Hall Plateaus Research Articles

Thermopower of quantum Hall states in Corbino geometry as a measure of quasiparticle entropy

Using the Onsager relation between electric and heat transport coefficients, and considering the very different roles played by the quantum Hall condensate and quasiparticles in transport, we argue that near the center of a quantum Hall plateau thermopower in a Corbino geometry measures entropy per quasiparticle per quasiparticle charge. This relation indicates that thermopower measurement in a Corbino setup is a more direct measure of quasiparticle entropy than in a Hall bar. Treating disorder within the self-consistent Born approximation, we show through an explicit microscopic calculation that this relation holds on an integer quantum Hall plateau at low temperatures. Applying this to non-Abelian quantum Hall states, we argue that Corbino thermopower at sufficiently low temperature becomes temperature independent and measures the quantum dimension of non-Abelian quasiparticles that determines the topological entropy they carry.

Snake states and Klein tunneling in a graphene Hall bar with a pn-junction

The Hall (RH) and bend (RB) resistances of a graphene Hall bar structure containing a pn-junction are calculated when in the ballistic regime. The simulations are done using the billiard model. Introducing a pn-junction—dividing the Hall bar geometry in two regions—leads to two distinct regimes exhibiting very different physics: (1) both regions are of n-type and (2) one region is n-type and the other p-type. In regime (1), a “Hall plateau”—an enhancement of the resistance—appears for RH. On the other hand, in regime (2), we found a negative RH, which approaches zero for large B. The bend resistance is highly asymmetric in regime (2) and the resistance increases with increasing magnetic field B in one direction while it reduces to zero in the other direction.

Quantum Hall Effect in Graphene with Superconducting Electrodes

We have realized an integer quantum Hall system with superconducting contacts by connecting graphene to niobium electrodes. Below their upper critical field of 4 T, an integer quantum Hall effect coexists with superconductivity in the leads but with a plateau conductance that is larger than in the normal state. We ascribe this enhanced quantum Hall plateau conductance to Andreev processes at the graphene-superconductor interface leading to the formation of so-called Andreev edge-states. The enhancement depends strongly on the filling-factor and is less pronounced on the first plateau due to the special nature of the zero energy Landau level in monolayer graphene.

Quasiparticles and excitons for the Pfaffian quantum Hall state

We propose trial wave functions for quasiparticle and exciton excitations of the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for fermions, and study these numerically. Our construction of trial wave functions employs a picture of the bosonic Moore-Read state as a symmetrized double layer composite fermion state. We obtain the number of independent angular momentum multiplets of quasiparticle and exciton trial states for systems of up to 20 electrons. We find that the counting for quasielectrons at large angular momentum on the sphere matches that expected from the conformal field theory (CFT) that describes the Moore-Read state's boundary theory. In particular, the counting for quasielectrons is the same as for quasiholes, in accordance with the idea that the CFT describing both sides of the Fractional Quantum Hall plateau should be the same. We also show that our trial wave functions have good overlaps with exact wave functions obtained using various interactions, including second Landau level Coulomb interactions and the three-body delta interaction for which the Pfaffian states and their quasiholes are exact ground states. We discuss how these results relate to recent work by Sreejith et al. on a similar set of trial wave functions for excitations over the Pfaffian state as well as to earlier work by Hansson et al., which has produced trial wave functions for quasiparticles based on conformal field theory methods and by Bernevig and Haldane, which produced trial wave functions based on clustering properties and ``squeezing.''

Quantum Hall effect in bottom-gated epitaxial graphene grown on the C-face of SiC

We demonstrate that the carrier concentration of epitaxial graphene devices grown on the C-face of a SiC substrate is efficiently modulated by a buried gate. The gate is fabricated via the implantation of nitrogen atoms in the SiC crystal. The charge neutrality point is observed close to gate voltage zero, and graphene can be populated by either holes or electrons down to low temperature (1.5 K). The hole concentration is hardly tuned by the gate voltage, possibly because of interface states below the Dirac point. A remarkably large quantum Hall plateau is observed for electrons.

Competing Topological Orders in theν=12/5Quantum Hall State

We provide numerical evidence that a p(x)-ip(y) paired Bonderson-Slingerland (BS) non-Abelian hierarchy state is a strong candidate for the observed ν=12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible ν=12/5 quantum Hall state with shift S=2 on the sphere, matching that of the BS state. The exact ground state of the Coulomb interaction at S=2 is shown to have a large overlap with the BS trial wave function. Larger overlaps are obtained with BS-type wave functions that are hierarchical descendants of general p(x)-ip(y) weakly paired states at ν=5/2. We perform a finite-size scaling analysis of the ground-state energies for ν=12/5 states at shifts corresponding to the BS (S=2) and 3-clustered Read-Rezayi (S=-2) universality classes. This analysis reveals very tight competition between these two non-Abelian topological orders.

