Theory for Cd3As2 thin films in the presence of magnetic fields

Zhang Z., Yu Z., Liu G., Li Z., Yang S.A., Yao Y.

We propose an efficient algorithm for constructing k⋅p effective Hamiltonians, which is much faster than previously proposed algorithms. This algorithm is implemented in MagneticKP package. The package applies to both single-valued (spinless) and double-valued (spinful) cases, and to both magnetic and nonmagnetic systems. By interfacing with SpaceGroupIrep or MSGCorep packages, it can directly output the k⋅p Hamiltonian around arbitrary momentum point and expanded to arbitrary order in k. Program title: MagneticKP CPC Library link to program files: https://doi.org/10.17632/pgnbjspy4f.1 Developer's repository link: https://github.com/zhangzeyingvv/MagneticKP Licensing provisions: GNU General Public Licence 3.0 Programming language: Two independent versions written in Mathematica and Python External routines/libraries: SpaceGroupIrep (Optional), MSGCorep (Optional) Nature of problem: Construct k⋅p Hamiltonian for arbitrary magnetic space group. Solution method: Linear algebra, iterative algorithm to solve common null space of operators.

Guo B., Miao W., Huang V., Lygo A.C., Dai X., Stemmer S.

We report a topological phase transition in quantum-confined cadmium arsenide (${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$) thin films under an in-plane Zeeman field when the Fermi level is tuned into the topological gap via an electric field. Symmetry considerations in this case predict the appearance of a two-dimensional Weyl semimetal (2D WSM), with a pair of Weyl nodes of opposite chirality at charge neutrality that are protected by space-time inversion (${C}_{2}T$) symmetry. We show that the 2D WSM phase displays unique transport signatures, including saturated resistivities on the order of $h/{e}^{2}$ that persist over a range of in-plane magnetic fields. Moreover, applying a small out-of-plane magnetic field, while keeping the in-plane field within the stability range of the 2D WSM phase, gives rise to a well-developed odd integer quantum Hall effect, characteristic of degenerate, massive Weyl fermions. A minimal four-band $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model of ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$, which incorporates first-principles effective $g$ factors, qualitatively explains our findings.

Bampoulis P., Castenmiller C., Klaassen D.J., van Mil J., Liu Y., Liu C., Yao Y., Ezawa M., Rudenko A.N., Zandvliet H.J.

Germanene undergoes a topological phase transition and then becomes a normal insulator when the strength of an applied electric field is dialed up.

Lygo A.C., Guo B., Rashidi A., Huang V., Cuadros-Romero P., Stemmer S.

Utilizing surface state hybridization, a 2D topological insulator state has been demonstrated in 20 nm thin film of a 3D topological insulator, Cd${}_{3}$As${}_{2}$, using gate-voltage-tuned magnetotransport measurements.

Guo B., Lygo A.C., Dai X., Stemmer S.

Graphene and topological insulators can feature a unique quantum Hall state with a filling factor of ν = 0 that supplies a wealth of information about the nature of the underlying electronic states. Here, we report on the observation of a ν = 0 Hall state in magnetotransport experiments on a 20-nm-thin, (001)-oriented cadmium arsenide film that is tuned by a gate voltage. While cadmium arsenide is a topological semimetal as a bulk material, thin films can host topological insulator phases. At high magnetic fields, we observe a highly resistive ν = 0 Hall state that we attribute to a widening gap between two zeroth Landau levels as the magnetic field is increased. We discuss possible scenarios that could give rise to the lifting of the degeneracy of zeroth Landau levels. Our results are most consistent with a scenario of hybridization of the topological surface states induced by quantum confinement.

Villar Arribi P., Zhu J., Schumann T., Stemmer S., Burkov A.A., Heinonen O.

We computationally study the Fermi arc states in a Dirac semimetal, both in a semi-infinite slab and in the thin-film limit. We use Cd$_3$A$_2$ as a model system, and include perturbations that break the $C_4$ symmetry and inversion symmetry. The surface states are protected by the mirror symmetries present in the bulk states and thus survive these perturbations. The Fermi arc states persist down to very thin films, thinner than presently measured experimentally, but are affected by breaking the symmetry of the Hamiltonian. Our findings are compatible with experimental observations of transport in Cd$_3$As$_2$, and also suggest that symmetry-breaking terms that preserve the Fermi arc states nevertheless can have a profound effect in the thin film limit.

Chorsi H.T., Yue S., Iyer P.P., Goyal M., Schumann T., Stemmer S., Liao B., Schuller J.A.

