Quantum oscillations in resistivity and magnetization at high magnetic fields are a macroscopic fingerprint of the energy quantization due to the cyclotron motion of quasiparticles. In a thin Weyl semimetal, a unique thickness dependent Weyl-orbit quantum oscillation was proposed to exist, originating from a nonlocal cyclotron orbit via the electron tunneling between the top and bottom Fermi-arc surface states. Here, untwinned and high crystalline Weyl metal SrRuO$_3$ thin films with different thicknesses were grown on miscut SrTiO$_3$ (001) substrates. Magneto-transport measurements were carried out in magnetic fields up to 35 T, and quantum oscillations with different frequencies were observed and compared to the calculated band structure. In particular, we discovered a frequency $F \approx$ 30 T at low temperatures and above 3 T that corresponds to a small Fermi pocket with a light effective mass. Its oscillation amplitude appears to be at maximum for film thicknesses in a range of 10 to 20 nm, and the phase of the oscillation exhibits a systematic change with the film thickness. After isolating the well separated frequencies, the constructed Landau fan diagram shows an unusual concave downward curvature in the 1/$μ_0H_n$-$n$ curve, where $n$ is the Landau level index. Based on the rigorous analysis of the thickness and field-orientation dependence of the quantum oscillations, the oscillation with $F \approx$ 30 T is attributed to be of surface origin, which is related to the Fermi-arc surface state originating from non-overlapping Weyl nodes projected on the film's surface plane. Those findings can be understood within the framework of the Weyl-orbit quantum oscillation effect with non-adiabatic corrections.
In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for determining and understanding topological properties. A prominent example is Hall anomalies observed in SrRuO3 films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect (THE) or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the AHE of SrRuO3 ultrathin films with controllable inhomogeneities in film thickness (tSRO). By harnessing the st…
We present ultrafast x-ray diffraction experiments on thin films of metallic SrRuO$_3$ (SRO) after their excitation with ultrashort intense laser pulses. Depending on the layer thickness, the data exhibit a transient splitting of the (002) SRO Bragg peak evidencing the generation and propagation of sharp acoustic strain waves. These distinct structural dynamics are due to the exceptionally fast electron-phonon relaxation that gives rise to a quasi-instantaneous thermal stress in SRO. The interpretation is corroborated by numerical simulations which show excellent agreement with the experimenta…
We reconsider the problem of the anomalous Hall effect in ferromagnetic SrRuO$_3$, incorporating insights from the recently developed theory of Weyl semimetals. We demonstrate that SrRuO$_3$ possesses a large number of Weyl nodes, separated in momentum space, in its bandstructure. While the nodes normally do not coincide with the Fermi energy, unless the material is doped, we show that even the nodes inside the Fermi sea have a significant effect on the physical properties of the material. In particular, we show that the common belief that (non-quantized part of) the intrinsic anomalous Hall c…
Topological spin textures in an itinerant ferromagnet, SrRuO$_3$ is studied combining Hall transport measurements and numerical simulations. We observe characteristic signatures of the Topological Hall Effect associated with skyrmions. A relatively large thickness of our films and absence of heavy metal layers make the interfacial Dzyaloshinskii-Moriya interaction an unlikely source of these topological spin textures. Additionally, the transport anomalies exhibit an unprecedented robustness to magnetic field tilting and temperature. Our numerical simulations suggest that this unconventional be…
In a Weyl orbit, the Fermi arc surface states on opposite surfaces of the topological semimetal are connected through the bulk Weyl or Dirac nodes. Having a real-space component, these orbits accumulate a sample-size-dependent phase. Following recent work on the three-dimensional Dirac semimetal cadmium arsenide (Cd3As2), we have sought evidence for this thickness-dependent effect in quantum oscillations and quantum Hall plateaus in (112)-oriented Cd3As2 thin films grown by molecular beam epitaxy. We compare quantum transport in films of varying thickness at apparently identical gate-tuned car…
The growth of SrRuO$_3$ (SRO) thin film with high-crystallinity and low residual resistivity (RR) is essential to explore its intrinsic properties. Here, utilizing the adsorption-controlled growth technique, the growth condition of initial SrO layer on TiO$_2$-terminated SrTiO$_3$ (STO) (001) substrate was found to be crucial for achieving a low RR in the resulting SRO film grown afterward. The optimized initial SrO layer shows a $c$(2 x 2) superstructure that was characterized by electron diffraction, and a series of SRO films with different thicknesses ($t$s) were then grown. The resulting S…
We report a robust anomalous Nernst effect in Co2MnGa thin films in the thickness regime between 20 and 50 nm. The anomalous Nernst coefficient varied in the range of -2.0 to -3.0 uV/K at 300 K. We demonstrate that the anomalous Hall and Nernst coefficients exhibit similar behavior and fulfill the Mott relation. We simultaneously measure all four transport coefficients of the longitudinal resistivity, transversal resistivity, Seebeck coefficient, and anomalous Nernst coefficient. We connect the values of the measured and calculated Nernst conductivity by using the remaining three magneto-therm…
Bulk 1T$^\prime$-MoTe$_2$ shows a structural phase transition from 1T$^\prime$ to Weyl semimetallic (WSM) $ T_{d} $ phase at $\sim$ 240 K. This phase transition and transport properties in the two phases have not been investigated on ultra-thin crystals. Here we report electrical transport, $1/f$ noise and Raman studies in ultra-thin 1T$^\prime$-MoTe$_2$ ($\sim$ 5 to 16 nm thick) field-effect transistors (FETs) devices as a function of temperature. The electrical resistivities for thickness 16 nm and 11 nm show maxima at temperatures 208 K and 178 K, respectively, making a transition from semi…
