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The scanning superconducting quantum interference device (SQUID) fabricated on the tip of a sharp quartz pipette (SQUID-on-tip) has emerged as a versatile tool for nanoscale imaging of magnetic, thermal, and transport properties of microscopic devices of quantum materials. We present the design and performance of a scanning SQUID-on-tip microscope in a top-loading probe of a cryogen-free dilution refrigerator. The microscope is enclosed in a custom-made vacuum-tight cell mounted at the bottom of the probe and is suspended by springs to suppress vibrations caused by the pulse tube cryocooler. Two capillaries allow in-situ control of helium exchange gas pressure in the cell that is required for thermal imaging. A nanoscale heater is used to create local temperature gradients in the sample, which enables quantitative characterization of the relative vibrations between the tip and the sample. The spectrum of the vibrations shows distinct resonant peaks with maximal power density of about 27 nm/Hz$^{1/2}$ in the in-plane direction. The performance of the SQUID-on-tip microscope is demonstrated by magnetic imaging of the MnBi$_2$Te$_4$ magnetic topological insulator, magnetization and current distribution imaging in a SrRuO$_3$ ferromagnetic oxide thin film, and by thermal imaging of dissipation in graphene., Submitted to Review of Scientific Instruments

In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been realized in band theory of solid. Next, the simplest non-trivial insulating phase (Integer Quantum Hall State) and the concept of topological order in condensed matter electronic system have been introduced. In the following sections, we discussed Quantum Spin Hall (QSH) State in two dimensions (2D), and reviewed the theoretical and experimental developments from 2D QSH state to 3D topological insulators (TI). Subsequently, we gave a brief overview on theoretical and experimental understanding on recently discovered topological Dirac semimetals, Weyl semimetals, three-, six- , and eight-fold degenerate semimetals, and Nodal line semimetals. Then, topological crystalline insulator, which can not be considered as a descendent of Quantum Spin Hall or Integer Quantum Hall insulator, has been introduced. Finally, we discussed the presence of magnetism in some topological materials and its consequence on electronic band structure., Comment: 25 pages, 28 figures

Though Weyl fermions have recently been observed in several materials with broken inversion symmetry, there are very few examples of such systems with broken time reversal symmetry. Various ${\mathrm{Co}}_{2}$-based half-metallic ferromagnetic Heusler compounds are lately predicted to host Weyl-type excitations in their band structure. These magnetic Heusler compounds with broken time reversal symmetry are expected to show a large momentum space Berry curvature, which introduces several exotic magnetotransport properties. In this paper, we present a systematic analysis of experimental results on the anomalous Hall effect (AHE) in ${\mathrm{Co}}_{2}\mathrm{Ti}X$ ($X=\mathrm{Si}$ and Ge). This study is an attempt to understand the role of Berry curvature on AHE in the ${\mathrm{Co}}_{2}\mathrm{Ti}X$ family of materials. Anomalous Hall resistivity is observed to scale quadratically with longitudinal resistivity for both compounds. The detailed analysis indicates that in anomalous Hall conductivity, the intrinsic Karplus-Luttinger Berry phase mechanism dominates over the extrinsic skew scattering and side-jump mechanism.

By employing x-ray photoelectron spectroscopy, we present a detailed study of the core level spectra of LaTe3 in its charge density wave phase at room temperature. The analysis of the Te 3d spectrum by curve fitting using least square error minimization reveals that the Te atoms exist in two different charge states: the two Te atoms in the Te-Te layer has a valency of −0.5, whereas the Te atom in La-Te layer has a valency of −2. The La 3d spectrum shows three peaks for each spin orbit component, where the main peak and the satellite peaks appear due to different final states related to charge transfer from different ligand Te states.

