Session S13: 2D Materials: Semimetals

Dirac Semimetals in Two Dimensions

Graphene is well-known for its unusual band structure, which features a pair of two dimensional Dirac points -- band degeneracies with linear dispersion -- at the Fermi level, and has served as the canonical platform for exploring the novel physics that arises near such points. However, spin-orbit interaction breaks the degeneracy at the Dirac points, so that graphene is formally a quantum spin Hall insulator. In this talk I will discuss the theory of two dimensional materials with Dirac points that \textit{persist} in the presence of spin-orbit interaction. These Dirac points are preserved by nonsymmorphic symmetries, which describe lattice invariance under a combined point group operation and fractional translation. This is the only means of protecting Dirac points against spin-orbit coupling in two dimensions, and such Dirac points are unique in marking the transition between topological and trivial insulating states. I will describe the general properties of these Dirac points and the nature of their protection by nonsymmorphic symmetry operations, and contrast them with Dirac points protected by symmorphic symmetries in both the three dimensional case and the spin-orbit-free two dimensional case. I will then delineate the possible configurations of two dimensional Dirac materials, classifying them by protective symmetries. The role of 2D Dirac materials as transition phases will be described in detail, and the topological and trivial phases that result from various modes of symmetry breaking will be explored. Finally, I will discuss the potential for realization of both Dirac materials and their derivative phases, paying special attention to relevant chemical considerations.   

Bosonization of Weyl Fermions

The electron, discovered by Thomson by the end of the nineteenth century, was the first experimentally observed particle. The Weyl fermion, though theoretically predicted since a long time, was observed in a condensed matter environment in an experiment reported only a few weeks ago. Is there any linking thread connecting the first and the last observed fermion (quasi)particles? The answer is positive. By generalizing the method known as bosonization, the first time in its full complete form, for a spacetime with 3+1 dimensions, we are able to show that both electrons and Weyl fermions can be expressed in terms of the same boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The bosonized form of the Weyl chiral currents lead to the angle-dependent magneto-conductance behavior observed in these systems.   

Coulomb interaction effect in tilted Weyl fermion in two dimensions

Weyl fermions with tilted linear dispersions characterized by several different velocities appear in some systems including the quasi-two-dimensional organic semiconductor $\alpha$-(BEDT-TTF)$_2$I$_3$ and three-dimensional WTe$_2$. The Coulomb interaction between electrons modifies the velocities in an essential way in the low energy limit, where the logarithmic corrections dominate. Taking into account the coupling to both the transverse and longitudinal electromagnetic fields, we derive the renormalization group equations for the velocities of the tilted Weyl fermions in two dimensions, and found that they increase as the energy decreases and eventually hit the velocity of light $c$ to result in the Cherenkov radiation. Especially, the system restores the isotropic Weyl cone even when the bare Weyl cone is strongly tilted and the velocity of electrons becomes negative in certain directions.   

Strong Correlation and Topological States in Orbital-Active Dirac Materials

Two dimensional Dirac materials, starting with graphene, have drawn tremendous research interests in the past decade. Instead of focusing on the $p_z$ orbital as in graphene, we go a step further and study its two orbitals counterpart, namely the $p_x$ and $p_y$ orbitals on a honeycomb lattice. The model applies to both optical lattices and several solid state systems including organic material, fluoridated tin film, BiX/SBX (X=H.F.CI.Br). In the band structure, besides the well known Dirac points in the graphene band structure, the orbital degrees of freedom give rise to flat bands as well as quadratic band touching points. These new features provide an even wider playground for searching exotic states of matter. With help of mean field theory and functional renormalization group (FRG) method, we explore the effects of interaction on the system and investigate the consequential interesting states such as ferromagnetism, Wigner crystallization, quantum anomalous Hall states and f-wave superconductivity.   

Three-dimensional Anisotropy and Kohler's Rule Scaling of the Magnetoresistance in WTe$_2$

Tungsten ditelluride (WTe$_2$) was recently discovered to have extremely large magnetoresistance (XMR) at low temperatures and exhibits a transformative 'turn-on' temperature behavior: when the applied magnetic field $H$ is above a certain value, the resistivity versus temperature $\rho(T)$ curve shows a minimum at a field dependent temperature $T^*(H)$. Since WTe$_2$ is a layered compound with metal layers sandwiched between adjacent insulating chalcogenide layers, it is typically considered to be a two dimensional (2D) material, whereby the anisotropic magnetoresistance is attributed only to the perpendicular component of the magnetic field. Moreover, the 'turn-on' temperature behavior has been interpreted as a magnetic-field-driven metal-insulator transition or attributed to an electronic structure change. In this talk I will report on two scaling behaviors of the magnetoresistance in WTe$_2$. The first shows that the angle dependence of the magnetoresistance follows a conventional 3D anisotropy scaling and hence reveals the electrical 3D nature of WTe$_2$ [1]. The second demonstrates that the $\rho(T,H)$ curves, including those with 'turn-on' temperature behavior, can be scaled with Kohler's rule [2]. The observed Kohler's rule scaling excludes the possible existence of a magnetic-field-driven metal-insulator transition or significant contribution of an electronic structure change to the low-temperature XMR in WTe$_2$. It indicates that both the XMR and the 'turn-on' behavior originate from the high mobilities of the charge carriers, which are strongly temperature dependent in WTe$_2$. We also derived quantitative expressions for the magnetic field dependence of the 'turn-on' temperature $T^*(H)$ and for the temperature dependence of the resistivity $\rho(T^*,H)$ at the onset of the XMR behavior. \\ \vspace{\baselineskip} \\ In collaboration with L. R. Thoutam, Z. L. Xiao, J. Hu, S. Das, Z. Q. Mao, J. Wei, R. Divan, A. Luican-Mayer, G. W. Crabtree, and W. K. Kwok \\ \medskip \\ References: \\ $[1]$ L. R. Thoutam, Y. L.Wang et al., Phys. Rev. Lett. 115, 046602 (2015) \\ $[2]$ Y. L. Wang et al. Phys. Rev. B 92, 180402(R) (2015)   

