Magnetic resonance imaging of spin-wave transport and interference in a magnetic insulator
Iacopo Bertelli, Joris J. Carmiggelt, Tao Yu, Brecht G. Simon, Coosje C. Pothoven, Gerrit E. W. Bauer, Yaroslav M. Blanter, Jan Aarts, Toeno van der Sar
Spin waves - the elementary excitations of magnetic materials - are prime candidate signal carriers for low dissipation information processing. Being able to image coherent spin-wave transport is crucial for developing interference-based spin-wave devices. We introduce a platform for probing coherent spin waves based on magnetic resonance imaging with electron spins in diamond. Focusing on a thin-film magnetic insulator, we quantify spin-wave amplitudes, visualize the dispersion, and demonstrate time-domain measurements of spin-wave packets. We use our platform to study spin-wave interference, revealing uni-directional, autofocused spin-wave patterns with frequency-controlled numerical apertures. A theoretical analysis explains the patterns in terms of chiral spin-wave excitation and stray-field coupling to the sensor spins. These results pave the way for probing spin waves in atomically thin magnets, even when embedded between opaque materials.
The energy-momentum relationship of electrons on the surface of an ideal "Hydrogen-Atom" Topological Insulator forms a cone - a Dirac cone, which, when warped and distorted (no longer described by the Dirac equation), can lead to unusual phenomena such as enhanced electronic interference around defects (observed in STM) and a magnetically ordered broken symmetry surface with lost topological protection. A detailed spin-texture and hexagonal warping maps on Bi2Te3 are presented in this context as a Viewpoint on L.Fu, Phys. Rev. Lett. \textbf{103}, 266801 (2009).
We theoretically investigate quasiparticle interference in superconducting topological insulators with the nematic order parameter. This order parameter spontaneously breaks the rotational symmetry of the crystal. Such rotational symmetry breaking is visible in the quasiparticle interference picture both in coordinate and momentum spaces. For a small bias voltages quasiparticle interference incommensurate with the crystal symmetry and shows nematic behavior. If the bias voltage is comparable with the value of the order parameter interference picture is similar to the interference picture of th…
Constant energy contour (CEC) of the surface bands in topological insulators varies not only with materials but also at different energies. The quasiparticle interference caused by scattering-off from defects on the surface of topological insulators is an effective way to reveal the topologies of the CEC and can be probed by scanning tunneling microscopy (STM). Using stationary phase approach, a general analytic formulation of the local density of states as well as the power laws of the Friedel oscillation are present, based only on the time-reversal symmetry and the local geometry around the …
The quasiparticle interference of the spectroscopic imaging scanning tunneling microscopy has been investigated for the surface states of the large gap topological insulator Bi$_2$Te$_3$ through the T-matrix formalism. Both the scalar potential scattering and the spin-orbit scattering on the warped hexagonal isoenergy contour are considered. While backscatterings are forbidden by time-reversal symmetry, other scatterings are allowed and exhibit strong dependence on the spin configurations of the eigenfunctions at k points over the isoenergy contour. The characteristic scattering wavevectors fo…
We propose an entanglement detector composed of two quantum spin Hall insulators and a side gate deposited on one of the edge channels. For an ac gate voltage, the differential noise contributed from the entangled electron pairs exhibits the nontrivial step structures, from which the spin entanglement concurrence can be easily obtained. The possible spin dephasing effects in the quantum spin Hall insulators are also included.