The effect of high pressure (up to 8 GPa) on normal and superconducting state properties of PrFeAsO0.6F0.12, an 1111-type iron based superconductor close to optimal doped region, has been investigated by measuring the temperature dependence of resistivity. Initially, the superconducting transition temperature (T c ) is observed to increase slowly by about 1 K as pressure (P) increases from 0 to 1.3 GPa. With further increase in pressure above 1.3 GPa, T c decreases at the rate of ~1.5 K/GPa. The normal-state resistivity decreases monotonically up to 8 GPa. We have also measured the pressure dependence of magnetization (M) on the same piece of PrFeAsO0.6F0.12 sample up to 1.1 GPa and observed T c as well as the size of the Meissner signal to increase with pressure in this low-pressure region. In contrast, for an over-doped PrFeAsO0.6F0.14 sample, magnetization measurements up to 1.06 GPa show that both T c and the Meissner signal decrease with pressure. The present study clearly reveals two distinct regions in the dome-shaped (T c -P) phase diagram of PrFeAsO0.6F0.12.

We have investigated the critical phenomenon associated with the magnetic phase transition in the half-metallic full-Heusler ${\mathrm{Co}}_{2}\mathrm{TiGe}$. The compound undergoes a continuous paramagnetic-to-ferromagnetic phase transition below the Curie temperature ${T}_{C}=371.5$ K. The analysis of magnetization isotherms in the vicinity of ${T}_{C}$, following a modified Arrott plot method, the Kouvel-Fisher technique, and a critical isotherm plot, yields the asymptotic critical exponents $\ensuremath{\beta}=0.495, \ensuremath{\gamma}=1.324$, and $\ensuremath{\delta}=3.67$. The self-consistency and reliability of the obtained exponents are further verified by the Widom scaling relation and scaling equations of state. The mean-field-like value of the critical exponent $\ensuremath{\beta}$ suggests a long-range nature of the exchange interactions, whereas the values of the critical exponents $\ensuremath{\gamma}$ and $\ensuremath{\delta}$ imply sizable critical spin fluctuations. The half-metallic itinerant character of ${\mathrm{Co}}_{2}\mathrm{TiGe}$ in the presence of magnetic inhomogeneity may result in such a strong deviation from the three-dimensional Heisenberg values ($\ensuremath{\beta}=0.369, \ensuremath{\gamma}=1.38$, and $\ensuremath{\delta}=4.8$) of the critical exponents toward the mean-field values ($\ensuremath{\beta}=0.5, \ensuremath{\gamma}=1$, and $\ensuremath{\delta}=3)$. The results suggest the complex nature of exchange couplings that stabilize the long-range ferromagnetic ordering in the system and are consistent with the earlier theoretical studies on the exchange mechanism in ${\mathrm{Co}}_{2}\mathrm{TiGe}$.

Magnetic lanthanide half-Heuslers ($R\mathrm{PtBi}$; $R$ being the lanthanide) represent an attractive subgroup of the Heusler family and have been identified as ideal candidates for time-reversal symmetry-breaking topological Weyl semimetals. In this paper, we present the detailed analysis of the magnetotransport properties of frustrated antiferromagnet TbPtBi. This material shows large, nonsaturating magnetoresistance (MR) with unusual magnetic field dependence. The MR of TbPtBi is significantly anisotropic with respect to the magnetic field, applied along different crystallographic directions, and indicates the anisotropic nature of the Fermi surface. The chiral-anomaly-induced negative longitudinal magnetoresistance confirms the presence of Weyl fermions. At low temperature, Berry-phase-driven large anomalous Hall conductivity has been observed. The calculated anomalous Hall angle is the largest reported so far.

TaSb2 has been predicted theoretically to be a weak topological insulator. Whereas, the earlier magnetotransport experiment has established it as a topological semimetal. In the previous works, the Shubnikov-de Haas oscillation has been analyzed to probe the Fermi surface, with magnetic field along a particular crystallographic axis only. By employing a sample rotator, we reveal highly anisotropic transverse magnetoresistance by rotating the magnetic field along different crystallographic directions. To probe the anisotropy in the Fermi surface, we have performed magnetization measurements and detected strong de Haas-van Alphen (dHvA) oscillations for the magnetic field applied along a and b axes as well as perpendicular to ab plane of the crystals. Three Fermi pockets have been identified by analyzing the dHvA oscillations. With the application of magnetic field along different crystal directions, the cross-sectional areas of the Fermi pockets have been found significantly different, i.e., the Fermi pockets are highly anisotropic in nature. Three-band fitting of electrical and Hall conductivity reveals two high mobility electron pockets and one low mobility hole pocket. The angular variation of transverse magnetoresistance has been qualitatively explained using the results of dHvA oscillations and three-band analysis.

