Recently topological states of matter have witnessed a new physical phenomenon where both edge modes and gapless bulk coexist at topological quantum criticality. The presence and absence of edge modes on a critical line can lead to an unusual class of topological phase transition between the topological and non-topological critical phases. We explore the existence of this new class of topological phase transitions in a generic model representing the topological insulators and superconductors and we show that such transition occurs at a multicritical point i.e. at the intersection of two critical lines. To characterize these transitions we reconstruct the theoretical frameworks which include bound state solution of the Dirac equation, winding number, correlation factors and scaling theory of the curvature function to work for the criticality. Critical exponents and scaling laws are discussed to distinguish between the multicritical points which separate the critical phases. Entanglement entropy and its scaling in the real-space provide further insights into the unique transition at criticality revealing the interplay between fixed point and critical point at the multicriticalities.
Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the hopfion's locally uncompensated emergent field leads to a topological Hall signature, although the topological Hall effect vanishes on the global level. The topological Hall signature is switchable by magnetic fields or electric currents and occurs independently of the anomalous and conventional Hall effects. It can therefore be exploited to electrically detect …
We study one-component fermions in chain lattices with proximity-induced superconducting gap and interparticle short-range interaction, capable of hosting Majorana fermions. By systematically tracking various physical quantities, we show that topological states and topological phase transitions in the system can be identified by multiple signatures in thermodynamic quantities and pair-condensate properties, in good agreement with the known signatures in the ground-state energy and entanglement spectrum. We find the disappearance of the topological phase in a largely attractive regime, in which…
We consider a modified setup for measuring the Aharonov-Casher phase which consists of a Josephson vortex trapped in an annular topological superconducting junction. The junction encloses both electric charge and magnetic flux. We discover a deviation from the Aharonov-Casher prediction whose origin we identify in an additive universal topological phase that remarkably depends only on the parity of the number of vortices enclosed by the junction. We show that this phase is $\pm 2π$ times the topological spin of the Josephson vortex and is proportional to the Chern number. The presence of this …
Neutron scattering played an important role in the experimental exploration of the theoretical ideas of Thouless, Haldane, and Kosterlitz, who won the Nobel Prize in Physics in 2016. This article reviews the signatures of Haldane's predicted topological quantum ground state and their observation in early neutron scattering experiments, which overturned the wisdom of the day.
Axion electrodynamics, first proposed in the context of particle physics, manifests itself in condensed matter physics in the topological field theory description of 3d topological insulators and gives rise to magnetoelectric effect, where applying magnetic (electric) field $\mathbf{B}(\mathbf{E})$ induces polarization (magnetization) $\mathbf{p}(\mathbf{m})$. We use linear response theory to study the associated topological current using the Fu-Kane-Mele model of 3d topological insulators in the presence of time-dependent uniform weak magnetic field. By computing the dynamical current suscept…
We study a double-nanowire setup proximity coupled to an $s$-wave superconductor and search for the bulk signatures of the topological phase transition that can be observed experimentally, for example, with an STM tip. Three bulk quantities, namely, the charge, the spin polarization, and the pairing amplitude of intrawire superconductivity are studied in this work. The spin polarization and the pairing amplitude flip sign as the system undergoes a phase transition from the trivial to the topological phase. In order to identify promising ways to observe bulk signatures of the phase transition i…
We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator $\hat{\mathcal{L}}$ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes -- localized eigenmodes of $\hat{\mathcal{L}}$. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed syst…
In this work we explore experimental signatures of fractional topological insulators in three dimensions. These are states of matter with a fully gapped bulk that host exotic gapless surface states and fractionally charged quasiparticles. They are partially characterized by a non-trivial magneto-electric response while preserving time reversal. We describe how these phases appear in a variety of probes including photoemmission, tunneling, and quantum oscillations. We also discuss the effects of doping and proximate superconductivity. We argue that despite our current theoretical inability to p…
Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in …
We investigate the scattering off dilute magnetic impurities placed on the surface of three-dimensional topological insulators. In the low-temperature limit, the impurity moments are Kondo-screened by the surface-state electrons, despite their exotic locking of spin and momentum. We determine signatures of the Kondo effect appearing in quasiparticle interference (QPI) patterns as recorded by scanning tunneling spectroscopy, taking into account the full energy dependence of the T matrix as well as the hexagonal warping of the surface Dirac cones. We identify a universal energy dependence of the…