Topological insulators have surface states with unique spin-orbit coupling. With impurities on the surface, the quasiparticle interference pattern is an effective way to reveal the topological nature of the surface states, which can be probed by the scanning tunneling microscopy. In this paper, we present a general analytic formulation of the local density of states using the stationary phase approximation. The power laws of Friedel oscillations are discussed for a constant energy contour with a generic shape. In particular, we predict unique signature of magnetic impurities in comparison with…
Topological crystalline insulators represent a novel topological phase of matter in which the surface states are protected by discrete point group-symmetries of the underlying lattice. Rock-salt lead-tin-selenide alloy is one possible realization of this phase which undergoes a topological phase transition upon changing the lead content. We used scanning tunneling microscopy (STM) and angle resolved photoemission spectroscopy (ARPES) to probe the surface states on (001) Pb$_{1-x}$Sn$_{x}$Se in the topologically non-trivial (x=0.23) and topologically trivial (x=0) phases. We observed quasiparti…
The surface conductivity for conduction electrons with a fixed chirality in a topological insulator with impurities scattering is considered. The surface excitations are described by the Weyl Hamiltonian. For a finite chemical potential one projects out the hole band and one obtains a single electronic band with a fixed chirality. One obtains a model of spinless electrons which experience a half vortex when they return to the origin. As a result the conductivity is equivalent to a spinless problem with correlated noise which gives rise to anti-localization. We compute conductivity as a functio…
Electrons on the surface of a strong topological insulator, such as Bi2Te3 or Bi1-xSnx, form a topologically protected helical liquid whose excitation spectrum contains an odd number of massless Dirac fermions. A theoretical survey and classification is given of the universal features, observable by the ordinary and spin-polarized scanning tunneling spectroscopy, in the interference patterns resulting from the quasiparticle scattering by magnetic and non-magnetic impurities in such a helical liquid. Our results confirm the absence of backscattering from non-magnetic impurities observed in rece…
Topological insulators have an insulating bulk but a metallic surface. In the simplest case, the surface electronic structure of a 3D topological insulator is described by a single 2D Dirac cone. A single 2D Dirac fermion cannot be realized in an isolated 2D system with time-reversal symmetry, but rather owes its existence to the topological properties of the 3D bulk wavefunctions. The transport properties of such a surface state are of considerable current interest; they have some similarities with graphene, which also realizes Dirac fermions, but have several unique features in their respons…
Motivated by the experimental difficulty to produce topological insulators (TIs) of the Bi$_2$Se$_3$ family with pure surface-state conduction, we study the effect that the bulk can have on the low-temperature transport properties of gated thin TI films. In particular, we focus on interference corrections, namely weak localization (WL) or weak-antilocalization (WAL), and conductance fluctuations (CFs) based on an effective low-energy Hamiltonian. Utilizing diagrammatic perturbation theory we first analyze the bulk and the surface separately and subsequently discuss WL/WAL and CFs when a tunnel…
We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator. However, upon applyi…
Topological insulators represent novel phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport measurements. Recently, Bi2Se3 and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface and verified by angle-resolved photoemission spectroscopy experiments. Here, we show unambiguous transport evidence of topological surface states through periodic quantum interference effects in layered s…
We report on a >100-fold enhancement of Raman responses from Bi2Se3 thin films if laser photon energy switches from 2.33 eV (532 nm) to 1.58 eV (785 nm), which is due to direct optical coupling to Dirac surface states (SS) at the resonance energy of ~1.5 eV (a thickness-independent enhancement) and due to nonlinearly excited Dirac plasmon (a thickness-dependent enhancement). Owing to the direct optical coupling, we observed an in-plane phonon mode of hexagonally arranged Se-atoms associated with a continuous network of Dirac SS. This mode revealed a Fano lineshape for films <15 nm thick, resul…
Using non-equilibrium Green's functions, we studied numerically the transport properties of a Josephson junction, superconductor-topological insulator-superconductor hybrid system. Our numerical calculation shows first that proximity-induced superconductivity is indeed observed in the edge states of a topological insulator adjoining two superconducting leads and second that the special characteristics of topological insulators endow the edge states with an enhanced proximity effect with a superconductor but do not forbid the bulk states to do the same. In a size-dependent analysis of the local…
