Finite-temperature conductivity and magnetoconductivity of topological insulators

Weak Antilocalization and Negative Magnetoresistance of the Gate-Tunable PbTe Thin Films

We have systematically studied the electromagnetic transport properties of PbTe thin films under gate voltage modulation. The system demonstrates pronounced electron-electron interactions exclusively within the gate voltage range where only hole carriers are present. Furthermore, the Berry phase is utilized to qualitatively elucidate the transition between weak antilocalization (WAL) and weak localization (WL) through the regulation of gate voltage and temperature. Using the three-resistor model, we have effectively explained the correlation between the characteristic temperature of the R-T curve, the coexistence of electron-hole carriers, and the nonmonotonic temperature dependence of negative magnetoresistance (NMR), consistently indicating that complex magnetotransport phenomena are caused by microscopic disorder. Our research findings open up new avenues for exploring and manipulating the magnetotransport properties of PbTe thin films.

Observation of Anomalous Planar Hall Effect Induced by One-Dimensional Weak Antilocalization

The confinement of electrons in one-dimensional (1D) space highlights the prominence of the role of electron interactions or correlations, leading to a variety of fascinating physical phenomena. The quasi-1D electron states can exhibit a unique spin texture under spin-orbit interaction (SOI) and thus could generate a robust spin current by forbidden electron backscattering. Direct detection of such 1D spin or SOI information, however, is challenging due to complicated techniques. Here, we identify an anomalous planar Hall effect (APHE) in the magnetotransport of quasi-1D van der Waals (vdW) topological materials as exemplified by Bi4Br4, which arises from the quantum interference correction of 1D weak antilocalization (WAL) to the ordinary planar Hall effect and demonstrates a deviation from the usual sine and cosine curves. The occurrence of 1D WAL is correlated to the line-shape Fermi surface and persistent spin texture of (100) topological surface states of Bi4Br4, as revealed by both our angle-resolved photoemission spectroscopy and first-principles calculations. By generalizing the observation of APHE to other non-vdW bulk materials, this work provides a possible characteristic of magnetotransport for identifying the spin/SOI information and quantum interference behavior of 1D states in 3D topological material.

Proximity induced band gap opening in topological-magnetic heterostructure (Ni80Fe20/p-TlBiSe2/p-Si) under ambient condition

The broken time reversal symmetry states may result in the opening of a band gap in TlBiSe2 leading to several interesting phenomena which are potentially relevant for spintronic applications. In this work, the quantum interference and magnetic proximity effects have been studied in Ni80Fe20/p-TlBiSe2/p-Si (Magnetic/TI) heterostructure using physical vapor deposition technique. Raman analysis shows the symmetry breaking with the appearance of A21u mode. The electrical characteristics are investigated under dark and illumination conditions in the absence as well as in the presence of a magnetic field. The outcomes of the examined device reveal excellent photo response in both forward and reverse bias regions. Interestingly, under a magnetic field, the device shows a reduction in electrical conductivity at ambient conditions due to the crossover of weak localization and separation of weak antilocalization, which are experimentally confirmed by magnetoresistance measurement. Further, the photo response has also been assessed by the transient absorption spectroscopy through analysis of charge transfer and carrier relaxation mechanisms. Our results can be beneficial for quantum computation and further study of topological insulator/ferromagnet heterostructure and topological material based spintronic devices due to high spin orbit coupling along with dissipationless conduction channels at the surface states.

Crossover from gapped-to-gapless Dirac surface states in magnetic topological insulator MnBi2Te4

Intrinsic magnetic topological insulators (MTIs) host exotic topological phases such as quantized anomalous Hall insulating phase, arising due to the large magnetic exchange gap. However, the interplay of magnetism and topology in these systems in different temperature regimes remains elusive. In this work, we present the logarithmic temperature-dependence of conductivity for sub-100 nm thick exfoliated flakes of MTI MnBi2Te4in the presence of out-of-plane magnetic fields and extracted the linear slope,κ. We observed a characteristic change,Δκ∼-0.5in the low-temperature regime, indicating the gapped Dirac surface state according to Lu-Shen theory. We also report the recovery of topological properties in the system via the weak-antilocalization effect in the vicinity of antiferromagnetic to paramagnetic transition and in the paramagnetic regime. Hikami-Larkin-Nagaoka analysis suggested the presence of topological surface states. Therefore, our study helps in understanding how intrinsic magnetism masks topological properties in an MTI as long as magnetic ordering persists.