As Dirac semimetal Cd3As2 exhibits very high mobility charge carrier and large thermoelectric power(S), one might think of its possible thermoelectric application. Whether it will be useful in thermoelectric application or not is mainly determined by the thermoelectric figure of merit (ZT). We observe that ZT of this material linearly increases with increasing temperature like S and no sign of saturation up to 350 K. At that temperature, the value of ZT has been found to be large ∼ 0.16, comparable to the well-known thermoelectric material Bi2Te3. We believe that the values of thermoelectric parameters (S, ZT) in Cd3As2 can be enhanced further to reach the practical limit for the application by increasing the temperature and sample modification (doping, nanostructuring, inclusion of nanocomposite, etc.).

The study of electronic properties in topological systems is one of the most fascinating topics in condensed matter physics, which has generated enormous interests in recent times. New materials are frequently being proposed and investigated to identify their non-trivial band structure. While sophisticated techniques such as angle-resolved photoemission spectroscopy have become popular to map the energy-momentum relation, the transport experiments lack any direct confirmation of Dirac and Weyl fermions in a system. From band structure calculations, VAl$_{3}$ has been proposed to be a type II topological Dirac semimetal. This material represents a large family of isostructural compounds, all having similar electronic band structure and is an ideal system to explore the rich physics of Lorentz symmetry violating Dirac fermions. In this work, we present a detailed analysis on the magnetotransport properties of VAl$_{3}$. A large, non-saturating magnetoresistance has been observed. Hall resistivity reveals the presence of two types of charge carriers with high mobility. Our measurements show a large planar Hall effect in this material, which is robust and can be easily detectable up to high temperature. This phenomenon originates from the relativistic chiral anomaly and non-trivial Berry curvature, which validates the theoretical prediction of the Dirac semimetal phase in VAl$_{3}$., Comment: 6 pages, 5 figures

In this report, we present the magnetotransport and magnetization properties of LaSbTe single crystals. Magnetic field-induced turn-on behavior and low-temperature resistivity plateau have been observed. By adopting both metal-semiconductor crossover and Kohler scaling analysis, we have discussed the possible origin of the temperature and magnetic field dependence of resistivity. At 5 K and 9 T, a large, non-saturating transverse magnetoresistance (MR) $\sim$ 5$\times$10$^{3}$ \% has been obtained. The MR shows considerable anisotropy, when the magnetic field is applied along different crystallographic directions. The non-linear field dependence of the Hall resistivity confirms the presence of two types of charge carriers. From the semiclassical two-band fitting of Hall conductivity and longitudinal conductivity, very high carrier mobilities and almost equal electron and hole densities have been deduced, which result in large MR. The Fermi surface properties have been analyzed from de Haas-van Alphen oscillation. From the magnetization measurement, the signature of non-trivial surface state has been detected, which confirms that LaSbTe is a topological insulator, consistent with the earlier first-principles calculations., Comment: 11 pages, 11 figures

While the discovery of Dirac and Weyl type excitations in electronic systems is a major breakthrough in recent condensed matter physics, finding appropriate materials for fundamental physics and technological applications, is an experimental challenge. In all the reported materials, linear dispersion survives only up to a few hundred meV from the Dirac or Weyl nodes. On the other hand, real materials are subject to uncontrolled doping during preparation and thermal effect near room temperature can hinder the rich physics. In ZrSiS, ARPES measurements have shown an unusually robust linear dispersion (up to $\sim$2 eV) with multiple non-degenerate Dirac nodes. In this context, we present the magnetotransport study on ZrSiS crystal, which represents a large family of materials (\textit{WHM} with \textit{W} = Zr, Hf; \textit{H} = Si, Ge, Sn; \textit{M} = O, S, Se, Te) with identical band topology. Along with extremely large and non-saturating magnetoresistance (MR), $\sim$ 1.4 $\times$ 10$^{5}$ \% at 2 K and 9 T, it shows strong anisotropy depending on the direction of the magnetic field. Quantum oscillation and Hall effect measurements have revealed large hole and small electron Fermi pockets. Non-trivial $\pi$ Berry phase confirms the Dirac fermionic nature for both types of charge carriers. The long-sought relativistic phenomenon of massless Dirac fermions, known as Adler-Bell-Jackiw chiral anomaly, has also been observed., Comment: 10 pages, 13 figures

