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Register a new userEquilibration and Filtering of Quantum Hall Edge States in Few-Layer Black Phosphorus
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Added by
Chun Ning (Jeanie) Lau
Publication date
2020
fields
Physics
and research's language is
English
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We realize p-p-p junctions in few-layer black phosphorus (BP) devices, and use magneto-transport measurements to study the equilibration and transmission of edge states at the interfaces of regions with different charge densities. We observe both full equilibration, where all edge channels equilibrate and are equally partitioned at the interfaces, and partial equilibration, where only equilibration only takes place among modes of the same spin polarization. Furthermore, the inner p-region with low-doping level in the junction can function as a filter for highly doped p-regions which demonstrates gate-tunable transmission of edge channels.
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As a high mobility two-dimensional semiconductor with strong structural and electronic anisotropy, atomically thin black phosphorus (BP) provides a new playground for investigating the quantum Hall (QH) effect, including outstanding questions such as the functional dependence of Landau level (LL) gaps on magnetic field B, and possible anisotropic fractional QH states. Using encapsulating few-layer BP transistors with mobility up to 55,000 cm2/Vs, we extract LL gaps over an exceptionally wide range of B for QH states at filling factors { u}=-1 to -4, which are determined to be linear in B, thus resolving a controversy raised by its anisotropy. Furthermore, a fractional QH state at { u}~ -4/3 and an additional feature at -0.56+/- 0.1 are observed, underscoring BP as a tunable 2D platform for exploring electron interactions.
We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter -- playing the role of an effective interaction strength within an idealized model of thermal reservoirs -- is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.
Exciting phenomena may emerge in non-centrosymmetric two-dimensional (2D) electronic systems when spin-orbit coupling (SOC) interplays dynamically with Coulomb interactions, band topology, and external modulating forces, etc. Here, we report illuminating synergetic effects between SOC and Stark in centrosymmetric few-layer black arsenic (BAs), manifested as giant Rashba valley splitting and exotic quantum Hall states (QHS) reversibly controlled by electrostatic gating. The unusual finding is rooted in the puckering square lattice of BAs, in which heavy $4p$ orbitals form highly asymmetric $Gamma$ valley with the $p_{z}$ symmetry and $D$ valleys of the $p_{x}$ origin, located at the Brillouin zone (BZ) center and near the time reversal invariant momenta of $X$, respectively. When the structure inversion symmetry is broken by perpendicular electric field, giant Rashba SOC is activated for the $p_{x}$ bands to produce strong spin-polarized $D^{+}$ and $D^{-}$ valleys related by time-reversal symmetry, coexisting with weak $Gamma$ Rashba bands constrained by the $p_{z}$ symmetry. Intriguingly, strong Stark effect shows the same $p_{x}$-orbital selectiveness for $D$, collectively shifting the valence band maximum of $D^{pm}$ valleys to exceed the $Gamma$ pockets. Such an orchestrating effect between SOC and Stark allows us to realize gate-tunable spin valley manipulations for 2D hole gas, as revealed by unconventional magnetic field triggered even-to-odd transitions in QHS. For electron doping, the quantization of the $Gamma$ Rashba bands is characterized by peculiar density-dependent transitions in band topology from two parabolic valleys to a unique inner-outer helical structure when charge carrier concentrations increase.
Achieving good quality Ohmic contacts to van der Waals materials is a challenge, since at the interface between metal and van der Waals material, different conditions can occur, ranging from the presence of a large energy barrier between the two materials to the metallization of the layered material below the contacts. In black phosphorus (bP), a further challenge is its high reactivity to oxygen and moisture, since the presence of uncontrolled oxidation can substantially change the behavior of the contacts. In this study, we investigate the influence of the metal used for the contacts to bP against the variability between different flakes and different samples, using three of the most used metals as contacts: Chromium, Titanium, and Nickel. Using the transfer length method, from an analysis of ten devices, both at room temperature and at low temperature, Ni results to be the best metal for Ohmic contacts to bP, providing the lowest contact resistance and minimum scattering between different devices. Moreover, we investigate the gate dependence of the current-voltage characteristics of these devices. In the accumulation regime, we observe good linearity for all metals investigated.
The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH effect but have been measured with limited success. The QH edge states in graphene take on an even richer role as graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials but has eluded spatial measurements. In this report, we map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $ u=0,pm 1$ across the quantum Hall edge boundary using atomic force microscopy (AFM). Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moire superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.
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