Effects of pressure and temperature on topological electronic materials X2Y3 (X = As, Sb, Bi; Y = Se, Te) using first-principles

We systematically study the thermal and topological properties of X2Y3 (X = As, Sb, Bi; Y = Se, Te) and the effects of pressure and temperature on their electronic properties using first-principles. We find that the external pressure-induced electronic topological transition occurs at about 5 GPa for Bi2Se3, and the type of band gap tends to become indirect with the increase of pressure. We also investigate the lattice expansion with temperature in quasi-harmonic approximation and further explore the effect of temperature on the volume, band gap, and volumetric thermal expansion coefficient of the studied selenides and tellurides. Finally, we calculate the evolution of the Wannier charge center of X2Y3 to determine their topological invariants, and theoretically suggest that Bi2Se3 changes from a topological to an ordinary insulator when the pressure decreases to -8 GPa; As2Se3 is found to be an ordinary insulator, while all other four compounds are always strong topological insulators at any pressure or temperature.

Topological transport properties of highly oriented Bi2Te3thin film deposited by sputtering

Topological insulators (TIs) are the promising materials for next-generation technology due to their exotic features such as spin momentum locking, conducting surface states, etc. However, the high-quality growth of TIs by sputtering technique, which is one of the foremost industrial requirements, is extremely challenging. Also, the demonstration of simple investigation protocols to characterize topological properties of TIs using electron-transport methods is highly desirable. Here, we report the quantitative investigation of non-trivial parameters employing magnetotransport measurements on a prototypical highly textured Bi2Te3TI thin film prepared by sputtering. Through the systematic analyses of the temperature and magnetic field dependent resistivity, all topological parameters associated with TIs, such as coherency factorα, Berry phase (ΦB), mass term (m), the dephasing parameter (p), slope of temperature dependent conductivity correction (κ) and the surface state penetration depth (λ) are estimated by using the modified 'Hikami-Larkin-Nagaoka', 'Lu-Shen' and 'Altshuler-Aronov' models. The obtained values of topological parameters are well comparable to those reported on molecular beam epitaxy grown TIs. The epitaxial growth of Bi2Te3film using sputtering, and investigation of the non-trivial topological states from its electron-transport behavior are important for their fundamental understanding and technological applications.

Quantum transport and potential of topological states for thermoelectricity in Bi2Te3thin films

This paper reviews recent developments in quantum transport and it presents current efforts to explore the contribution of topological insulator boundary states to thermoelectricity in Bi₂Te₃thin films. Although Bi₂Te₃has been used as a thermoelectric material for many years, it is only recently that thin films of this material have been synthesized as 3D topological insulators with interesting physics and potential applications related to topologically protected surface states. A major bottleneck in Bi₂Te₃thin films has been eliminating its bulk conductivity while increasing its crystal quality. The ability to grow epitaxial films with high crystal quality and to fabricate sophisticated Bi₂Te₃-based devices is attractive for implementing a variety of topological quantum devices and exploring the potential of topological states to improve thermoelectric properties. Special emphasis is laid on preparing low-defect-density Bi₂Te₃epitaxial films, gate-tuning of normal-state transport and Josephson supercurrent in topological insulator/superconductor hybrid devices. Prospective quantum transport experiments on Bi₂Te₃thin-film devices are discussed as well. Finally, an overview of current progress on the contribution of topological insulator boundary states to thermoelectricity is presented. Future explorations to reveal the potential of topological states for improving thermoelectric properties of Bi₂Te₃films and realizing high-performance thermoelectric devices are discussed.

In-depth analysis of anisotropic magnetoconductance in Bi2Se3thin films with electron-electron interaction corrections

A combination of out-of-plane (OOP) and in-plane (IP) magnetoconductance (MC) study in topological insulators (TI) is often used as an experimental technique to probe weak anti-localization (WAL) response of the topological surface states (TSSs). However, in addition to the above WAL response, weak localization (WL) contribution from conducting bulk states are also known to coexist and contribute to the overall MC; a study that has so far received limited attention. In this article, we accurately extract the above WL contribution by systematically analyzing the temperature and magnetic field dependency of conductivity in Bi₂Se₃films. For accurate analysis, we quantify the contribution of electron-electron interactions to the measured MC which is often ignored in the WAL studies. Moreover, we show that the WAL effect arising from the TSSs with finite penetration depth, for OOP and IP magnetic field can together explain the anisotropic magnetoconductance (AMC) and, thus, the investigated AMC study can serve as a useful technique to probe the parameters like phase coherence length and penetration depth that characterise the TSSs in 3D TIs. We also demonstrate that increase in bulk-disorder, achieved by growing the films on amorphous SiO₂substrate rather than on crystalline Al₂O₃(0001), can lead to stronger decoupling between the top and bottom surface states of the film.