Topological crystalline insulators represent a new state of matter, in which the electronic transport is governed by mirror-symmetry protected Dirac surface states. Due to the helical spin-polarization of these surface states, the proximity of topological crystalline matter to a nearby superconductor is predicted to induce unconventional superconductivity and thus to host Majorana physics. We report on the preparation and characterization of Nb-based superconducting quantum interference devices patterned on top of topological crystalline insulator SnTe thin films. The SnTe films show weak anti…
Topological insulator (TI) nanoribbons (NRs) provide a unique platform for investigating quantum interference oscillations combined with topological surface states. One-dimensional subbands formed along the perimeter of a TI NR can be modulated by an axial magnetic field, exhibiting Aharonov-Bohm (AB) and Altshuler-Aronov-Spivak (AAS) oscillations of magnetoconductance (MC). Using Sb-doped Bi2Se3 TI NRs, we found that the relative amplitudes of the two quantum oscillations can be tuned by varying the channel length, exhibiting crossover from quasi-ballistic to diffusive transport regimes. The …
We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) made of Sb-doped Bi2Se3 topological insulator (TI) nanoribbon (NR) contacted with PbIn superconducting electrodes. When an external magnetic field was applied along the NR axis, the TI NR exhibited periodic magneto-conductance oscillations, the so-called Aharonov-Bohm oscillations, owing to one-dimensional subbands. Below the superconducting transition temperature of PbIn electrodes, we observed supercurrent flow through TI NR-based SQUID. The critical current periodically modulates with a m…
Josephson weak links made of two-dimensional topological insulators (TIs) exhibit magnetic oscillations of the supercurrent that are reminiscent of those in superconducting quantum interference devices (SQUIDs). We propose a microscopic theory of this effect that goes beyond the approaches based on the standard SQUID theory. For long junctions we find a temperature-driven crossover from Phi_0-periodic SQUID-like oscillations to a 2 Phi_0-quasiperiodic interference pattern with different peaks at even and odd values of the magnetic flux quantum Phi_0=ch/2e. This behavior is absent in short junc…
The discovery of two-dimensional gapless Dirac fermions in graphene and topological insulators (TI) has sparked extensive ongoing research toward applications of their unique electronic properties. The gapless surface states in three-dimensional insulators indicate a distinct topological phase of matter with a non-trivial Z2 invariant that can be verified by angle-resolved photoemission spectroscopy or magnetoresistance quantum oscillation. In TI nanowires, the gapless surface states exhibit Aharonov-Bohm (AB) oscillations in conductance, with this quantum interference effect accompanying a ch…
We study the variable-range hopping (VRH) of bosons in an array of sites with short-range interactions and a large characteristic coordination number. The latter leads to strong quantum interference phenomena yet allows for their analytical study. We develop a functional renormalization group scheme that repeatedly eliminates high-energy sites properly renormalizing the tunnelling between the low-energy ones. Using this approach we determine the temperature and magnetic field dependence of the hopping conductivity and find a large positive magnetoresistance. With increasing magnetic field the …
Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
Institute for Cross-Disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所）；Department of Physics, University of the Balearic Islands（巴利阿里大学物理系）
We report on the fabrication and electrical transport properties of superconducting quantum interference devices (SQUIDs) made from a (Bi_{1-x}Sb_x)_2Se_3 topological insulator (TI) nanoribbon (NR) connected with Pb0.5In0.5 superconducting electrodes. Below the transition temperature of the superconducting Pb0.5In0.5 electrodes, periodic oscillations of the critical current are observed in the TI NR SQUID under a magnetic field applied perpendicular to the plane owing to flux quantization. Also the output voltage modulates as a function of the external magnetic field. Moreover, the SQUID the S…
The quasiparticle interference (QPI) technique is a powerful tool that allows to uncover the structure and properties of electronic structure of a material combined with scattering properties of defects at surfaces. Recently this technique has been pivotal in proving the unique properties of the surface state of topological insulators which manifests itself in the absence of backscattering. In this work we derive a Green function based formalism for the ab initio computation of Fourier-transformed QPI images. We show the efficiency of our new implementation at the examples of QPI that forms ar…