We theoretically investigate the features of Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between two magnetic impurities, mediated by the interfacial bound states inside a domain wall (DW). The latter separates the two regions with oppositely signed inversion symmetry broken terms in graphene and Weyl semimetal. The DW is modelled by a smooth quantum well which hosts a number of discrete bound states including a pair of gapless, metallic zero-energy modes with opposite chiralities. We find clear signatures of these interfacial chiral bound states in spin response (RKKY exchange i…
We study one-dimensional disordered fermions that either undergo metal-insulator transitions or topological phase transitions to become trivial Anderson insulators. We focus on using entanglement to elucidate how the spatial, momentum, and internal degrees of freedom of fermions are affected by the presence of disorder in such cases. We develop entanglement tools that reveal the existence of metallic states in the presence of disorder and further show clear signatures of the corresponding localization transition even in the presence of interactions. In systems where the internal degrees of fre…
We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. Besides these magnetic phase transitions we find topological phase transitions within the spin-flop phase. Both types of transitions manifest …
There have been increasing efforts in realizing topological metallic phases with nontrivial surface states. It was suggested that orthorhombic perovskite iridates are classified as a topological crystalline metal (TCM) with flat surface states protected by lattice symmetries. Here we perform first-principles electronic structure calculations for epitaxially stabilized orthorhombic perovskite iridates. Remarkably, two different types of topological surface states are found depending on surface directions. On side surfaces, flat surface states protected by lattice symmetries emerge, manifesting …
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For non-interacting electrons, it is well understood that such transitions are continuous and always accompanied by a gap-closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that sufficiently strong electron-electron interaction can fundamentally change the situation: we discov…
The temperature and thickness dependencies of the in-plane anisotropic magnetoresistance (AMR) of SmB$_6$ thin films are reported. We find that the AMR changes sign from negative ($ρ_{||}<ρ_{\perp}$) at high temperatures to positive ($ρ_{||}>ρ_{\perp}$) at low temperatures. The temperature, T$_s$, at which this sign change occurs, decreases with increasing film thickness $t$ and T$_s$ vanishes for $t$ $>$ 30 nm. We interpret our results in the framework of a competition between two components: a negative bulk contribution and a positive surface AMR.
This paper has been withdrawn and superseded by a new version entitled "Singularity of the London penetration depth at quantum critical points in superconductors" by Debanjan Chowdhury, Brian Swingle, Erez Berg and Subir Sachdev, posted in arXiv:1305.2918. The more recent paper has a number of new interesting results and includes a comprehensive analysis of 3 different classes of QCPs, including the one that was originally considered.
In this article, we study non-analyticities or cusps near a topological phase transition driven by changes of global topologies rather than by the formation of conventional (local) order. The particular phase transitions between topologically ordered superfluids and non-topological superfluids studied in this article are always accompanied by the emergence or disappearance of Majorana boundary modes, while at the critical point these boundary modes are liberated and evolve into the bulk. Proliferation of massless Majorana fermions at the transition leaves unique thermodynamic signatures. For a…
We propose a procedure that characterizes free-fermion or interacting multipolar higher-order topological phases via their bulk entanglement structure. To this end, we construct nested entanglement Hamiltonians by first applying an entanglement cut to the ordinary many-body ground state, and then iterating the procedure by applying further entanglement cuts to the (assumed unique) ground state of the entanglement Hamiltonian. We argue that an $n$-th order multipolar topological phase can be characterized by the features of its $n$-th order nested entanglement Hamiltonian e.g., degeneracy in th…
We present a theory for the differential shot noise, $dS/dV$, as measured via shot-noise scanning tunneling spectroscopy, and the differential conductance, $dI/dV$, for tunneling into Majorana zero modes (MZMs) in the putative topological superconductor FeSe$_{0.45}$Te$_{0.55}$. We demonstrate that for tunneling into chiral Majorana edge modes near domain walls, as well as MZMs localized in vortex cores and at the end of defect lines, $dS/dV$ vanishes whenever $dI/dV$ reaches a quantized value proportional to the quantum of conductance. These results are independent of the particular orbital t…
The non-trivial topology in the layered $\text{FeTe}_{0.55}\text{Se}_{0.45}$ (FTS) superconductor has been suggested by both theory and experiment to be strongly dependent on the Te concentration. Motivated by this together with the Te fluctuations expected from alloy disorder, we develop a simple layered model for a strong topological insulator that allows us to describe a scenario where topologically trivial domains permeate the sample. We refer to such a phase as topological domain disordered and study the local density (LDOS) of the topological surface states that can be measured using sca…
Topological insulators with intrinsic magnetic order are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. To study these systems and their physics, people have proposed a variety of magnetic topological insulator systems, including HoSbTe, an antiferromagnetic weak topological insulator candidate. In this work, we use scanning tunneling microscopy to probe the electronic structure of HoSbTe with antiferromagnetic and ferromagnetic orders that are tuned by applying an external magnetic field. Although around the Fermi energy, w…
