[Paper Review] Landau quantization in buckled monolayer GaAs

Hsien-Ching Chung, Chih Wei Chiuy+2 more|arXiv (Cornell University)|May 17, 2017

Quantum and electron transport phenomena82 references3 citations

TL;DR

This study investigates Landau quantization in buckled monolayer GaAs using a generalized tight-binding model that incorporates spin-orbit coupling, multi-orbital bonding, electric and magnetic fields. It reveals three groups of spin-polarized Landau levels with linear magnetic-field dependence, field-controlled gap modulations, and phase transitions, offering design principles for top-gated and phase-change devices.

ABSTRACT

Magneto-electronic properties of buckled monolayer GaAs is studied by the developed generalized tight-binding model, considering the buckled structure, multi-orbital chemical bondings, spin-orbit coupling, electric field, and magnetic field simultaneously. Three group of spin-polarized Landau levels (LLs) near the Fermi level are induced by the magnetic quantization, whose initial energies, LL degeneracy, energy spacings, magnetic-field-dependence, and spin polarization are investigated. The Landau state probabilities describing the oscillation patterns, localization centers, and node regularities of the dominated/minor orbitals are analyzed, and their energy-dependent variations are discussed. The given density of states directly reflects the main features of the LL energy spectra in the structure, height, number, and frequency of the spin-polarized LL peaks. The electric field causes the monotonous/nonmonotonous LL energy dispersions, LL crossing, gap modulation, phase transition and spin splitting enhancement. The complex gap modulations and phase transitions based on the competition between magnetic and electric fields are explored in detail by the phase diagram. The field-controlled gap modulations and phase transitions are helpful in designing the top-gated and phase-change electronic devices. These predicted magneto-electronic properties could be verified by scanning tunneling spectroscopy measurements.

Motivation & Objective

• To understand the magneto-electronic properties of buckled monolayer GaAs under combined electric and magnetic fields.
• To investigate how spin-orbit coupling, orbital hybridization, and buckling influence Landau level (LL) formation and dispersion.
• To explore field-induced gap modulations and phase transitions due to competition between electric and magnetic fields.
• To predict experimentally verifiable signatures of LLs, such as peak structures in density of states and nodal patterns in wave functions.
• To provide a theoretical framework for designing 2D electronic and optoelectronic devices based on III-V monolayers.

Proposed method

• Development of a generalized tight-binding model including multi-orbital interactions, spin-orbit coupling, and geometric buckling in GaAs.
• Self-consistent solution of the Hamiltonian under perpendicular magnetic and electric fields to compute Landau level spectra.
• Analysis of Landau state probabilities to characterize orbital dominance, localization centers, and node regularities in wave functions.
• Computation of the density of states (DOS) to identify peak structures corresponding to LLs and their energy spacing.
• Construction of $E_z$-$B_z$ phase diagrams to map regions of distinct gap modulations and phase transitions.
• Comparison of LL energy dispersions with and without electric fields to reveal monotonous and non-monotonous behaviors.

Experimental results

Research questions

• RQ1 How do spin-polarized Landau levels emerge in buckled monolayer GaAs under magnetic fields?
• RQ2 What is the role of spin-orbit coupling and orbital hybridization in shaping the Landau level spectrum and wave function structure?
• RQ3 How do electric and magnetic fields jointly modulate the band gap and induce phase transitions?
• RQ4 What are the field-dependent variations in orbital dominance and node patterns in Landau state wave functions?
• RQ5 Can the predicted Landau level features be experimentally verified via scanning tunneling spectroscopy?

Key findings

• Three distinct groups of spin-polarized Landau levels emerge near the Fermi level, each exhibiting linear dependence on magnetic field strength.
• The Landau level energy spacing shrinks with increasing state energy, and each LL is doubly degenerate due to valley and mirror symmetry.
• Orbital probabilities show regular oscillation patterns with nodes; the s-orbital has one fewer node than px or py orbitals in each LL.
• Electric fields induce non-monotonous energy dispersions, LL crossing, and enhanced spin splitting, with gap shrinkage observed at critical fields.
• Phase diagrams reveal four characteristic regions in the $E_z$-$B_z$ plane, with two types of gap modulation under $E_z$ control and three under $B_z$ control.
• The predicted spin-splitting energy spacing exceeds room-temperature thermal energy, indicating robustness for device applications.