Recently, the topological classification of electronic states has been extended to a new class of matter known as topological crystalline insulators. Similar to topological insulators, topological crystalline insulators also have spin-momentum locked surface states; but they only exist on specific crystal planes that are protected by crystal reflection symmetry. Here, we report an ultra-low temperature scanning tunneling microscopy and spectroscopy study on topological crystalline insulator SnTe nanoplates grown by molecular beam epitaxy. We observed quasiparticle interference patterns on the …
Quasiparticle interference induced by cobalt adatoms on the surface of the topological insulator Bi$_{2}$Se$_{3}$ is studied by scanning tunneling microscopy, angle-resolved photoemission spectroscopy and X-ray magnetic circular dichroism. It is found that Co atoms are selectively adsorbed on top of Se sites and act as strong scatterers at the surface, generating anisotropic standing waves. A long-range magnetic order is found to be absent, and the surface state Dirac cone remains gapless. The anisotropy of the standing wave is ascribed to the heavily warped iso-energy contour of unoccupied st…
We consider scanning gate microscopy imaging of the double slit interference for a pair of quantum point contacts (QPCs) defined within the two-dimensional electron gas. The interference is clearly present in the scattered electron wave functions for each of the incident subbands. Nevertheless, we find that the interference is generally missing in the experimentally accessible conductance maps for many incident subbands. We explain this finding on the basis of the Landauer approach. A setup geometry allowing for observation of the double slit interference by the scanning gate microscopy is pro…
Without a periodic reference framework, local structures in noncrystalline solids are difficult to specify, but they still exert an enormous influence on materials properties. For example, thermomechanical responses of organic and inorganic glasses sensitively depend on the distribution of free volume or soft spots$^{1,2}$. Meanwhile, strong electron localization$^{3}$ that endows unparalleled electrical breakdown strengths to amorphous insulators is easily compromised by local defects that promote inelastic tunneling over a variable range$^{4,5}$. Here we report how metallic conduction can ov…
We predict that a single oscillation of a strong optical pulse can significantly populate the surface conduction band of a three-dimensional topological insulator, Bi2Se3. Both linearly- and circularly-polarized pulses generate chiral textures of interference fringes of population in the surface Brillouin zone. These fringes constitute a self-referenced electron hologram carrying information on the topology of the surface Bloch bands, in particular, on the effect of the warping term of the low-energy Hamiltonian. These electron-interference phenomena are in a sharp contrast to graphene where t…
A quantum interference effect is discussed for subgap tunneling over a distance comparable to the coherence length, which is a consequence of ``advanced-advanced'' and ``retarded-retarded'' transmission modes [Altland and Zirnbauer, Phys. Rev. B 55, 1142 (1997)]. Effects typical of disorder are obtained from the interplay between multichannel averaging and higher order processes in the tunnel amplitudes. Quantum interference effects similar to those occurring in normal tunnel junctions explain magnetoresistance oscillations of a CDW pierced by nanoholes [Latyshev et al., Phys. Rev. Lett. 78, 9…
We present angle resolved photoemission experiments and scanning tunneling spectroscopy results on the doped topological insulator Cu0.2Bi2Te3. Quasi-particle interference (QPI) measurements, based on high resolution conductance maps of the local density of states show that there are three distinct energy windows for quasi-particle scattering. Using a model Hamiltonian for this system two new scattering channels are identified: the first between the surface states and the conduction band and the second between conduction band states. We also observe that the real space density modulation has a…
We study symmetry protected features in the quasiparticle interference (QPI) pattern of 2D systems with mirror symmetries and time-reversal symmetry, around a single static point impurity. We show that, in the Fourier transformed local density of states (FT-LDOS), $ρ(\bq,ω)$, while the position of high intensity peaks generically depends on the geometric features of the iso-energy contour at energy $ω$, the \emph{absence} of certain peaks is guaranteed by the opposite mirror eigenvalues of the two Bloch states that are (i) on the mirror symmetric lines in the Brillouin zone (BZ) and (ii) separ…