We construct a global Lindblad master equation for a Kitaev quantum wire of finite length, weakly coupled to an arbitrary number of thermal baths, within the Born-Markov and secular approximations. We find that the coupling of an external bath to more than one lattice site generates quantum interference effects, arising from the possibility of fermions to tunnel through multiple paths. In the presence of two baths at different temperatures and/or chemical potentials, the steady-state particle current can be expressed through the Landauer-Büttiker formula, as in a ballistic transport setup, wit…
We study the main intra-band and inter-band transport properties at zero temperature of free electron-like system undergoing a topological reconstruction of the Fermi surface for the two-dimensional and three-dimensional case. The calculated intra-band properties include the single-particle density of states, the total and the effective concentrations of electrons and the thermopower. As for the inter-band case, the real part of the conductivity has been calculated within the vanishing inter-band relaxation approximation as a function of the incident photon energy. Within this approach, it is …
The fractional quantum Hall (FQH) state is a topological state of matter resulting from the many-body effect of interacting electrons and is of vast interest in fundamental physics. The experimental observation of topological surface states (SSs) in three-dimensional bulk solids has allowed the study of a correlated chiral Dirac fermion system, which can host a single Dirac valley without spin degeneracy. Recent theoretical studies suggest that the fractional quantum Hall effect (FQHE) might be observable in topological insulators. However, due to the dominant bulk conduction it is difficult t…
Topologically stable nontrivial spin structures, such as skyrmions and antiskyrmions, display a large topological Hall effect owing to their quantized topological charge. Here, we present the finding of a large topological Hall effect beyond room temperature in the tetragonal phase of a Mn-Ni-Ga based ferrimagnetic Heusler shape memory alloy system. The origin of the field induced topological phase, which is also evidenced by the appearance of dips in the ac-susceptibility measurements, is attributed to the presence of magnetic antiskyrmions driven by D2d symmetry of the inverse Heusler tetrag…
Topological transport phenomena in magnetic materials are a major topic of current condensed matter research. One of the most widely studied phenomena is the ``topological Hall effect'' (THE), which is generated via spin-orbit interactions between conduction electrons and topological spin textures such as skyrmions. We report a comprehensive set of Hall effect and magnetization measurements on epitaxial films of the prototypical ferromagnetic metal SrRuO$_3$ the magnetic and transport properties of which were systematically modulated by varying the concentration of Ru vacancies. We observe Hal…
We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break the protecting symmetry. Naïvely, one might expect that topology loses meaning when a protecting symmetry is broken. Defying this intuition, we illustrate, in an interacting Su-Schrieffer-Heeger (SSH) model, how this combination of symmetry breaking and quench dynamics can give rise to both single-particle and many-body signatures of topology. From the dynamics of the symmetry broken state, we find that we are able to dynamica…
As an unconventional realization of topological orders with an exotic interplay of topology and geometry, fracton (topological) orders feature subextensive topological ground state degeneracy and subdimensional excitations that are movable only within a certain subspace. It has been known in the exactly solvable three-dimensional X-cube model that universally represents the type-I fracton orders, that mobility constraints on subdimensional excitations originate from the absence of spatially deformable string-like operators. To unveil the interplay of topology and geometry, in this paper, we st…
The topological Hall effect (THE) of electrons in skyrmion crystals is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the skyrmion crystal (THE) or of the corre…
We investigate spinon band topology and engineering from the interplay between long-ranged magnetic order and fractionalized spinons, as well as Zeeman coupling under external magnetic fields, in honeycomb lattice magnets. The synergism of Néel order and magnetic fields could reconstruct the spinon bands and drive a topological phase transition from the coexisting phase of long-ranged order and chiral spin liquid with semion topological order to the conventional magnetic order. Our prediction can be immediately tested through thermal Hall transport measurements among the honeycomb lattice magn…
We report high pressure Raman experiments of Black phosphorus up to 24 GPa. The line widths of first order Raman modes A$^1_g$, B$_{2g}$ and A$^2_g$ of the orthorhombic phase show a minimum at 1.1 GPa. Our first-principles density functional analysis reveals that this is associated with the anomalies in electron-phonon coupling at the semiconductor to topological insulator transition through inversion of valence and conduction bands marking a change from trivial to nontrivial electronic topology. The frequencies of B$_{2g}$ and A$^2_g$ modes become anomalous in the rhombohedral phase at 7.4 GP…
Research on high-$T_c$ superconductors has generally not focused on analysis of the topological structure of electronic bands in these materials. In this article we collate and discuss several well-known experimental observables that signal that certain signatures of topology may be present. The topological signatures suggested by experiment include dimensional reduction, electronic transport determined by loop statistics, a winding number, Weyl fermions, and others. We suggest that topology, in a wider sense than band topology, may be key to the mechanism of high-$T_c$ superconductivity.