Magnetic Moments Induced by Atomic Vacancies in Transition Metal Dichalcogenide Flakes

2D magnetism plays a key role in both fundamental physics and potential device applications. However, the instability of the discovered 2D magnetic materials has been one main obstacle in deep research and potential application of 2D magnetism. Here, a localized magnetic moment induced by Pt vacancies in air-stable type-II Dirac semimetal PtSe₂ flakes is reported. The localized magnetic moments give rise to the Kondo effect, evidenced by logarithmic increment of resistance with decreasing temperature and isotropic negative longitudinal magnetoresistance. Additionally, the induced magnetic moment and Kondo temperature appear to depend on thickness in the thinner samples (<10 nm). The small magnetocrystalline anisotropy revealed by first-principles calculation indicates that the magnetic moments are randomly localized instead of long-range ordered. The findings demonstrate a new means to induce magnetism in 2D non-magnetic materials.

Highly Efficient Electric-Field Control of Giant Rashba Spin-Orbit Coupling in Lattice-Matched InSb/CdTe Heterostructures

Spin-orbit coupling (SOC), the relativistic effect describing the interaction between the orbital and spin degrees of freedom, provides an effective way to tailor the spin/magnetic orders using electrical means. Here, we report the manipulation of the spin-orbit interaction in the lattice-matched InSb/CdTe heterostructures. Owing to the energy band bending at the heterointerface, the strong Rashba effect is introduced to drive the spin precession where pronounced weak antilocalization cusps are observed up to 100 K. With effective quantum confinement and suppressed bulk conduction, the SOC strength is found to be enhanced by 75% in the ultrathin InSb/CdTe film. Most importantly, we realize the electric-field control of the interfacial Rashba effect using a field-effect transistor structure and demonstrate the gate-tuning capability which is 1-2 orders of magnitude higher than other materials. The adoption of the InSb/CdTe integration strategy may set up a general framework for the design of strongly spin-orbit coupled systems that are essential for CMOS-compatible low-power spintronics.

Permutation Symmetry in Coherent Electrons Scattering by Disordered Media

A non-Anderson weak localization of an electron beam scattered from disordered matter is considered with respect to the principle of electron indistinguishability. A weak localization of electrons of a new type is essentially associated with inelastic processing. The origin of inelasticity is not essential. We take into account the identity principle for electron beam and electrons of the atom of the scatterer with an open shell. In spite of isotropic scattering by each individual scatterer, the electron exchange contribution has a hidden parameters effect on the resulting angular dependence of the scattering cross-section. In this case, the electrons of the open shell of an atomic scatterer can be in the s-state, that is, the atomic shell remains spherically symmetric. The methods of an invariant time-dependent exchange perturbation theory and a Green functions with exchange were applied. An additional angular dependence of the scattering cross-section appears during the coherent scattering process. It is shown exactly for the helium scatterer that the role of exchange effects in the case of a singlet is negligible, while for the triplet state, it is decisive, especially for those values of the energy of incident electrons when de Broglie’s waves are commensurate with the atomic.

Two-Dimensional Electron Gas at the Spinel/Perovskite Interface: Suppression of Polar Catastrophe by an Ultrathin Layer of Interfacial Defects

Two-dimensional electron gas (2DEG) at the interface between two insulating perovskite oxides has attracted much interest for both fundamental physics and potential applications. Here, we report the discovery of a new 2DEG formed at the interface between spinel MgAl₂O₄ and perovskite SrTiO₃. Transport measurements, electron microscopy imaging, and first-principles calculations reveal that the interfacial 2DEG is closely related to the symmetry breaking at the MgAl₂O₄/SrTiO₃ interface. The critical film thickness for the insulator-to-metal transition is approximately 32 Å, which is twice as thick as that reported on the widely studied LaAlO₃/SrTiO₃ system. Scanning transmission electron microscopy imaging indicates the formation of interfacial Ti-Al antisite defects with a thickness of ∼4 Å. First-principles density functional theory calculations indicate that the coexistence of the antisite defects and surface oxygen vacancies may explain the formation of interfacial 2DEG as well as the observed critical film thickness. The discovery of 2DEG at the spinel/perovskite interface introduces a new material platform for designing oxide interfaces with desired characteristics.