Topological insulator nanoribbons (TI NRs) provide a useful platform to explore the phase-coherent quantum electronic transport of topological surface states, which is crucial for the development of topological quantum devices. When applied with an axial magnetic field, the TI NR exhibits magnetoconductance (MC) oscillations with a flux period of h/e, i.e., Aharonov-Bohm (AB) oscillations, and h/2e, i.e., Altshuler-Aronov-Spivak (AAS) oscillations. Herein, we present an extensive study of the AB and AAS oscillations in Sb doped Bi$_2$Se$_3$ TI NR as a function of the gate voltage, revealing ph…
The development of nanoscale solid-state devices exploiting the promising topological surface states of topological insulator materials requires careful device engineering and improved materials quality. For instance, the introduction of a substrate, device contact or the formation of oxide layers can cause unintentional doping of the material, spoiling the sought-after properties. In support of this, nanoscale imaging tools can provide useful materials information without the need for complex device fabrication. Here we study Bi$_2$Se$_3$ nanoribbons suspended across multiple material stacks …
We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in th…
We propose a new type of instanton interference effect in two-dimensional higher-order topological insulators. The intercorner tunneling consists of the instanton and the anti-instanton pairs that travel through the boundary of the higher-order topological insulator. The Berry phase difference between the instanton pairs causes the interference of the tunneling. This topological effect leads to the gate-tunable oscillation of the energy splitting between the corner states, where the oscillatory nodes signal the perfect suppression of the tunneling. We suggest this phenomenon as a unique featur…
We have performed scanning tunneling microscopy and differential tunneling conductance ($dI/dV$) mapping for the surface of the three dimensional topological insulator Bi$_{2}$Se$_{3}$. The fast Fourier transformation applied to the $dI/dV$ image shows an electron interference pattern near Dirac node despite the general belief that the backscattering is well suppressed in the bulk energy gap region. The comparison of the present experimental result with theoretical surface and bulk band structures shows that the electron interference occurs through the scattering between the surface states nea…
We report the instrumentation and experimental results of a cryogenic scanning microwave impedance microscope. The microwave probe and the scanning stage are located inside the variable temperature insert of a helium cryostat. Microwave signals in the distance modulation mode are used for monitoring the tip-sample distance and adjusting the phase of the two output channels. The ability to spatially resolve the metal-insulator transition in a doped silicon sample is demonstrated. The data agree with a semi-quantitative finite-element simulation. Effects of the thermal energy and electric fields…
We study the quantum Andreev oscillation induced by interference of the edge chiral Majorana fermions in junctions made of quantum anomalous Hall (QAH) insulators and superconductors (SCs). We show two chiral Majorana fermions on a QAH edge with SC proximity generically have a momentum difference $Δk$, which depends on the chemical potentials of both the QAH insulator and the SC. Due to the spatial interference induced by $Δk$, the longitudinal conductance of QAH-SC junctions oscillates with respect to the edge lengths and the chemical potentials, which can be probed via charge transport. Furt…
We study Fabry-Perot interference in hybrid devices, each consisting of a mesoscopic superconducting disk deposited on the surface of a three-dimensional topological insulator. Such structures are hypothesized to contain protected zero modes known as Majorana fermions bound to vortices. The interference manifests as periodic conductance oscillations of magnitude $\sim 0.1$ $e^2/h$. These oscillations show no strong dependence on bulk carrier density or sample thickness, suggesting that they result from phase coherent transport in surface states. However, the Fabry-Perot interference can be tun…
We study the microscopic origins of photocurrent generation in the topological insulator Bi$_2$Se$_3$ via time- and angle-resolved photoemission spectroscopy. We image the unoccupied band structure as it evolves following a circularly polarized optical excitation and observe an asymmetric electron population in momentum space, which is the spectroscopic signature of a photocurrent. By analyzing the rise times of the population we identify which occupied and unoccupied electronic states are coupled by the optical excitation. We conclude that photocurrents can only be excited via resonant optica…
Electrons in moiré flat band systems can spontaneously break time reversal symmetry, giving rise to a quantized anomalous Hall effect. Here we use a superconducting quantum interference device to image stray magnetic fields in one such system composed of twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap consistent with …