We consider the effective coupling between impurity spins on surfaces of a thin-film Weyl semimetal within Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory. If the spins are on the same surface, their coupling reflects the anisotropy and the spin-momentum locking of the Fermi arcs. By contrast when the spins are on opposite surfaces, their coupling is mediated by the Fermi arcs as well as by bulk states. In this case the coupling is both surprisingly strong and strongly thickness dependent, with a maximum at an optimum thickness. We demonstrate our results using analytical solutions of states in t…
We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools - semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals - we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically c…
The ability to break Kirchhoff s law is of fundamental importance in thermal radiation. Various nonreciprocal emitters have been proposed to break the balance between absorption and emission. However, the thicknesses of the nonreciprocal materials are usually larger than 1/10 times of the wavelength. Besides, the previous proposed nonreciprocal emitters are complex, thus they can hardly be fabricated in experiment to verify the Kirchhoff s law for nonreciprocal materials. In this paper, we investigate the nonreciprocal thermal radiation of the magnetic Weyl semimetal (MWSM) film atop of the me…
We theoretically investigate surface plasmon polaritons propagating in the thin-film Weyl semimetals. We show how the properties of surface plasmon polaritons are affected by hybridization between plasmons localized at the two metal-dielectric interfaces. Generally, this hybridization results in new mixed plasmon modes, which are called short-range surface plasmons and long-range surface plasmons, respectively. We calculate dispersion curves of these mixed modes for three principle configurations of the axion vector describing axial anomaly in Weyl semimetals. We show that the partial lack of …
We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as $1/k^2$, where $k$ is the distance to a hot-line in the surface Brillouin zone that connects the projection of Weyl nodes with opposite chirality but which is distinct from the Fermi arc itself. Such surface Berry curvature appears whenever the bulk Weyl dispersion has a velocity tilt toward the surface of interest. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally, and in particular leads to a surface Berry cu…
The surface states of Weyl semi-metals (SM's) consist of disjointed Fermi-arcs. This unusual surface-Fermiology provides a fingerprint of the topological features of the bulk Weyl-phase. Using a combination of semiclassical and numerical methods, we show that, in contrast to naive expectation, there are closed magnetic orbits involving the open- surface Fermi-arcs. Below a critical field strength that depends on sample thickness, these orbits produce periodic quantum oscillations of the density of states in a magnetic field, enabling a variety of experimental probes of the unconventional Fermi…
We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall s…
The existence of Weyl nodes in the momentum space is a hallmark of a Weyl semimetal (WSM). A WSM can be confirmed by observing its Fermi arcs with separated Weyl nodes. In this paper, we study the spin- orbit interaction of light on the surface of WSM in the limit that the thickness is ultra-thin and the incident surface does not support Fermi arc. Our results show that the spin-dependent splitting induced by the spin-orbit interaction is related to the separation of Weyl nodes. By proposing an amplification technique called weak measurements, the distance of the nodes can be precisely determi…
The disjointed Fermi-arcs in Weyl semimetals can intertwine with chiral bulk modes and participate in unusual closed magnetic orbits in the presence of a vertical magnetic field. Here we carry out the quantum oscillation study of such unusual Weyl magnetic orbits in Dirac semimetal Cd3As2, a close cousin of Weyl semimetals. We find that extra two-dimensional (2D) quantum oscillations emerge at high field, which superimpose on 3D bulk background and can be attributed to the Weyl magnetic orbits, when the thickness of nanoplates is smaller than the mean free path of the electrons. Further eviden…
The Weyl semimetal surface is modeled by applying the Bogolyubov boundary conditions, in which the quasiparticles have an infinite Dirac mass outside the semimetal. For a Weyl semimetal shaped as a slab of finite thickness, we derive an exact spectral equation for the quasiparticle states and obtain the spectrum of the bulk as well as surface Fermi arc modes. We also show that, in the presence of the magnetic field, the separation between Weyl nodes in momentum space and the length of the Fermi arcs in the reciprocal space are affected by the interactions. As a result, we find that the period …
Weyl semimetals harbor unusual surface states known as Fermi arcs, which are essentially disjoint segments of a two dimensional Fermi surface. We describe a prescription for obtaining Fermi arcs of arbitrary shape and connectivity by stacking alternate two dimensional electron and hole Fermi surfaces and adding suitable interlayer coupling. Using this prescription, we compute the local density of states -- a quantity directly relevant to scanning tunneling microscopy -- on a Weyl semimetal surface in the presence of a point scatterer and present results for a particular model that is expected …
Weyl semimetals (WSMs) have unusual optical response originated from unique topological properties of their bulk and surface electron states. Their third-order optical nonlinearity is expected to be very strong, especially at long wavelengths, due to linear dispersion and high Fermi velocity of three-dimensional Weyl fermions. Here we derive the third-order nonlinear optical conductivity of WSMs in the long-wavelength limit and calculate the intensity of the nonlinear four-wave mixing signal as it is transmitted through the WSM film or propagates away from the surface of the material in the re…