Quantum Transport Signatures of a Close Candidate for a Type II Nodal-Line Semimetal

The nodal-line semimetal is a new type of topological state of matter in which the crossing of two energy bands forms a nodal loop. In the absence of spin-orbit coupling, Mg₃Bi₂ is predicted as a type II nodal-line semimetal, which may evolve to a topological insulator with a small energy gap of ∼35 meV in the presence of spin-orbit coupling. However, the transport evidence is still lacking. Here, we measure the magneto-transport in Mg₃Bi₂. At low temperatures, the magnetoconductivity exhibits a weak antilocalization behavior. We fit the experimental data with a magnetoconductivity formula for the weak antilocalization effect of three-dimensional nodal-line semimetals as well as the well-known Hikami-Larkin-Nagaoka formula for two-dimensional weak (anti)localization effects. By comparing the fitting results of these two theories, we demonstrate that the weak antilocalization in Mg₃Bi₂ is better described by the theory for nodal-line semimetals. Our work will inspire more explorations to use the new weak localization theory to identify a large spectrum of nodal-line semimetals.

Anomalous Temperature Dependence of Quantum Correction to the Conductivity of Magnetic Topological Insulators

Quantum transport in magnetic topological insulators reveals a strong interplay between magnetism and topology of electronic band structures. A recent experiment on magnetically doped topological insulator Bi_{2}Se_{3} thin films showed the anomalous temperature dependence of the magnetoconductivity while their field dependence presents a clear signature of weak antilocalization [Tkac et al., Phys. Rev. Lett. 123, 036406 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.036406]. Here, we demonstrate that the tiny mass of the surface electrons induced by the bulk magnetization leads to a temperature-dependent correction to the π Berry phase and generates a decoherence mechanism to the phase coherence length of the surface electrons. As a consequence, the quantum correction to conductivity can exhibit nonmonotonic behavior by decreasing the temperature. This effect is attributed to the close relation of the Berry phase and quantum interference of the topological surface electrons in quantum topological materials.

Nonvolatile Control of the Electronic Properties of In2-xCrxO3 Semiconductor Films by Ferroelectric Polarization Charge

A series of Cr-doped In_2-xCr_xO₃ (ICO) semiconductor thin films were epitaxially grown on (111)-oriented 0.71Pb(Mg_1/3Nb_2/3)O₃-0.29PbTiO₃ (PMN-0.29PT) single-crystal substrates by the pulsed laser deposition. Upon the application of an electric field to the PMN-0.29PT substrate along the thickness direction, we realized in situ, reversible, and nonvolatile control of the electronic properties and Fermi level of the films, which are manifested by abundant physical phenomena such as the n-type to p-type transformation, metal-semiconductor transition, metal-insulator transition, crossover of the magnetoresistance (MR) from negative to positive, and a large nonvolatile on-and-off ratio of 5.5 × 10⁴% at room temperature. We also strictly disclose that both the sign and the magnitude of MR are determined by the electron carrier density of ICO films, which could modify the s-d exchange interaction and weak localization effect. Our results demonstrate that the ferroelectric gating approach using PMN-PT can be utilized to gain deeper insight into the carrier-density-related electronic properties of In₂O₃-based semiconductors and provide a simple and energy efficient way to construct multifunctional devices which can utilize the unique properties of composite materials.

Influence of an Anomalous Temperature Dependence of the Phase Coherence Length on the Conductivity of Magnetic Topological Insulators

Magnetotransport constitutes a useful probe to understand the interplay between electronic band topology and magnetism in spintronic devices. A recent theory of Lu and Shen [Phys. Rev. Lett. 112, 146601 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.146601] on magnetically doped topological insulators predicts that quantum corrections Δκ to the temperature dependence of conductivity can change sign across the Curie transition. This phenomenon has been attributed to a suppression of the Berry phase of the topological surface states at the Fermi level, caused by a magnetic energy gap. Here, we demonstrate experimentally that Δκ can reverse its sign even when the Berry phase at the Fermi level remains unchanged. The contradictory behavior to theory predictions is resolved by extending the model by Lu and Shen to a nonmonotonic temperature scaling of the inelastic scattering length showing a turning point at the Curie transition.