In this paper, a detailed analysis of the temperature‐dependent optical properties of epitaxially grown cadmium arsenide (Cd3As2), a newly discovered 3D Dirac semimetal is reported. Fermi level tuning—instigated from Pauli‐blocking in the linear Dirac cone—and varying Drude response, generate large variations in the mid‐ and far‐infrared optical properties. Thermo‐optic shifts larger than those of traditional III–V semiconductors are demonstrated. Electron scattering rate, plasma frequency edge, Fermi level shift, optical conductivity, and electron effective mass analysis of Cd3As2 thin‐films are quantified and discussed in detail. The ab initio density functional study and experimental analysis of epitaxially grown Cd3As2 promise applications for nanophotonic and nanoelectronic devices, such as reconfigurable metamaterials and metasurfaces, nanoscale thermal emitters, and on‐chip directional antennas.

Wang D., Tang F., Ji J., Zhang W., Vishwanath A., Po H.C., Wan X.

Two-dimensional (2D) topological materials (TMs) have attracted tremendous attention due to the promise of revolutionary devices with non-dissipative electric or spin currents. Unfortunately, the scarcity of 2D TMs holds back the experimental realization of such devices. In this work, based on our recently developed, highly efficient TM discovery algorithm using symmetry indicators, we explore the possible 2D TMs in all non-magnetic compounds in four recently proposed materials databases for possible 2D materials. We identify hundreds of 2D TM candidates, including 205 topological (crystalline) insulators and 299 topological semimetals. In particular, we highlight MoS, with a mirror Chern number of -4, as a possible experimental platform for studying the interaction-induced modification to the topological classification of materials. Our results winnow out the topologically interesting 2D materials from these databases and provide a TM gene pool which for further experimental studies.

Cao C., Chen J.

Akzyanov R.S.

We study the spin conductivity of the surface states in a thin film of a topological insulator within Kubo formalism. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap, spin conductivity is enhanced. These findings indicate that a thin film of a topological insulator is a promising material for spintronic applications.

Burkov A.A.

Topological semimetals is a new class of condensed matter systems with nontrivial electronic structure topology. Their unusual observable properties may often be understood in terms of quantum anomalies. In particular, Weyl and Dirac semimetals, which have point band touching nodes, are characterized by the chiral anomaly, which leads to the Fermi arc surface states, anomalous Hall effect, negative longitudinal magnetoresistance and planar Hall effect. In this paper we explore analogous phenomena in nodal line semimetals. We demonstrate that such semimetals realize a three dimensional analog of the parity anomaly, which is a known property of two dimensional Dirac semimetals arising, for example, on the surface of a three dimensional topological insulator. We relate one of the characteristic properties of nodal line semimetals, namely the drumhead surface states, to this anomaly, and derive the field theory, which encodes the corresponding anomalous response.

Wu S., Fatemi V., Gibson Q.D., Watanabe K., Taniguchi T., Cava R.J., Jarillo-Herrero P.

Heating up the quantum spin Hall effect Taking practical advantage of the topologically protected conducting edge states of topological insulators (TIs) has proven difficult. Semiconductor systems that have been identified as two-dimensional TIs must be cooled down to near liquid helium temperatures to bring out their topological character. Wu et al. fabricated a heterostructure consisting of a monolayer of WTe2 placed between two layers of hexagonal boron nitride and found that its topological properties persisted up to a relatively high temperature of 100 K. Engineering this so-called quantum spin Hall effect in a van der Waals heterostructure makes it possible to apply many established experimental tools and functionalities. Science, this issue p. 76 Transport measurements show that the monolayer of WTe2 has helical edge modes at elevated temperatures. A variety of monolayer crystals have been proposed to be two-dimensional topological insulators exhibiting the quantum spin Hall effect (QSHE), possibly even at high temperatures. Here we report the observation of the QSHE in monolayer tungsten ditelluride (WTe2) at temperatures up to 100 kelvin. In the short-edge limit, the monolayer exhibits the hallmark transport conductance, ~e2/h per edge, where e is the electron charge and h is Planck’s constant. Moreover, a magnetic field suppresses the conductance, and the observed Zeeman-type gap indicates the existence of a Kramers degenerate point and the importance of time-reversal symmetry for protection from elastic backscattering. Our results establish the QSHE at temperatures much higher than in semiconductor heterostructures and allow for exploring topological phases in atomically thin crystals.

Reis F., Li G., Dudy L., Bauernfeind M., Glass S., Hanke W., Thomale R., Schäfer J., Claessen R.

