arXiv subjects

Wenchen Luo

Publications and source records attributed to Wenchen Luo.

28 records · Page 2Linked to original sources

arXiv2017

The Pfaffian state in an electron gas with small Landau level gaps

Landau level mixing plays an important role in the Pfaffian (or anti-Pfaffian) states. In ZnO the Landau level gap is essentially an order of magnitude smaller than that in a GaAs quantum well. We introduce the screened Coulomb interaction in a single Landau level to tackle that situation. Here we study the overlap of the ground state and the Pfaffian (or anti-Pfaffian) state at evendenominator fractional quantum Hall (FQH) states present in ZnO. The overlap is strongly system size-dependent which suggests a newly proposed particle-hole symmetry Pfaffian ground state in the extreme Landau level mixing limit. When the ratio of Coulomb interaction to the Landau level gap \k{appa} varies, we find a possible topological phase transition in the range 2 < \k{appa} < 3, which was actually observed in an experiment. We then study how the width of quantum well combined with screening influences the overlap.

cond-mat.mes-hall↗

arXiv2016

Tilt-Induced Phase Transitions in Even-Denominator Fractional Quantum Hall States at the ZnO Interface

Even denominator fractional quantum Hall states in a ZnO quantum well reveal interesting phase transitions in a tilted magnetic field. We have analyzed the planar electron gas in ZnO, confined in a parabolic potential in the third dimension, perpendicular to the plane of the electron gas. Since the Landau level gap is very small in this system we have included the screened Coulomb potential in order to include the effects of all the Landau levels. We observe an incompressible state - compressible state phase transition induced by the tilted field. Additionally, the 5/2 state has been experimentally found to be missing in this system. We however propose that a wider quantum well may help to stabilize the incompressible phase at the 5/2 filling factor.

cond-mat.mes-hall↗

arXiv2015

Understanding the Missing Fractional Quantum Hall States in ZnO

We have analyzed the crucial role the Coulomb interaction strength plays on the even and odd denominator fractional quantum Hall effects in a two-dimensional electron gas (2DEG) in the ZnO heterointerface. In this system, the Landau level gaps are much smaller than those in conventional GaAs systems. The Coulomb interaction is also very large compared to the Landau level gap even in very high magnetic fields. We therefore consider the influence of higher Landau levels by considering the screened Coulomb potential in the random phase approximation. Interestingly, our exact diagonalization studies of the collective modes with this screened potential successfully explain recent experiments of even and odd denominator fractional quantum Hall effects, in particular, the unexpected absence of the 5/2 state and the presence of 9/2 state in ZnO.

cond-mat.mes-hall↗

arXiv2015

Quantum Hall ferromagnets and transport properties of buckled Dirac materials

We study the ground states and low-energy excitations of a generic Dirac material with spin-orbit coupling and a buckling structure in the presence of a perpendicular magnetic field. The ground states can be classified into three types under different conditions: SU(2), easy-plane, and Ising quantum Hall ferromagnets. For the SU(2) and the easy-plane quantum Hall ferromagnets there are goldstone modes in the collective excitations, while all the modes are gapped in an Ising-type ground state. We compare the Ising quantum Hall ferromagnet with that of bilayer graphene and present the domain wall solution at finite temperatures. We then specify the phase transitions and transport gaps in silicene in Landau levels 0 and 1. The phase diagram strongly depends on the magnetic field and the dielectric constant. We note that there exists triple points in the phase diagrams in Landau level N = 1 that could be observed in experiments.

cond-mat.quant-gas↗

arXiv2015

Excitation Gap of Fractal Quantum Hall States in Graphene

In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, in which we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.

cond-mat.mes-hall↗

arXiv2014

Transport gap and hysteretic behavior of the Ising quantum Hall ferromagnets in Landau levels $\left\vert N\right\vert >0$ of bilayer graphene

The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $ν_{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavior of the Ising quantum Hall ferromagnets. We compute the transport gap due to different excitations: bulk electron-hole pairs, electron-hole pairs confined to the coherent region of a valley-pseudospin domain wall, and spin or valley-pseudospin skyrmion-antiskyrmion pairs. We determine which of these excitations has the lowest energy at a given value of the Zeeman coupling, bias, and magnetic field.

cond-mat.mes-hall↗

arXiv2014

Ising quantum Hall ferromagnetism in Landau levels $\left\vert N\right\vert \geq 1$ of 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 $N=0,\pm 1,\pm 2,...$ While Landau level $N=0$ is eighfold degenerate, higher Landau levels ($ \left\vert N\right\vert \geq 1$) are fourfold degenerate when counting spin and valley degrees of freedom. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $ \widetilde{ν}=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 the ground states in Landau level $N=0.$ At even filling, $\widetilde{ν}=2,$ the C2DEG is either fully spin polarized with electrons occupying both valleys or spin unpolarized with electron 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.

cond-mat.mes-hall↗

arXiv2013

Zeeman coupling and screening corrections to skyrmion excitations in graphene

At half filling of the fourfold degenerate Landau levels |n| \geq 1 in graphene, the ground states are spin polarized quantum Hall states that support spin skyrmion excitations for |n| =1,2,3. Working in the Hartree-Fock approximation, we compute the excitation energy of an unbound spin skyrmion-antiskyrmion excitation as a function of the Zeeman coupling strength for these Landau levels. We find for both the bare and screened Coulomb interactions that the spin skyrmion-antiskyrmion excitation energy is lower than the excitation energy of an unbound spin 1/2 electron-hole pair in a finite range of Zeeman coupling in Landau levels |n| =1,2,3. This range decreases rapidly for increasing Landau level index and is extremely small for |n| =3. For valley skyrmions which should be present at 1/4 and 3/4 fillings of the Landau levels |n| =1,2,3, we show that screening corrections are more important in the latter case. It follows that an unbound valley skyrmion-antiskyrmion excitation has lower energy at 3/4 filling than at 1/4. We compare our results with recent experiments on spin and valley skyrmion excitations in graphene.

cond-mat.mes-hall↗

arXiv2011

Bilayer graphene as an helical quantum Hall ferromagnet

The two-dimensional electron gas in a bilayer graphene in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N=0 at integer filling factors $ν\in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $ν=-1,3$, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias where \textit{electric} dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that by further increasing the bias at these two filling factors, the two-dimensional electron gas goes first through a Skyrmion crystal state and then into an helical state where the pseudospins rotate in space. The pseudospin textures in both the Skyrmion and helical states are due to the presence of a Dzyaloshinskii-Moriya interaction in the effective pseudospin Hamiltonian when orbital coherence is present in the ground state. We study in detail the electronic structure of the helical and Skyrmion crystal states as well as their collective excitations and then compute their electromagnetic absorption.

cond-mat.mes-hall↗

arXiv2010

Orbital and interlayer Skyrmions crystals in bilayer graphene

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash ω_{c}^{\ast}$ where $ω_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,...$ All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states

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