Quantum Interference Theory of Magnetoresistance in Dirac Materials

Magnetoresistance in many samples of Dirac semimetals and topological insulators displays nonmonotonic behavior over a wide range of magnetic fields. Here a formula of magnetoconductivity is presented for massless and massive Dirac fermions in Dirac materials due to quantum interference of Dirac fermions in scalar impurity scattering potentials. It reveals a striking crossover from positive to negative magnetoresistivity, uncovering strong competition between weak localization and weak antilocalization in multiple Cooperon channels at different chemical potentials, effective masses, and finite temperatures. This work sheds light on the important role of strong coupling of the conduction and valence bands in the quantum interference transport in topological nontrivial and trivial Dirac materials.

The dimensional crossover of quantum transport properties in few-layered Bi2Se3 thin films

Topological insulator bismuth selenide (Bi₂Se₃) thin films with a thickness of 6.0 quintuple layers (QL) to 23 QL are deposited using pulsed laser deposition (PLD). The arithmetical mean deviation of the roughness (R _a) of these films is less than 0.5 nm, and the root square mean deviation of the roughness (R _q) of these films is less than 0.6 nm. Two-dimensional localization and weak antilocalization are observed in the Bi₂Se₃ thin films approaching 6.0 nm, and the origin of weak localization should be a 2D electron gas resulting from the split bulk state. Localization introduced by electron-electron interaction (EEI) is revealed by the temperature dependence of the conductivity. The enhanced contribution of three-dimensional EEI and electron-phonon interaction in the electron dephasing process is found by increasing the thickness. Considering the advantage of stoichiometric transfer in PLD, it is believed that the high quality Bi₂Se₃ thin films might provide more paths for doping and multilayered devices.

Weak Localization and Antilocalization in Nodal-Line Semimetals: Dimensionality and Topological Effects

New materials such as nodal-line semimetals offer a unique setting for novel transport phenomena. Here, we calculate the quantum correction to conductivity in a disordered nodal-line semimetal. The torus-shaped Fermi surface and encircled π Berry flux carried by the nodal loop result in a fascinating interplay between the effective dimensionality of electron diffusion and band topology, which depends on the scattering range of the impurity potential relative to the size of the nodal loop. For a short-range impurity potential, backscattering is dominated by the interference paths that do not encircle the nodal loop, yielding a 3D weak localization effect. In contrast, for a long-range impurity potential, the electrons effectively diffuse in various 2D planes and the backscattering is dominated by the interference paths that encircle the nodal loop. The latter leads to weak antilocalization with a 2D scaling law. Our results are consistent with symmetry consideration, where the two regimes correspond to the orthogonal and symplectic classes, respectively. Furthermore, we present weak-field magnetoconductivity calculations at low temperatures for realistic experimental parameters and predict that clear scaling signatures ∝sqrt[B] and ∝-lnB, respectively. The crossover between the 3D weak localization and 2D weak antilocalization can be probed by tuning the Fermi energy, giving a unique transport signature of the nodal-line semimetal.

Nonvolatile and Reversible Ferroelectric Control of Electronic Properties of Bi2Te3 Topological Insulator Thin Films Grown on Pb(Mg1/3Nb2/3)O3-PbTiO3 Single Crystals

Single-phase (00 l)-oriented Bi₂Te₃ topological insulator thin films have been deposited on (111)-oriented ferroelectric 0.71Pb(Mg_1/3Nb_2/3)O₃-0.29PbTiO₃ (PMN-PT) single-crystal substrates. Taking advantage of the nonvolatile polarization charges induced by the polarization direction switching of PMN-PT substrates at room temperature, the carrier density, Fermi level, magnetoconductance, conductance channel, phase coherence length, and quantum corrections to the conductance can be in situ modulated in a reversible and nonvolatile manner. Specifically, upon the polarization switching from the positively poled P_r⁺ state (i.e., polarization direction points to the film) to the negatively poled P_r^- (i.e., polarization direction points to the bottom electrode) state, both the electron carrier density and the Fermi wave vector decrease significantly, reflecting a shift of the Fermi level toward the Dirac point. The polarization switching from P_r⁺ to P_r^- also results in significant increase of the conductance channel α from -0.15 to -0.3 and a decrease of the phase coherence length from 200 to 80 nm at T = 2 K as well as a reduction of the electron-electron interaction. All these results demonstrate that electric-voltage control of physical properties using PMN-PT as both substrates and gating materials provides a simple and a straightforward approach to realize reversible and nonvolatile tuning of electronic properties of topological thin films and may be further extended to study carrier density-related quantum transport properties of other quantum matter.