Weyl semimetals have recently attracted extensive attention due to their anomalous band structure manifested by topological properties that lead to some unusual and unique physical properties. We investigate novel features of surface plasmon polaritons in a slot waveguide comprised from two semi-infinite Weyl semimetals. We consider symmetric Voigt-Voigt and Faraday-Faraday configurations for plasmon polaritons in two interfaces of waveguide and show that the resulting dispersion is symmetric and the propagation of surface plasmon polaritons is bidirectional. We introduce exotic and novel asym…
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and two-fold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional two-fold rotation symmetry is mediated by an emergent stable two-dimensional Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry…
We investigate the influence of surface states on the nonlinear Hall response of non-centrosymmetric time-reversal invariant Weyl semimetals. To do so, we perform a tomography of the Berry curvature dipole in a slab system using a minimal two-band model. We find that in the type-I phase, the nonlinear Hall response is not particularly sensitive to the presence of Fermi arcs or other trivial surface states. However, in the type-II phase, we find that these surface states contribute substantially to the Berry curvature dipole, leading to a strong thickness dependence of the nonlinear Hall respon…
The intrinsic magnetic topological insulators, Mn(Bi1-xSbx)2Te4, in their spin-aligned strong field configuration have been identified as a Weyl semimetal with single pair of Weyl nodes1-4. A direct consequence of the Weyl state is the layer-dependent Chern number (C) in thin film quantization. Previous reports in MnBi2Te4 thin films revealed the higher C states in the spin alignment by either increasing the film thickness5 or controlling chemical potential into electron doping6-8. A clear picture of the higher Chern states is still missing as the situation is complicated by the emerging of su…
Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor $ν=0$ under an external magnetic field if there is a finite potential difference between the top and bottom surfaces. We calculate energy spectra of surface Weyl fermions in the $ν=0$ QHE and find that gapped edge states with helical spin structure are formed from Weyl fermions on the side surfaces under certain conditions. These edge channels account for the nonlocal charge transport in the $ν=0$ QHE which is observed in a recent experiment on (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ …
The observation of the electrically tunable and highly confined plasmons in graphene has stimulated the exploration of interesting properties of plasmons in other two dimensional materials. Recently, hyperbolic plasmon resonance modes are observed in exfoliated WTe2 films, a type-II Weyl semimetal with layered structure, providing a platform for the assembly of plasmons with hyperbolicity and exotic topological properties. However, the plasmon modes were observed in relatively thick and small-area films, which restrict the tunability and application for plasmons. Here, large-area (~ cm) WTe2 f…
Tunable Chern superconductivity of PtBi$_2$ in slab geometry
Leibniz Institute for Solid State and Materials Research, IFW Dresden（德累斯顿莱布尼茨固体与材料研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）；Institute for Theoretical Physics, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
Dirac semi-metals show a linear electronic dispersion in three dimension described by two copies of the Weyl equation, a theoretical description of massless relativistic fermions. At the surface of a crystal, the breakdown of fermion chirality is expected to produce topological surface states without any counterparts in high-energy physics nor conventional condensed matter systems, the so-called "Fermi Arcs". Here we present Shubnikov-de Haas oscillations involving the Fermi Arc states in Focused Ion Beam prepared microstructures of Cd$_3$As$_2$. Their unusual magnetic field periodicity and de…
Magnetism and spin-orbit coupling (SOC) are two quintessential ingredients underlying novel topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by SOC, the nodal structures become a source of Berry curvature; this leads to a large anomalous Hall effect (AHE). Contrary to three-dimensional systems that naturally host nodal points/lines, two-dimensional (2D) systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that 2D spin-polarized band structures…
Dirac semimetals (DSMs) have topologically robust three-dimensional Dirac (doubled Weyl) nodes with Fermi-arc states. In heterostructures involving DSMs, charge transfer occurs at the interfaces, which can be used to probe and control their bulk and surface topological properties through surface-bulk connectivity. Here we demonstrate that despite a band gap in DSM films, asymmetric charge transfer at the surface enables one to accurately identify locations of the Dirac-node projections from gapless band crossings and to examine and engineer properties of the topological Fermi-arc surface state…
Quantum materials harbor a cornucopia of exotic transport phenomena challenging our understanding of condensed matter. Among these, a giant, non-saturating linearmagnetoresistance (MR) has been reported in various systems, from Weyl semi-metals to topological insulators. Its origin is often ascribed to unusual band structure effects but it may also be caused by extrinsic sample disorder. Here, we report a very large linear MR in a SrTiO$_3$ two-dimensional electron gas and, by combining transport measurements with electron spectro-microscopy, show that it is caused by nanoscale inhomogeneities…
Evolution of topological phases in atomically thin WTe2 films
Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院淞江研究院）；Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）
