviation of the exciton Hamiltonian from the hydrogen model. We observe the exciton polarizability in the electric field to scale as $n^7$. In magnetic field the crossover field strength from a hydrogen-like exciton to a magnetoexciton dominated by electron and hole Landau level quantization scales as $n^{-3}$. The ionization voltages demonstrate a $n^{-4}$ scaling as for atoms. The width of the absorption lines remains constant before dissociation for high enough $n$, while for small $n \lesssim 12$ an exponential increase with the field is found. These results are in excellent agreement with theoretical calculations.

Composite fermion states around the two-dimensional hole Landau level filling factor 32 in tilted magnetic fields

Transport measurements under tilted magnetic fields were performed on a series of C-doped (001) GaAs/AlGaAs two-dimensional hole quantum wells. Due to a large $g$ factor, Zeeman energy is large and comparable to the cyclotron energy in these samples. On the other hand, it was found that the in-plane component ${g}_{\ensuremath{\parallel}}$ is small, and the effect of a tilted magnetic field is mainly to increase the effective mass of the holes. We investigate the spin transition of composite fermion states around Landau level (LL) filling factor 3/2. We found that the $\ensuremath{\nu}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}4/3$ state encounters a partial- to full-spin-polarization transition, conforming to the same pattern as that of electron samples. In addition, a high-resistance phase emerges at $\ensuremath{\nu}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}3/2$ under very high tilt angles. We interpret both of these phenomena as a consequence of LL crossing under a purely perpendicular magnetic field.

Magnetoplasma excitations and the effect of electron and hole velocity renormalization in free-hanging graphene studied by Raman scattering

The properties of plasma and magnetoplasma excitations in free-hanging graphene have been studied for the first time by Raman scattering. In addition to single-particle excitations associated with transitions between empty Landau levels of electrons and holes, collective plasma and magnetoplasma excitations in the system of electrons (and holes) of various densities have been discovered for the first time. Hybridization of plasma and cyclotron modes corresponding to the Kohn law has been shown to occur in the limit of high filling factors, which allows measuring directly the plasma and cyclotron energies. The dependence of the electron and hole velocities on their density has been investigated via the magnetic-field dependence of the cyclotron energy in free-hanging graphene. The effect of strong renormalization of the electron and hole dispersion relations seen as an increase in the velocity (by 40–50%) with a decrease in the charge-carrier density to 1011 cm–2 has been discovered. The charge-carrier density dependences of the widths of magnetoplasma resonances in free-hanging graphene and graphene lying on a silicon dioxide surface have been measured and shown to be at least 3.5 and 14.8 meV, respectively.

Magnetic field dependence of energy levels in biased bilayer graphene quantum dots

Using the tight-binding approach, we study the influence of a perpendicular magnetic field on the energy levels of hexagonal, triangular, and circular bilayer graphene (BLG) quantum dots (QDs) with zigzag and armchair edges. We obtain the energy levels for AB (Bernal)-stacked BLG QDs in both the absence and the presence of a perpendicular electric field (i.e., biased BLG QDs). We find different regions in the spectrum of biased QDs with respect to the crossing point between the lowest-electron and -hole Landau levels of a biased BLG sheet. Those different regions correspond to electron states that are localized at the center, edge, or corner of the BLG QD. Quantum Hall corner states are found to be absent in circular BLG QDs. The spatial symmetry of the carrier density distribution is related to the symmetry of the confinement potential, the position of zigzag edges, and the presence or absence of interlayer inversion symmetry.

Probe of the Band Structure of MBE Grown p-Type InMnAs at Ultrahigh Magnetic Fields

We present a theoretical and experimental study on electronic and magneto-optical properties of p-type paramagnetic InMnAs dilute magnetic semiconductor (DMS) alloys in ultrahigh (> 100 T) external magnetic fields (B). Theoretical calculations are based on an 8-band Pidgeon–Brown model which is generalized to include the wavevector dependence of the electronic states along B as well as s–d and p–d exchange interactions with localized Mn d-electrons. The spin-dependent electronic structure as a function of Mn doping is computed and the dependence of the valence band structure on parameters such as the sp–d exchange interaction strength and effective masses in paramagnetic p- InMnAs alloys are examined. The cyclotron resonance (CR) and magneto-optical properties of InMnAs are calculated using Fermi's golden rule. Two strong CR peaks are observed in p-type InMnAs alloys which correspond to the transitions within either heavy-hole (HH) or light-hole (LH) Landau levels. Furthermore, we also observed strong resonance absorption for electron-active polarization which can occur in p-type semiconductors originating from transitions between the light and heavy hole Landau levels.

Magnetothermoelectric transport properties in graphene superlattices with one-dimensional periodic potentials

We numerically study the thermoelectric transport in graphene superlattice in the presence of a strong magnetic field and disorder, with a one-dimensional periodic potential barrier oriented along the armchair direction of graphene. The thermoelectric coefficients exhibit novel properties as functions of the superlattice period length. When the period length is taken to be the smallest, we find that the thermoelectric transport exhibits properties similar to those in the absence of the superlattice potential. The thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs). In the high-temperature regime, the transverse thermoelectric conductivity saturates to a universal value at the center of each LL, and displays a linear temperature dependence at low temperatures. We attribute this unique behavior to the coexistence of particle and hole LLs. Both the Nernst signal and the thermopower show a large peak around the central LL. However, with increasing the superlattice period length, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. displays a pronounced valley at low temperatures. This behavior can be understood as due to the split of the valley degeneracy in the central LL. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the superlattice period length.