Kondo effect with tunable spin-orbit interaction in LaTiO3/CeTiO3/SrTiO3 heterostructure

We have fabricated epitaxial films of CeTiO₃ (CTO) on (0 0 1) oriented SrTiO₃ (STO) substrates, which exhibit highly insulating and diamagnetic properties. X-ray photoelectron spectroscopy was used to establish the 3+  valence state of the Ce and Ti ions. Furthermore, we have also fabricated δ (CTO) doped LaTiO₃ (LTO)/SrTiO₃ thin films which exhibit variety of interesting properties including Kondo effect and spin-orbit interaction (SOI) at low temperatures. The SOI shows a non-monotonic behaviour as the thickness of the CTO layer is increased and is reflected in the value of characteristic SOI field ([Formula: see text]) obtained from weak anti-localization fitting. The maximum value of [Formula: see text] is 1.00 T for δ layer thickness of 6 u.c. This non-monotonic behaviour of SOI is attributed to the strong screening of the confining potential at the interface. The screening effect is enhanced by the CTO layer thickness and the dielectric constant of STO which increases at low temperatures. Due to the strong screening, electrons confined at the interface are spread deeper into the STO bulk where it starts to populate the Ti [Formula: see text] subbands; consequently the Fermi level crosses over from [Formula: see text] to the [Formula: see text] subbands. At the crossover region of [Formula: see text] where there is orbital mixing, SOI goes through a maximum.

Proximity-Induced Magnetic Order in a Transferred Topological Insulator Thin Film on a Magnetic Insulator

Breaking the time reversal symmetry (TRS) in a topological insulator (TI) by introducing a magnetic order gives rise to exotic quantum phenomena. One of the promising routes to inducing a magnetic order in a TI is utilizing magnetic proximity effect between a TI and a strong magnetic insulator (MI). In this article, we demonstrate a TI/MI heterostructure prepared through transferring a molecular beam epitaxy (MBE)-grown Bi₂Se₃ film onto a yttrium iron garnet (YIG) substrate via wet transfer. The transferred Bi₂Se₃ exhibits excellent quality over a large scale. Moreover, through wet transfer we are able to engineer the interface and perform a comparative study to probe the proximity coupling between Bi₂Se₃ and YIG under different interface conditions. A detailed investigation of both the anomalous Hall effect and quantum corrections to the conductivity in magnetotransport measurements reveals an induced magnetic order as well as TRS breaking in the transferred Bi₂Se₃ film on YIG. In contrast, a thin layer of AlO _x at the interface obstructs the proximity coupling and preserves the TRS, indicating the critical role of the interface in mediating magnetic proximity effect.

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Proximity Effect induced transport Properties between MBE grown (Bi1-xSbx)2Se3 Topological Insulators and Magnetic Insulator CoFe2O4

In this study, we investigate the proximity effect in topological insulator (TI) and magnetic insulator bilayer system. (Bi_1−xSb_x)₂Se₃/CoFe₂O₄ (CFO) heterostructure was fabricated using molecular beam epitaxy and pulsed laser deposition system respectively. As revealed from the magnetoresistance measurement, the weak anti-localization (WAL) is strongly suppressed by proximity effect in (Bi_1−xSb_x)₂Se₃/CFO interface. Modified Hikama-Larkin-Nagaoka equation was used to fit the WAL results so that the size of surface state gap can be extracted successfully. The temperature-dependent resistance of the heterostructures at small and large perpendicular magnetic fields were also measured and analyzed. The results indicate that the surface band gap can be induced in TI and continuously enlarged up to 9 T, indicating the gradual alignment of the magnetic moment in CFO under perpendicular magnetic field. The approaches and results accommodated in this work show that CFO can effectively magnetize (Bi_1−xSb_x)₂Se₃ and the heterostructures are promising for TI-based spintronic device applications.

