Correlated Quantum Phenomena in Confined Two-Dimensional Hexagonal Crystals

Abstract

Low-energy fermionic excitations in two-dimensional materials deviate from the conventional Schrödinger description and are instead governed by Dirac equations. Such Dirac fermions give rise to a variety of unconventional quantum phenomena that have no direct analogues in traditional condensed matter systems. Among these materials, graphene and transition metal dichalcogenides (TMDs) represent two prototypical platforms, hosting massless and massive Dirac particles, respectively, and exhibiting rich electronic, optical, and valley dependent properties. Here we review the effect of the quantum confinement in these two-dimensional hexagonal materials that provides a powerful route to enhance Coulomb interactions and stabilizing correlated quantum states. In graphene- and TMD-based quantum dots, externally imposed confinement leads to discrete electronic and excitonic spectra, where interaction effects are strongly amplified. In twisted van der Waals heterostructures, the moiré superlattices generate emergent confinement and induce nontrivial band topology, giving rise to a wealth of novel phenomena. More generally, reduced dimensionality and spatial localization in two-dimensional materials promote a diverse range of correlated states. Recent experimental and theoretical advances highlight the central role of confinement in shaping quantum behavior and reveal new opportunities for applications based on these states. In this review, we provide an overview of recent progress in confinement-induced correlated phenomena in two-dimensional materials from both theoretical and experimental perspectives.

Figures (17)

• Figure 1: Crystal lattice structures of representative 2D materials including graphene, hBN, MoS2, other transition metal dichalcogenides, and layered oxides.
• Figure 2: Electronic band structures of MoS2 and WS2 along the high-symmetry path $\Gamma$–$M$–$K$–$\Gamma$. (a) Monolayer MoS2 without spin-orbit coupling. (b) Bilayer MoS2 without spin-orbit coupling. (c) Monolayer MoS2 with spin-orbit coupling. (d) Monolayer WS2 with spin-orbit coupling. The band structures are obtained from tight-binding model calculations, with spin-orbit coupling included in panels (c) and (d) to capture the effects of spin-dependent interactions on the electronic properties of the materials.
• Figure 3: Schematic of graphene and TMDs drawing of the band structure at the band edges located at the $K$ and $K'$ points. Adapted from Ref. tapashl2010reviewyao2012tmds
• Figure 4: Schematic of different QDs structure. (a) A circular QD defined in monolayer graphene by a radial confinement potential of radius $R$. (b)Monolayer MoS2 circular QD of radius $R$ (indicated by the red circle) and a perpendicular magnetic field $B$ is applied to the MoS2 plane. Adapted from Ref. grapheneqdsqu2017tunable
• Figure 5: Low-lying energy spectra of a MoS2 QD with radius $R = 20\text{nm}$ at zero magnetic field ($B = 0\text{T}$). The red and blue dots represent the electron and hole states, respectively. The left panels correspond to spin-up ($s = +1$) states, while the right panels correspond to spin-down ($s = -1$) states.