Inside a three-dimensional strong topological insulator, a tube with $h/2e$ magnetic flux carries a pair of protected one-dimensional linear fermionic modes. This phenomenon is known as the "wormhole effect". In this work, we find that the "wormhole effect", as a unique degree of freedom, introduces exotic transport phenomena and thus manipulates the transport properties of topological insulators. Our numerical results demonstrate that the transport properties of a double-wormhole system can be manipulated by the wormhole interference. Specifically, the conductance and local density of states …
Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interfer…
We discuss devices for detection of the topological insulator phase based on the two-path electron interference. For that purpose we consider buckled silicene for which a local energy gap can be opened by vertical electric field to close one of the paths and for which the quantum spin Hall insulator conditions are controlled by the Fermi energy. In quantum spin Hall phase the interference is absent due to the separation of the spin currents and the conductance of the devices include sharp features related to localized resonances. In the normal transport conditions the two-path interference pro…
Hybrid structures between conventional, s-wave superconductors and two-dimensional topological insulators (2D TIs) are a promising route to topological superconductivity. Here, we investigate planar Josephson junctions fabricated from hybrid structures that use thin films of cadmium arsenide (Cd3As2) as the 2D TI material. Measurements of superconducting interference patterns in a perpendicular magnetic field are used to extract information about the spatial distribution of the supercurrent. We show that the interference patterns are distinctly different in junctions with and without mesa-isol…
Excitonic insulators host a condensate of electron-hole pairs at equilibrium, giving rise to collective many-body effects. Although several materials have emerged as excitonic insulator candidates, evidence of long-range coherence is lacking and the origin of the ordered phase in these systems remains controversial. Here, using ultrafast pump-probe microscopy, we investigate the possible excitonic insulator Ta$_2$NiSe$_5$. Below 328 K, we observe the anomalous micrometer-scale propagation of coherent modes at velocities of the order of $\sim10^5$ m/s, which we attribute to the hybridization be…
Giant universal conductance fluctuations in the antiferromagnetic topological insulator MnBi2Te4
Leibniz Institute for Solid State and Materials Research, IFW Dresden（德累斯顿IFW固体与材料研究所）；TU Dresden（德累斯顿工业大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；CEA（法国原子能和替代能源委员会）；Technical University of Dortmund（多特蒙德工业大学）；Research Center ”Future Energy Materials and Systems”（未来能源材料与系统研究中心）；Laboratoire National des Champs Magnetiques Intenses LNCMI（强磁场国家实验室）
The electronic transport experiments on topological insulators exhibit a dilemma. A negative cusp in magnetoconductivity is widely believed as a quantum transport signature of the topological surface states, which are immune from localization and exhibit the weak antilocalization. However, the measured conductivity drops logarithmically when lowering temperature, showing a typical feature of the weak localization as in ordinary disordered metals. Here, we present a conductivity formula for massless and massive Dirac fermions as a function of magnetic field and temperature, by taking into accou…
We describe a new type of scanning probe microscope based on a superconducting quantum interference device (SQUID) that resides on the apex of a sharp tip. The SQUID-on-tip is glued to a quartz tuning fork which allows scanning at a tip-sample separation of a few nm. The magnetic flux sensitivity of the SQUID is 1.8 μ_0/Hz^{1/2} and the spatial resolution is about 200 nm, which can be further improved. This combination of high sensitivity, spatial resolution, bandwidth, and the very close proximity to the sample provides a powerful tool for study of dynamic magnetic phenomena on the nanoscale.…
We study the transport properties of a Josephson junction consisting of two identical $s$-wave superconductors separated by an even-layer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT). Using recursive Green's function method, we calculate the supercurrent in the presence of a perpendicular magnetic field and find that its quantum interference exhibits distinct patterns when the MBT is in different magnetic states. In the antiferromagnetic state, the MBT is an axion insulator supporting an extended "hinge" supercurrent, which leads to a sinusoidal interference pattern decaying with the field str…
We study the dissipation physics of one dimensional mesoscopic superconducting quantum interference device array by using the field-theoretical renormalization group method. We observe length scale dependent superconductor-insulator quantum phase transition at very low temperature and also observe the dual behaviour of the system for the higher and lower values of magnetic field. At a critical magnetic field, we also observe a critical behaviour where the resistance is independent of length.