Large-Area and Transferred High-Quality Three-Dimensional Topological Insulator Bi2-xSbxTe3-ySey Ultrathin Film by Catalyst-Free Physical Vapor Deposition

Uniform and large-area synthesis of bulk insulating ultrathin films is an important subject toward applications of a surface of three-dimensional topological insulators (3D-TIs) in various electronic devices. Here we report epitaxial growth of bulk insulating three-dimensional topological insulator (3D-TI) Bi_2-xSb_xTe_3-ySe_y (BSTS) ultrathin films, ranging from a few quintuple to several hundreds of layers, on mica in a large-area (1 cm²) via catalyst-free physical vapor deposition. These films can nondestructively be exfoliated using deionized water and transferred to various kinds of substrates as desired. The transferred BSTS thin films show good ambipolar characteristics as well as well-defined quantum oscillations arising from the topological surface states. The carrier mobility of 2500-5100 cm²/(V s) is comparable to the high-quality bulk BSTS single crystal. Moreover, tunable electronic states from the massless to the massive Dirac fermion were observed with a decrease in the film thickness. Both the feasible large-area synthesis and the reliable film transfer process can promise that BSTS ultrathin films will pave a route to many applications of 3D-TIs.

Suppressed weak antilocalization in the topological insulator Bi2Se3 proximity coupled to antiferromagnetic NiO

Time-reversal symmetry (TRS) breaking of the topological insulators (TIs) is a prerequisite to observe the quantum anomalous Hall effect (QAHE) and topological magnetoelectric effect (TME). Although antiferromagnetism as well as ferromagnetism could break the TRS and generate massive Dirac surface states in the TIs, no attention has been paid to the antiferromagnet-TI heterostructures. Herein, we report the magnetotransport measurements of Bi₂Se₃ proximately coupled to antiferromagnetic NiO. Thin films of Bi₂Se₃ were successfully grown on the NiO (001) single crystalline substrates by molecular beam epitaxy. Unexpectedly, we observed a strong suppression of the weak antilocalization effect, which is similar to the case of TIs coupled to the ferromagnetic materials. For the 5 nm-thick Bi₂Se₃ sample on NiO, we even observed a crossover to weak localization at 2 K. These behaviors are attributed to the strong magnetic exchange field from the Ni 3d electrons. Our results show the effectiveness of the antiferromagnetic materials in breaking the TRS of TIs by the proximity effect and their possible applications for QAHE and TME observations.

Tuning the transport and magnetism in a Cr–Bi2Se3topological insulator by Sb doping

High-quality crystalline (Cr,Sb)-doped Bi₂Se₃(Cr-BSS) films were synthesized using molecular beam epitaxy (MBE).

Andreev Reflection in an s-Type Superconductor Proximized 3D Topological Insulator

We investigate transport and shot noise in lateral normal-metal-3D topological-insulator-superconductor contacts, where the 3D topological insulator (TI) is based on Bi. In the normal state, the devices are in the elastic diffusive transport regime, as demonstrated by a nearly universal value of the shot noise Fano factor F_{N}≈1/3 in magnetic field and in a reference normal-metal contact. In the absence of magnetic field, we identify the Andreev reflection (AR) regime, which gives rise to the effective charge doubling in shot noise measurements. Surprisingly, the Fano factor F_{AR}≈0.22±0.02 is considerably reduced in the AR regime compared to F_{N}, in contrast to previous AR experiments in normal metals and semiconductors. We suggest that this effect is related to a finite thermal conduction of the proximized, superconducting TI owing to a residual density of states at low energies.

Thickness-dependent transport channels in topological insulator Bi2Se3 thin films grown by magnetron sputtering

We study the low-temperature transport properties of Bi₂Se₃ thin films grown by magnetron sputtering. A positive magnetoresistance resulting from the weak antilocalization (WAL) effect is observed at low temperatures. The observed WAL effect is two dimensional in nature. Applying the Hikami-Larkin-Nagaoka theory, we have obtained the dephasing length. It is found that the temperature dependence of the dephasing length cannot be described only by the Nyquist electron-electron dephasing, in conflict with prevailing experimental results. From the WAL effect, we extract the number of the transport channels, which is found to increase with increasing the thickness of the films, reflecting the thickness-dependent coupling between the top and bottom surface states in topological insulator. On the other hand, the electron-electron interaction (EEI) effect is observed in temperature-dependent conductivity. From the EEI effect, we also extract the number of the transport channel, which shows similar thickness dependence with that obtained from the analysis of the WAL effect. The EEI effect, therefore, can be used to analyze the coupling effect between the top and bottom surface states in topological insulator like the WAL effect.