Making a large-gap topological insulator Although of interest to basic research, topological insulators (TIs) have not yet lived up to their technological potential. This is partly because their protected surface-edge state usually lives within a narrow energy gap, with its exotic transport properties overwhelmed by the ordinary bulk material. Reis et al. show that a judicious choice of materials can make the gap wide enough for the topological properties to be apparent at room temperature. Numerical calculations indicate that a monolayer of Bismuth grown on SiC(0001) is a two-dimensional TI with a large energy gap. The researchers fabricated such a heterostructure and characterized it using scanning tunneling spectroscopy. The size of the experimentally measured gap was consistent with the calculations. Science, this issue p. 287 Scanning tunneling spectroscopy indicates a large energy gap and conducting edge states, consistent with calculations. Quantum spin Hall materials hold the promise of revolutionary devices with dissipationless spin currents but have required cryogenic temperatures owing to small energy gaps. Here we show theoretically that a room-temperature regime with a large energy gap may be achievable within a paradigm that exploits the atomic spin-orbit coupling. The concept is based on a substrate-supported monolayer of a high–atomic number element and is experimentally realized as a bismuth honeycomb lattice on top of the insulating silicon carbide substrate SiC(0001). Using scanning tunneling spectroscopy, we detect a gap of ~0.8 electron volt and conductive edge states consistent with theory. Our combined theoretical and experimental results demonstrate a concept for a quantum spin Hall wide-gap scenario, where the chemical potential resides in the global system gap, ensuring robust edge conductance.

Tang S., Zhang C., Wong D., Pedramrazi Z., Tsai H., Jia C., Moritz B., Claassen M., Ryu H., Kahn S., Jiang J., Yan H., Hashimoto M., Lu D., Moore R.G., et. al.

A combination of photoemission and scanning tunnelling spectroscopy measurements provide compelling evidence that single layers of 1T'-WTe2 are a class of quantum spin Hall insulator. A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling1,2. By investigating the electronic structure of epitaxially grown monolayer 1T'-WTe2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulk bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T'-WTe2 as a new class of QSH insulator with large bandgap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).

Fei Z., Palomaki T., Wu S., Zhao W., Cai X., Sun B., Nguyen P., Finney J., Xu X., Cobden D.H.

Experiments showing that a single layer of WTe2 can conduct electricity along its edges while insulating in the interior suggests that this material is a two-dimensional topological insulator. A two-dimensional topological insulator (2DTI) is guaranteed to have a helical one-dimensional edge mode1,2,3,4,5,6,7,8,9,10,11 in which spin is locked to momentum, producing the quantum spin Hall effect and prohibiting elastic backscattering at zero magnetic field. No monolayer material has yet been shown to be a 2DTI, but recently the Weyl semimetal WTe2 was predicted12 to become a 2DTI in monolayer form if a bulk gap opens. Here, we report that, at temperatures below about 100 K, monolayer WTe2 does become insulating in its interior, while the edges still conduct. The edge conduction is strongly suppressed by an in-plane magnetic field and is independent of gate voltage, save for mesoscopic fluctuations that grow on cooling due to a zero-bias anomaly, which reduces the linear-response conductance. Bilayer WTe2 also becomes insulating at low temperatures but does not show edge conduction. Many of these observations are consistent with monolayer WTe2 being a 2DTI. However, the low-temperature edge conductance, for contacts spacings down to 150 nm, never reaches values higher than ∼20 μS, about half the predicted value of e2/h, suggesting significant elastic scattering in the edge.

Litvinov V.

Abstract Quantum anomalous Hall effect generates dissipationless chiral conductive edge states in materials with large spin-orbit coupling and strong, intrinsic, or proximity magnetisation. The topological indexes of the energy bands are robust to smooth variations in the relevant parameters. Topological quantum phase transitions between states with different Chern numbers require the closing of the bulk bandgap: | C | = 1 → C = 1 / 2 corresponds to the transition from a topological insulator to a gapless state in k = 0 - quantum anomalous semimetal. Within the Bernevig-Hughes-Zhang (BHZ) model of 2D topological quantum well, this study identifies another type of topological phase transition induced by a magnetic field. The transition C = ± 1 → C = ∓ 1 occurs when the monotonic Zeeman field reaches the threshold value and thus triggers the reversal of edge modes chirality. The calculated threshold depends on the width of the conduction and valence bands and is more experimentally achievable the flatter the bands. The effect of the topological phase transition | Δ C | = 2 can be observed experimentally as a jump in magnetoresistance.