Transition metal dipnictides (TMDs) have recently been identified as possible candidates to host topology protected electronic band structure. These materials belong to an isostructural family and show several exotic transport properties. Especially, the large values of magnetoresistance (MR) and carrier mobility have drawn significant attention from the perspective of technological applications. In this report, we have investigated the magnetotransport and Fermi surface properties of single crystalline MoAs$_{2}$, another member of this group of compounds. Field induced resistivity plateau and a large MR have been observed, which are comparable to several topological systems. Interestingly, in contrast to other isostructural materials, the carrier density in MoAs$_{2}$ is quite high and shows single-band dominated transport. The Fermi pockets, which have been identified from the quantum oscillation, are largest among the members of this group and have significant anisotropy with crystallographic direction. Our first-principles calculations reveal a substantial difference between the band structures of MoAs$_{2}$ and other TMDs. The calculated Fermi surface consists of one electron pocket and another 'open-orbit' hole pocket, which has not been observed in TMDs so far., Comment: 8 pages, 9 figures

Topological materials provide an exclusive platform to study the dynamics of relativistic particles in table-top experiments and offer the possibility of wide-scale technological applications. ZrSiS is a newly discovered topological nodal-line semimetal and has drawn enormous interests. In this report, we have investigated the lattice dynamics and electron-phonon interaction in single crystalline ZrSiS using Raman spectroscopy. Polarization and angle resolved measurements have been performed and the results have been analyzed using crystal symmetries and theoretically calculated atomic vibrational patterns along with phonon dispersion spectra. Wavelength and temperature dependent measurements show the complex interplay of electron and phonon degrees of freedom, resulting in resonant phonon and quasielastic electron scatterings through inter-band transitions. Our high-pressure Raman studies reveal vibrational anomalies, which were further investigated from the high-pressure synchrotron x-ray diffraction (HPXRD) spectra. From HPXRD, we have clearly identified pressure-induced structural transitions and coexistence of multiple phases, which also indicate possible electronic topological transitions in ZrSiS. The present study not only provides the fundamental information on the phonon subsystem, but also sheds some light in understanding the topological nodal-line phase in ZrSiS and other iso-structural systems.

ZrSiS was recently shown to be a new material with topologically non-trivial band structure which exhibits multiple Dirac nodes and a robust linear band dispersion up to an unusually high energy of 2\,eV. Such a robust linear dispersion makes the topological properties of ZrSiS insensitive to perturbations like carrier doping or lattice distortion. Here we show that a novel superconducting phase with a remarkably high $T_c$ of 7.5\,K can be induced in single crystals of ZrSiS by a non-superconducting metallic tip of Ag. From first-principles calculations we show that the observed superconducting phase might originate from dramatic enhancement of density of states due to the presence of a metallic tip on ZrSiS. Our calculations also show that the emerging tip-induced superconducting phase co-exists with the well preserved topological properties of ZrSiS., with supplementary materials

We report semiconductor to metal-like crossover in the temperature dependence of resistivity (ρ) due to the switching of charge transport from bulk to surface channel in three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. Unlike earlier studies, a much sharper drop in ρ(T) is observed below the crossover temperature due to the dominant surface conduction. Remarkably, the resistivity of the conducting surface channel follows a rarely observable T 2 dependence at low temperature, as predicted theoretically for a two-dimensional Fermi liquid system. The field dependence of magnetization shows a cusp-like paramagnetic peak in the susceptibility (χ) at zero field over the diamagnetic background. The peak is found to be robust against temperature and χ decays linearly with the field from its zero-field value. This unique behavior of the χ is associated with the spin-momentum locked topological surface state in Bi1.5Sb0.5Te1.7Se1.3. The reconstruction of the surface state with time is clearly reflected through the reduction of the peak height with the age of the sample.

Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T

We report semiconductor to metal-like crossover in the temperature dependence of resistivity (ρ) due to the switching of charge transport from bulk to surface channel in three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. Unlike earlier studies, a much sharper drop in ρ(T) is observed below the crossover temperature due to the dominant surface conduction. Remarkably, the resistivity of the conducting surface channel follows a rarely observable T2 dependence at low temperature, as predicted theoretically for a two-dimensional Fermi liquid system. The field dependence of magnetization shows a cusp-like paramagnetic peak in the susceptibility (χ) at zero field over the diamagnetic background. The peak is found to be robust against temperature and χ decays linearly with the field from its zero-field value. This unique behavior of the χ is associated with the spin-momentum locked topological surface state in Bi1.5Sb0.5Te1.7Se1.3. The reconstruction of the surface state with time is clearly reflected through the reduction of the peak height with the age of the sample.

Although, the long-standing debate on the resistivity anomaly in ZrTe$_{5}$ somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe$_{5}$ to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe$_{5}$ single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe$_{5}$ is a novel 3D topological insulator having massless Dirac fermionic excitation in its bulk gap state. Whereas, no 3D topological insulator known in material science holds linear band dispersion in its insulating bulk. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature ($T$$, Comment: 12 pages, 11 figures

We report transport properties of single-crystalline Pd$_{3}$Bi$_{2}$S$_{2}$, which has been predicted to host an unconventional electronic phase of matter beyond three-dimensional Dirac and Weyl semimetals. Similar to several topological systems, the resistivity shows field induced metal-semiconductor-like crossover at low temperature. Large, anisotropic and non-saturating magnetoresistance (MR) has been observed in transverse experimental configuration. At 2 K and 9 T, the MR value reaches as high as $\sim$1.1$\times$10$^{3}$ \%. Hall resistivity reveals the presence of two types of charge carriers and has been analyzed using two-band model. In spite of the large density ($>$ 10$^{21}$ cm$^{-3}$), the mobility of charge carriers is found to be quite high ($\sim$ 0.75$\times$10$^{4}$ cm$^{2}$ V$^{-1}$ s$^{-1}$ for hole and $\sim$ 0.3$\times$10$^{4}$ cm$^{2}$ V$^{-1}$ s$^{-1}$ for electron). The observed magneto-electrical properties indicate that Pd$_{3}$Bi$_{2}$S$_{2}$ may be a new member of the topological semimetal family, which can have a significant impact in technological applications., Five pages and five figures

We have observed Shubnikov--de Haas and de Haas--van Alphen effects in the single crystals of the three-dimensional Dirac semimetal ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ up to 50 K, traceable at fields as low as 2 and 1 T, respectively. The values of the Fermi wave vector, the Fermi velocity, and the effective cyclotron mass of the charge carrier, calculated from both techniques, are close to each other and match well with earlier reports. However, the de Haas--van Alphen effect clearly reflects the existence of two different Fermi surface cross sections along certain directions and a nontrivial Berry's phase, which is the signature of a three-dimensional Dirac fermion in ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$.

To probe the charge scattering mechanism in Cd$_{3}$As$_{2}$ single crystal, we have analyzed the temperature and magnetic field dependence of the Seebeck coefficient ($S$). The large saturation value of $S$ at high field clearly demonstrates the linear energy dispersion of three-dimensional Dirac fermion. A wide tunability of the charge scattering mechanism has been realized by varying the strength of the magnetic field and carrier density via In doping. With the increase in magnetic field, the scattering time crosses over from being nearly energy independent to a regime of linear dependence. On the other hand, the scattering time enters into the inverse energy-dependent regime and the Fermi surface strongly modifies with 2\% In doping at Cd site. With further increase in In content from 2 to 4\%, we did not observe any Shubnikov-de Haas oscillation up to 9 T field, but the magnetoresistance is found to be quite large as in the case of undoped sample., 11 pages, 13 figures