Observation of Anderson localization in ultrathin films of three-dimensional topological insulators

Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here, we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi_{1-x}Sb_{x})_{2}Te_{3} films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually, positive magnetoconductivity emerges when the electron system becomes strongly localized. This work reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.

Highly tunable Berry phase and ambipolar field effect in topological crystalline insulator Pb(1-x)Sn(x)Se

Recently, rock-salt IV-VI semiconductors, such as Pb(1-x)Sn(x)Se(Te) and SnTe, have been observed to host topological crystalline insulator (TCI) states. The nontrivial states have long been believed to exhibit ambipolar field effects and possess massive Dirac Fermions in two-dimension (2D) limit due to the surface hybridization. However, these exciting attributes of TCI remain previously inaccessible owing to the complicated control over composition and thickness. Here, we systematically investigate doping and thickness-induced topological phase transitions by electrical transport. We demonstrate the first evidence of the ambipolar properties in Pb(1-x)Sn(x)Se thin films. Surface gap opening is observed in 10 nm TCI originated from the strong finite-size effect. Importantly, magnetoconductance hosts a competition between weak antilocalization and weak localization, suggesting a strikingly tunable Berry phase evolution and strong electron-electron interaction. Our findings serve as a new probe to study electron behavior and pave the way for further exploring and manipulating this novel 2D TCI phase.

Diabolical points in multi-scatterer optomechanical systems

Diabolical points, which originate from parameter-dependent accidental degeneracies of a system's energy levels, have played a fundamental role in the discovery of the Berry phase as well as in photonics (conical refraction), in chemical dynamics, and more recently in novel materials such as graphene, whose electronic band structure possess Dirac points. Here we discuss diabolical points in an optomechanical system formed by multiple scatterers in an optical cavity with periodic boundary conditions. Such configuration is close to experimental setups using micro-toroidal rings with indentations or near-field scatterers. We find that the optomechanical coupling is no longer an analytic function near the diabolical point and demonstrate the topological phase arising through the mechanical motion. Similar to a Fabry-Perot resonator, the optomechanical coupling can grow with the number of scatterers. We also introduce a minimal quantum model of a diabolical point, which establishes a connection to the motion of an arbitrary-spin particle in a 2D parabolic quantum dot with spin-orbit coupling.

In situ magnetotransport measurements in ultrathin Bi films: evidence for surface-bulk coherent transport

We performed in situ magnetotransport measurements on ultrathin Bi(111) films [4-30 bilayers (BLs), 16-120 Å thick] to elucidate the role of bulk or surface states in the transport phenomena. We found that the temperature dependence of the film conductivity shows no thickness dependence for the 6-16 BL films and is affected by the electron-electron scattering, suggesting surface-state dominant contribution. In contrast, the weak antilocalization effect observed by applying a magnetic field shows clear thickness dependence, indicating bulk transport. This apparent inconsistency is explained by a coherent bulk-surface coupling that produces a single channel transport. For the films thicker than 20 BLs, the behavior changes drastically which can likely be interpreted as a bulk dominant conduction.

Tunable interaction-induced localization of surface electrons in antidot nanostructured Bi2Te3 thin films

Recently, a logarithmic decrease of conductivity has been observed in topological insulators at low temperatures, implying a tendency of localization of surface electrons. Here, we report quantum transport experiments on the topological insulator Bi2Te3 thin films with arrayed antidot nanostructures. With increasing density of the antidots, a systematic decrease is observed in the slope of the logarithmic temperature-dependent conductivity curves, indicating the electron-electron interaction can be tuned by the antidots. Meanwhile, the weak antilocalization effect revealed in magnetoconductivity exhibits an enhanced dominance of electron-electron interaction among decoherence mechanisms. The observation can be understood from an antidot-induced reduction of the effective dielectric constant, which controls the interactions between the surface electrons. Our results clarify the indispensable role of the electron-electron interaction in the localization of surface electrons and indicate the localization of surface electrons in an interacting topological insulator.