Session F31: Quantum Transport

``Designer'' spin-orbit interaction in graphene on semiconducting transition metal dichalcogenides

Inducing a large spin-orbit interaction (SOI) in graphene while preserving the Dirac nature of electrons is of great interest to create new topological insulating states and to study a variety of spintronic effects. Earlier work succeeded in inducing SOI at the expenses of destroying the Dirac spectrum or of increasing the amount of disorder. We show that a very strong SOI can be induced while preserving an extremely high quality of graphene simply by using semiconducting transition metal dichalchogenides (TMDs) as substrates. Being extremely flat and having no unsaturated bonds at their surface, layered van der Waals materials like WS2, WSe2, and MoS2 are ideal substrates that allow very large carrier mobility values to be reached in graphene. The magnitude of SOI in these TMDs is enormous, reaching a large fraction of an eV in the valence band. We find that using semiconducting TMDs as substrates allows the SOI to be ``imprinted'' into graphene. This is shown experimentally by the occurrence of a fully developed weak antilocalization correction to the conductivity, with no sign of weak localization, observed in 100{\%} of the devices investigated, irrespective of the carrier mobility, position of the Fermi level, whether graphene is mono, bi, or trilayer, alignment of the TMD and graphene lattice, and of the specific TMD used. In addition, a splitting in the frequency of the Shubnikov-de Haas resistance oscillations show that the induced SOI is due to a modification of the graphene band structure. The gate dependence of this splitting shows that the dominant SOI term is of the Rashba type and that its magnitude is approximately 10-15 meV, nearly three orders of magnitude larger than the intrinsic SOI present in graphene. Work done in collaboration with Z. Wang, D.-K. Ki, H. Chen, J.H. Khoo, D. Mauro, H. Berger, A.H. MacDonald, and L.S. Levitov   

Transport and magneto-transport study of ultrathin $WSe_2$

Atomically thin transition metal dichalcogenides is a promising materials platform for a new generation of electronic and spintronic applications. We fabricate monolayer and bilayer hBN/graphene/$WSe_2$ four-terminal devices using a dry van der Waals transfer technique, where few-layer graphene serves as the electrical contact to $WSe_2$. We discuss the importance of temperature control at each step of the transfer process. A High $\kappa$ $HfO_2$ back gate enables the devices to reach high carrier densities of a few $\times 10^{13}$/cm$^2$. The graphene contacts are ambipolar, ohmic and enable four-terminal measurements at low temperatures. We measure the magnetic field dependence of $\rho_{xx}$ for both electrons and holes in the same device. As the Fermi level is continuously tuned from the valence band to the conduction band, the magneto-resistance exhibits a variety of behavior including weak localization, weak anti-localization and more complex non-monotonic field dependences. We compare our data with theoretical models.   

Carrier Density Dependent Quantum Hall States Sequence of Holes in WSe$_2$

The high intrinsic hole mobility and existence of Ohmic contacts to the valence band have enabled the magnetotransport study of holes in WSe$_2$. Using multiple monolayer and bilayer WSe$_2$ samples encapsulated in hexagonal boron nitride, we report an unusual carrier density-dependent quantum Hall states (QHSs) sequence in hole-doped WSe$_2$. At a fixed carrier density, the samples exhibit either a predominantly even or a predominantly odd QHSs sequence, which is insensitive to an applied transverse electric field. As the density is reduced from $9\times10^{12}$ cm$^{-2}$ to $2\times10^{12}$ cm$^{-2}$, we observe a transition from even to odd, and back to even QHS filling factors. Furthermore, magnetotransport measurements in a tilted magnetic field reveal that the QHSs sequence is insensitive to the in-plane magnetic field, indicating that the electron spin is locked perpendicular to the WSe$_2$ plane. These findings suggest that the Landau level Zeeman splitting depends linearly on the perpendicular magnetic field via a carrier density dependent $g$-factor, as a result of electron-electron interaction.   

Tuning the chirality of Dirac electrons in van der Waals heterostructures

Chirality is fundamental for the Dirac quasiparticles in graphene and topological insulators. It plays a crucial role in such relativistic phenomena, as Klein tunneling, the absence of backscattering in graphene p-n junctions, and a peculiar half-integer quantum Hall effect. However, it has proved difficult to image directly the chirality in transport measurements. I will present the direct observation and manipulation of chirality and pseudospin polarization in the tunneling of electrons between two almost perfectly aligned graphene crystals. To this end, a strong in-plane magnetic field was used to resolve the contributions of the chiral states -- a new technique for preparing graphene Dirac electrons in a particular quantum chiral state in a selected valley. The technique can be extended to tunneling devices in which surface states of topological insulators are used as electrodes, allowing for an all-electrical injection of spin-polarized currents.   

Probing the Electronic Structure of Two-Dimensional Materials in the Quantum Hall Regime with Tunneling Field Effect Transistors

Scanning tunneling spectroscopy (STS) is a powerful tool for the investigation of electronic structure of two-dimensional (2D) materials. However, STS measurements are difficult to implement under experimental conditions that are crucial for quantum Hall phenomena, such as ultra-high magnetic fields and low temperatures. This incompatibility limits the application of STS measurements for studying quantum Hall effects in 2D materials. To address this issue, we utilize tunneling field effect transistors to probe the electronic structure of 2D materials. These transistors, which are comprised of layered 2D materials, function in high magnetic fields and ultra-low temperatures that are required for the study of quantum Hall phenomena. We will discuss our latest experimental progress towards using these nanodevices to measure the electronic structure of graphene and molybdimum disulfide in the quantum Hall regime.   