Fractional Quantum Hall Effect atν=1/2in Hole Systems Confined to GaAs Quantum Wells

We observe the fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor ν=1/2 in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50nm and having bilayerlike charge distributions. The ν=1/2 FQHE is stable when the charge distribution is symmetric and only in a range of intermediate densities, qualitatively similar to what is seen in two-dimensional electron systems confined to approximately twice wider GaAs quantum wells. Despite the complexity of the hole Landau level structure, originating from the coexistence and mixing of the heavy- and light-hole states, we find the hole ν=1/2 FQHE to be consistent with a two-component, Halperin-Laughlin (Ψ331) state.

Magnetoabsorption in narrow-gap HgCdTe epitaxial layers in the terahertz range

The magnetoabsorption and photoconductivity spectra are investigated in the terahertz (THz) range at a temperature of T = 4.2 K for n-Hg1 − xCdxTe bulk epitaxial layers of various compositions (both semiconductor and semimetallic) grown by molecular-beam epitaxy. Within the framework of the Kane 8 · 8 model, the electron and hole Landau levels are calculated. It is shown that, in contrast to the results of previous investigations, all observed resonance lines are related to transitions between the Landau levels of free carriers (the cyclotron resonance in the conduction band and the transitions between heavy-hole and electron Landau levels), which is evidence of the high purity and structural perfection of the samples. The possibility of using zero-gap Hg1 − xCdxTe solid solutions as THz photodetectors tunable by magnetic field is shown.

Cyclotron resonance in HgCdTe-based heterostructures in strong magnetic fields

Cyclotron resonance (CR) study of HgCdTe-based quantum wells with both inverted and normal band structures in quantizing magnetic fields was performed. In normal-band sample in addition to electron CR transitions a strong absorption line presumably related to impurity transitions was discovered. Anticrossing of electron and hole Landau levels was observed in inverted-band sample. In semimetallic HgTe quantum wells with inverted band structure, a hole CR line was observed for the first The obtained results were interpreted within the Kane 8 × 8 model, the valence band offset of CdTe and HgTe, and the Kane parameter EP being adjusted.

Layer stacking dependence on thermoelectric properties of massive Dirac fermions in bilayer graphene

We numerically study the thermoelectric transport in AB- and AA-stacked bilayer graphene in the presence of a strong magnetic field and disorder. In the AB-stacked case, we find that the thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs), similar to those of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity α xy saturates to a universal value 5.54k B e/h at the center of each LL, and displays a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak with a height of the order of k B /e, and the thermopower changes sign at the central LL. We attribute this unique behavior to the coexistence of particle and hole LLs. In the AA-stacked bilayer case, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point.

THERMOELECTRIC TRANSPORT PROPERTIES IN TRILAYER GRAPHENE SYSTEMS

We numerically study the thermoelectric transport properties in trilayer graphene in the presence of a strong perpendicular magnetic field and disorder. In the unbiased case, we find that the thermoelectric transport has similar properties as in monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity αxy saturates to a universal value 8.31 kBe/h at the center of each Landau level (LL), and displays a linear temperature dependence at low temperatures. The Nernst signal has a peak at the central LL with a height of the order of kB/e, while the thermopower changes sign. We attribute this to the coexistence of particle and hole LLs around the Dirac point. When a finite interlayer bias is applied and a band gap is opened, it is found that the transport properties are consistent with those of a band insulator.

Long spin relaxation time of holes in InGaAs/GaAs quantum wells probed by cyclotron resonance spectroscopy

In this paper, we report on a long, ms range, hole spin relaxation time in InGaAs/GaAs quantum wells probed by cyclotron resonance spectroscopy in pulsed magnetic fields. In our experiments, we found strong hysteresis in the spectral weights of cyclotron resonance absorption lines when rapidly changing magnetic field is used for the experiment. The hysteresis vanishes when a much slower changing magnetic field is used. We attribute this behavior to a long energy relaxation time between the two lowest spin-split hole Landau levels, i.e., a long hole spin relaxation time. We also present transition frequencies calculated using a $4\ifmmode\times\else\texttimes\fi{}4$ Luttinger Hamiltonian, which confirm our findings.

Landau spectrum and twin boundaries of bismuth in the extreme quantum limit

The Landau spectrum of bismuth is complex and includes many angle-dependent lines in the extreme quantum limit. The adequacy of single-particle theory to describe this spectrum in detail has been an open issue. Here, we present a study of angle-resolved Nernst effect in bismuth, which maps the angle-resolved Landau spectrum for the entire solid angle up to 28T. The experimental map is in good agreement with the results of a theoretical model with parabolic dispersion for holes and an extended Dirac Hamiltonian for electrons. The angular dependence of additional lines in the Landau spectrum allows us to uncover the mystery of their origin. They correspond to the lines expected for the hole Landau levels in a secondary crystal tilted by 108°, the angle between twinned crystals in bismuth. According to our results, the electron reservoirs of the two identical tilted crystals have different chemical potentials, and carriers across the twin boundary have different concentrations. An exceptional feature of this junction is that it separates two electron-hole compensated reservoirs. The link between this edge singularity and the states wrapping a three-dimensional electron gas in the quantum limit emerges as an outstanding open question.