TRANSPORT VIA CLASSICAL PERCOLATION AT QUANTUM HALL PLATEAU TRANSITIONS

We consider transport properties of disordered two-dimensional electron gases under high perpendicular magnetic field, focusing in particular on the peak longitudinal conductivity [Formula: see text] at the quantum Hall plateau transition. We use a local conductivity model, valid at temperatures high enough such that quantum tunneling is suppressed, taking into account the random drift motion of the electrons in the disordered potential landscape and inelastic processes provided by electron-phonon scattering. A diagrammatic solution of this problem is proposed, which leads to a rich interplay of conduction mechanisms, where classical percolation effects play a prominent role. The scaling function for [Formula: see text] is derived in the high temperature limit, which can be used to extract universal critical exponents of classical percolation from experimental data.

Magnetotransport property of HgCdTe inversion layer

HgCdTe-based metal-insulator-semiconductor field effect transistor is fabricated by low-cost liquid phase epitaxy technique. Clear SdH oscillation in xx and quantum Hall plateaus of xy are observed, indicating that it is a good transistor. By measuring the magnetoresistance near zero field, we observe the weak antilocalization effect in our sample, suggesting a relatively strong spin-orbit coupling. The experimental data can be well fitted by the ILP theory. The fitting-obtained spin-splitting energy increases with increasing electron concentration, and the maximum reaches up to 9.06 meV. From the obtained spin-splitting energy, we calculate the spin-orbit coupling parameter and find that it increases with increasing electron concentration, which is contrary to the observations in a wide quantum well.

Transport measurements on ultra-clean dual-gated suspended bilayer graphene

We fabricate ultra clean contactless dual-gated devices comprised of suspended bilayer graphene (BLG) and investigate their low temperature electron transport properties as functions of charge density n, magnetic field B and electric field E. We find that for devices with moderate mobility, conductance remains finite at the charge neutrality point and decreases monotonically with increasing |E|, as expected in the picture of single particle behavior. In contrast, devices with highest mobility display an insulating state at B=E=n=0, and conductance's dependence on E is non-monotonic. This surprising behavior arises from electronic interactions. In finite B, we observe quantum Hall plateaus with the 8-fold degeneracy of the lowest Landau level completely broken, as well as a fractional state.

Investigation of Serial Quantum Hall arrays as a Quantum Resistance Standard

In this work, we test the feasibility of a resistance standard based on a serial array of ten lithographically interconnected quantum Hall bars based on an Al(Ga)As heterostructure. Our investigation involves a novel multiple layer process for the fabrication of our samples which allows to realize a thin SiO2 insulations by means of a lift-off process. Additionally, we have performed preliminary precision measurements of the i = 2 Hall plateau in order to characterize the metrological properties of our samples.

High-field magneto-transport at charge neutrality point in monolayer graphene

We have investigated the magneto-transport around filling factor ν = 0 in monolayer graphene sheet. Zero Hall plateau of Hall conductivity and minimum of longitudinal conductivity have been clearly observed despite the highly fluctuated behaviour of magneto-resistance above 10 T. These phenomena can be understood by the transport of counter-propagating electron and hole edge states at the charge neutrality point. We tried to explain the origin of remarkable fluctuations in magneto-resistance by the energy relaxations among the counter-propagating edge channels.

Magnetic field dependency of spin-splitting in In0.75Ga0.25As/ In0.75Al0.25As two dimensional electron gas with strong Rashba spin-orbit coupling

High-field magneto-resistance (MR) properties including Shubnikov de-Haas (SdH) oscillation and integer quantum Hall effect are observed and analyzed in high In-content InGaAs/InAlAs two-dimensional electron gas (2DEG) with strong Rashba effect. From the results, conventional longitudinal resistance oscillations with Zeeman splittng as well as quantum Hall plateaus are confirmed and a transition from zero-field spin-splitting to high-field Zeeman splitting is discussed. The two-kind spin splittings are seem to be connected via the sign changing process at finite (∼3 Tesla) magnetic field, the value of which is about two times larger than that in high In-content InGaSb/InAlSb system.

Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition

The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these mesoscopic fluctuations in a Corbino geometry: The amplitude of the magnetoconductance oscillations has an e^2/h resonance in the transition region, signaling a change in the topological quantum number of the insulating bulk. This resonance provides a signed scaling variable for the critical exponent of the phase transition (distinct from existing positive definite scaling variables).

A transfer technique for high mobility graphene devices on commercially available hexagonal boron nitride

We present electronic transport measurements of single and bilayer graphene on commercially available hexagonal boron nitride. We extract mobilities as high as 125 000 cm2 V−1 s−1 at room temperature and 275 000 cm2 V−1 s−1 at 4.2 K. The excellent quality is supported by the early development of the ν = 1 quantum Hall plateau at a magnetic field of 5 T and temperature of 4.2 K. We also present a fast, simple, and accurate transfer technique of graphene to hexagonal boron nitride crystals. This technique yields atomically flat graphene on boron nitride which is almost completely free of bubbles or wrinkles. The potential of commercially available boron nitride combined with our transfer technique makes high mobility graphene devices more accessible.

Evidence for a fractionally quantized Hall state with anisotropic longitudinal transport

At high magnetic fields, where the Fermi level lies in the N=0 lowest Landau level (LL), a clean two-dimensional electron system (2DES) exhibits numerous incompressible liquid phases which display the fractional quantized Hall effect (FQHE) (Das Sarma and Pinczuk, 1997). These liquid phases do not break rotational symmetry, exhibiting resistivities which are isotropic in the plane. In contrast, at lower fields, when the Fermi level lies in the $N\ge2$ third and several higher LLs, the 2DES displays a distinctly different class of collective states. In particular, near half filling of these high LLs the 2DES exhibits a strongly anisotropic longitudinal resistance at low temperatures (Lilly et al., 1999; Du et al., 1999). These "stripe" phases, which do not exhibit the quantized Hall effect, resemble nematic liquid crystals, possessing broken rotational symmetry and orientational order (Koulakov et al., 1996; Fogler et al., 1996; Moessner and Chalker, 1996; Fradkin and Kivelson, 1999; Fradkin et al, 2010). Here we report a surprising new observation: An electronic configuration in the N=1 second LL whose resistivity tensor simultaneously displays a robust fractionally quantized Hall plateau and a strongly anisotropic longitudinal resistance resembling that of the stripe phases.

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

Abstract It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-AlxGa1−x As heterojunction. The results are in good agreement with the existing experimental data.

Quantum hall effect in inhomogeneous trilayer graphene

We have performed magneto-transport experiments in trilayer graphene, at temperatures between 2 and 190 K and magnetic fields up to 22 T. Here we report the integer quantum Hall effect in trilayer graphene, showing the quantum Hall plateau at ν=6 and studying its temperature dependence. The symmetry properties of the resistance in the quantum Hall regime and at low magnetic fields are also investigated. The measurements obey the reciprocity relation, and reveal new symmetries that relate the resistances measured with different contact configurations.

Electric- and magnetic-field-tuned Landau levels and Hall conductivity in AA-stacked bilayer graphene

We theoretically study the combined effect of magnetic and electric fields on the Landau levels and Hall conductivity in AA-stacked bilayer graphene. From the analytic expressions derived, we obtain explicit criterions for determining the zero-energy Landau level and different level crossings in the graphene bilayer. For providing a scheme of experimental verification, we further explore the quantum Hall effect in such a biased bilayer. It is found that the zero-conductance Hall plateau in this system can vanish at certain specific combinations of magnetic and electric fields, accompanying with the occurrence of resonance Hall conductivity steps.

Two-dimensional quantum liquids from interacting non-Abelian anyons

A set of localized, non-Abelian anyons—such as vortices in a px+ipy superconductor or quasiholes in certain quantum Hall states—gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here, we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.

Microscopic models of interacting Yang–Lee anyons

Collective states of interacting non-Abelian anyons have recently been studied mostly in the context of certain fractional quantum Hall states, such as the Moore–Read state proposed to describe the physics of the quantum Hall plateau at filling fraction ν=5/2. In this paper, we further expand this line of research and present non-unitary generalizations of interacting anyon models. In particular, we introduce the notion of Yang–Lee anyons, discuss their relation to the so-called ‘Gaffnian’ quantum Hall wave function and describe an elementary model for their interactions. A one-dimensional (1D) version of this model—a non-unitary generalization of the original golden chain model—can be fully understood in terms of an exact algebraic solution and numerical diagonalization. We discuss the gapless theories of these chain models for general su(2)k anyonic theories and their Galois conjugates. We further introduce and solve a 1D version of the Levin–Wen model for non-unitary Yang–Lee anyons.