Transport properties of the bulk state in bilayer WTe$_{\mathrm{2}}$

Three-dimensional WTe$_{\mathrm{2}}$ was recently reported to have a large, non-saturating magnetoresistance. Monolayer WTe$_{\mathrm{2}}$, on the other hand, was recently predicted to be a topologically nontrivial semimetal. However, we find that monolayer WTe$_{\mathrm{2}}$ encapsulated in h-boron nitride becomes insulating in the 2D bulk at temperatures below about 100 K, while the edge remains conducting, as in a topological insulator. In bilayer WTe$_{\mathrm{2}}$, we find that the 2D bulk behaves similarly to that in monolayer WTe$_{\mathrm{2}}$ but at lower temperatures (insulating below \textasciitilde 20 K). The edge conduction, however, is absent in the bilayer, providing the opportunity to study the bulk state without complications from the edge. By fabricating a Hall bar device in a bilayer, we can therefore determine the magnetoresistance and the Hall effect and their dependence on temperature and gate voltage.   

Edge conduction in monolayer $WTe_{2}$

We report evidence for edge conduction in gated monolayer $WTe_{2}$, which was recently predicted to be a topologically nontrivial semimetal. We find that at temperatures below about 100 K a gap appears and the two-dimensional bulk becomes insulating near zero gate voltage, while the edges remain conducting. At lower temperatures, the edge conduction is strongly suppressed by in-plane magnetic field, as expected for a helical quantum spin Hall edge. In this regime the conductance is approximately activated with an activation energy proportional to magnetic field. This can be modeled by a Zeeman-type gap opening in the edge mode combined with disorder. The conductance between adjacent contacts remains below the quantum conductance even for the shortest edges (150 nm), but can be of the same order even for 5 micron edges. We will compare and contrast this behavior with that other possible quantum spin Hall systems.   

Quantum Hall effect in few-layer black phosphorus devices:~beyond the Hall bar geometry.

As a member of two-dimensional (2D) material family, few- layer black phosphorus (FLBP) has attracted intensive interests recent years. One reason is its high mobility compared with other 2D semiconductors, which allowed the recent observation of quantum Hall effect in conventional Hall bar geometries. Careful studies of quantum Hall effect in different device geometries lead us to further understandings of this material, and here we will present our effort with advanced geometry. High quality dual-gated FLBP devices form a tunable wide quantum well with ambipolar charge densities, and integer quantum Hall effect states on both surfaces. In van der pauw devices, we observe the discrepancy between different current flow directions that may be related to the structural anisotropy of FLBP.   

Quantum Hall Effect in Black Phosphorus Two-dimensional System

Recent advent of black phosphorus two-dimensional electron systems (2DESs) has attracted great attention because of its exceptional electronic and optoelectronic properties. In this talk, we will present our recent experimental progress on integer quantum Hall effect in high quality black phosphorus 2DESs. In extremely high magnetic fields, temperature and tilt angle dependent electronic transport measurements reveal a wealth of information on the charge carriers in this new 2DES. We will discuss the implication of our findings in the fractional quantum Hall regime.   

Magnetotransport in HgTe double quantum well

We present a study of a double quantum well (DQW) made of two-dimensional layers with inverted energy band spectrum: HgTe. The magnetotransport reveals a considerably larger overlap of the conduction and valence subbands, than is known for HgTe single quantum wells (QW). Thus, the critical field $B_c$ for opening the gap in the energy spectrum shifts towards much higher fields with respect to $B_c$ in single QWs. The accompanying specific features in magnetotransport, such as multiple inversions in $\rho_{xy}$(B ), zero-filling-factor state with a concomitant manifestation of its insulator character in $\rho_{xx}$(B ), etc., also move towards higher fields, where the quantum Hall regime is well realized. The overlap can be regulated by a gate voltage $V_g$ and the coexisting electrons and holes were found in the whole investigated range of positive and negative $V_g$. The electron density n remains almost constant in the whole range of investigated $V_g$, while the hole density p drops down passing through the charge-neutrality point. This difference between n and p stems from an order of magnitude larger density of states for holes than for electrons. We analyze our observations on the basis of a calculated picture of magnetic levels in a DQW.   

Magneto-transport and Strain Experiments in Anisotropic High Mobility van der Waals Semiconductor

The current research on low dimensional materials is mainly based on 2D material, which the materials are composed of atomic interaction along in-plane $x$ and $y$ directions, and van der Walls forces along out-of-plane vertical $z$ direction. Some 2D materials, such as black phosphorus/phosphorene and ZrTe$_{5}$ we have been intensively studying, are anisotropic in $x$-$y$ plan due to their unique atomic structures, which lead to anisotropic transport, optical, thermal and mechanical properties. In this work, we present an extreme case in anisotropy in van der Walls materials. Multiple experimental methods have been introduced to verify and study its anisotropic van der Walls properties including orientation dependent low temperature magneto-transport, polarized Raman spectroscopy, and mechanic strain experiments.