# Wenchen Luo - Université de Sherbrooke

## Publications Authored By Wenchen Luo

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. Read More

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. Read More

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. Read More

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. Read More

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. Read More

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 $\nu _{N}=1,3$ 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. Read More

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,... Read More

**Affiliations:**

^{1}Université de Sherbrooke,

^{2}Université de Sherbrooke

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. Read More

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 $\nu \in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $\nu =-1,3$, 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. Read More

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,... Read More