Electronic Transport in Ultra-Thin 1T'-WTe$_{\mathrm{2}}$

We report low-temperature electronic transport measurements of 1T'-WTe$_{\mathrm{2}}$ in the few-layer limit. Thin layers of WTe$_{\mathrm{2}}$ are obtained by the mechanical exfoliation technique and are subsequently encapsulated between thin hexagonal Boron Nitride crystals via a dry crystal transfer technique. These devices are fabricated entirely inside an inert-atmosphere glove box to avoid degradation. We report on the temperature, magnetic field, and electrostatic gate voltage dependence of these devices for several different thicknesses.   

Spin Orbit Induced Electronic Structure and Magnetotransport in WTe$_2$

We report electronic structure studies of WTe$_2$, which shows an XMR behavior and is non-centrosymmetric. We find a spin-orbit split semimetallic band structure with a different Fermi surface topology than that initially reported, including Rashba split bands with Fermi surface around the zone center. The metallic properties are not one dimensional and are best described in terms of an anisotropic 3D metal with compensating low carrier density Fermi surfaces. The spin texture and transport is discussed as the origin of the XMR effect and in particular is consistent with the geometry in which the XMR effect is observed and its angle dependence.   

Electronic and Magnetic Anisotropy of Layered IrTe$_{\mathrm{2}}$ Single Crystals

Layered IrTe$_{\mathrm{2}}$ is known to exhibit extremely rich physical properties with two successive phase transitions at T$_{\mathrm{1}}$ \textasciitilde 280 K and T$_{\mathrm{2}}$ \textasciitilde 180 K. We have grown IrTe$_{\mathrm{2}}$ single crystals with typical sizes of 4×5×1.2 mm$^{\mathrm{3}}$. This allows us to experimentally investigate physical properties along different directions. While the lattice parameter ratio c/a is small, both electrical resistivity and magnetic susceptibility show much higher anisotropy. In particular, we only observe resistivity and susceptibility anomaly along the ab plane at T$_{\mathrm{2}}$, indicating the 2D character of electronic and magnetic properties at low temperatures.   

Magnetoresistance Anisotropy in WTe$_{\mathrm{2}}$

We report the angle dependence of the magnetoresistance in WTe$_{\mathrm{2}}$. Being a layered material, WTe$_{\mathrm{2}}$ is considered to be electronically two-dimensional (2D). Our results demonstrate that it is in fact 3D with an anisotropy of effective mass as small as 2. We measured the magnetic field dependence of the sample resistance R(H) at various angles between the applied magnetic field with respect to the c-axis of the crystal and found that they can be scaled based on the mass anisotropy, which changes from \textasciitilde 2 to \textasciitilde 5 with decreasing temperature in the Fermi liquid state. We will also discuss the origin of the turn-on temperature behavior in this material.   

Magnetotransport Measurements of Thin Layered WTe2

Tungsten Telluride, a semimetallic layered transition-metal dichalcogenide, was recently found to have extremely large magnetoresistance at helium temperatures. The unconventional non-saturating behavior may be related to near-perfect charge compensation between electron and hole pockets, but this is still debated. Since that discovery there have been several studies of angle-resolved photoemission and quantum transport on the bulk material which found the fermi surface to be rather complex. It is clear that insights stand to be gained from the variation of the properties on thinning down to a single monolayer. Measurements of thin exfoliated crystals have indicated that the carriers become increasingly localized on approaching the monolayer limit. This may be an intrinsic feature or it may be a result of the disorder produced by oxidation of the surface layers. We report transport measurements on few-layer and monolayer WTe2 with and without encapsulation in hBN, including the dependence on thickness, crystal axis, temperature, gate voltage and magnetoresistance, which resolve this question.   

Magnetotransport properties of nearly-free electrons in two-dimensional hexagonal metals and application to the Mn$+$1AXn phases

We propose a general model for explaining the weak field magneto-transport properties of the Mn$+$1AXn phases in their crystalline form. By using this model to describe the magnetotransport properties of nearly-free electrons in two-dimensional hexagonal metals, we modify it so as to be applicable for Mn$+$1AXn phases. It is demonstrated that the values of the in-plane Hall coefficient and magnetoresistance are due to the specific shape of the Fermi surface of almost two-dimensional hole and electron bands. If the contribution of the electron pockets to in-plane resistivity can be predicted to be a minor one, in contrast, both holes and electrons should substantially contribute to the overall value of the in-plane Hall coefficient. The relevance of this model is then supported by elementary considerations, analytical computations and a set of experimental data obtained from single crystals of V$_{2}$AlC and Cr$_{2}$AlC as a function of temperature and magnetic field, both in the basal plane and along the c-axis.