A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and π-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particular attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo--based calculations.
The Gutzwiller wave function for a strongly correlated model can, if supplemented with a long-range Jastrow factor, provide a proper variational description of Mott insulators, so far unavailable. We demonstrate this concept in the prototypical one-dimensional $t-t^\prime$ Hubbard model, where at half filling we reproduce all known phases, namely the ordinary Mott undimerized insulator with power-law spin correlations at small $t^\prime/t$, the spin-gapped metal above a critical $t^\prime/t$ and small $U$, and the dimerized Mott insulator at large repulsion.
We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low bias voltages $V$. We show that $G(V)$ exhibits an unconventional dependence on the direction of magnetization of the tip and can be used to measure the magnitude of the local out-of-plane spin orientation of the Dirac Fermions on the surface. We also demonstrate that if the in-plane rotational symmetry on the surface of the topological insulator is broken by an external field, then $G(V)$ acquires a depen…
Kondo insulators are primary candidates in the search for strongly correlated topological quantum phases, which may host topological order, fractionalization, and non-Abelian statistics. Within some Kondo insulators, the hybridization gap is predicted to protect a nontrivial topological invariant and to harbor emergent heavy Dirac fermion surface modes. We use high-energy-resolution spectroscopic imaging in real and momentum space on the Kondo insulator, SmB$_6$. On cooling through $T^*_Δ\approx$ 35 K we observe the opening of an insulating gap that expands to $Δ\approx$ 10 meV at 2 K. Within …
The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with two fold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that a…
Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transitions induced by the stripe of charge density in an interacting two-dimensional Dirac fermion system. The stripe will introduce the transport anisotropy and insulating intermediate phase into the system, accompanied by the change of band structure and a peak of density of states around Fermi energy. In the case of strong correlation, stripe exhibits competition with Coulomb repulsion through closing the energy gap and disrupting the magnetic order, and finally drives the system in Mott insulating phase b…
A Dirac fermion emerges as a result of interplay between symmetry and topology in condensed matter. Current research moves towards investigating the Dirac fermions in the presence of manybody effects in correlated system. Here, we demonstrate the emergence of correlation-induced symmetry-protected Dirac semimetal state in the lightly-doped spin-orbit-coupled Mott insulator Sr$_2$IrO$_4$. We find that the nonsymmorphic crystalline symmetry stabilizes a Dirac line-node semimetal and that the correlation-induced symmetry-breaking electronic order further leads to a phase transition from the Dirac…
We study the transport properties of the Dirac fermions with Fermi velocity $v_F$ on the surface of a topological insulator across a ferromagnetic strip providing an exchange field ${\mathcal J}$ over a region of width $d$. We show that the conductance of such a junction changes from oscillatory to a monotonically decreasing function of $d$ beyond a critical ${\mathcal J}$. This leads to the possible realization of a magnetic switch using these junctions. We also study the conductance of these Dirac fermions across a potential barrier of width $d$ and potential $V_0$ in the presence of such a …
We study a layered three-dimensional heterostructure in which two types of Kondo insulators are stacked alternatingly. One of them is the topological Kondo insulator SmB 6 , the other one an isostructural Kondo insulator AB 6 , where A is a rare-earth element, e.g., Eu, Yb, or Ce. We find that if the latter orders ferromagnetically, the heterostructure generically becomes a magnetic Weyl Kondo semimetal, while antiferromagnetic order can yield a magnetic Dirac Kondo semimetal. We detail both scenarios with general symmetry considerations as well as concrete tight-binding calcu-lations and show…
Correlated Dirac semimetal phases emerge in lightly doped (Tb- or La-doped) Mott insulator Sr$_2$IrO$_4$, where a d-wave symmetry-breaking order underlying a pseudogap plays a crucial role in determining the nature of Dirac degeneracy, i.e., whether it is a Dirac line node or Dirac point node. Here, using a realistic five-orbital tight-binding model with a Hubbard U and a semiclassical Boltzmann transport theory, we systematically study the low-energy electrodynamic properties of the Dirac semimetal phases in the paramagnetic lightly doped Sr$_2$IrO$_4$. We investigate the effects of the d-wav…
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…
In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the…
We report a systematic angle-resolved photoemission spectroscopy on topological insulator (TI) TlBi1-xSbxTe2 which is bulk insulating at 0.5 < x < 0.9 and undergoes a metal-insulator-metal transition with the Sb content x. We found that this transition is characterized by a systematic hole doping with increasing x, which results in the Fermi-level crossings of the bulk conduction and valence bands at x~ 0 and x~1, respectively. The Dirac point of the topological surface state is gradually isolated from the valence-band edge, accompanied by a sign reversal of Dirac carriers. We also found that …
We discuss a non-fermi liquid gapless metallic surface state of the topological band insulator. It has an odd number of gapless Dirac fermions coupled to a non-compact U(1) gauge field. This can be viewed as a vortex dual to the conventional Dirac fermion surface state. This surface duality is a reflection of a bulk dual description discussed recently for the gauged topological insulator. All the other known surface states can be conveniently accessed from the dual Dirac liquid, including the surface quantum hall state, the Fu-Kane superconductor, the gapped symmetric topological order and the…
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving Dirac fermions that behave as massless relativistic particles. These Dirac fermions are responsible for achieving a number of novel and exotic quantum phenomena in the topological insulators and for their potential applications in spintronics and quantum computations. It is thus essential to understand the electron dynamics of the Dirac fermions, i.e., how they interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemis…
We have performed angle-resolved photoemission spectroscopy (ARPES) on the (111) surface of the topological crystalline insulator SnTe. Distinct from a pair of Dirac-cone surface states across the X_bar point of the surface Brillouin zone on the (001) surface, we revealed two types of Dirac-cone surface states each centered at the G_bar and M_bar points, which originate from the bulk-band inversion at the L points. We also found that the energy location of the Dirac point and the Dirac velocity are different from each other. This ARPES experiment demonstrates the surface states on different cr…
We reconsider the problem of surface states spectrum in type One Dirac metals. We find that the surface states, despite being gapped, always form branches terminating at Dirac points. Furthermore, we consider evolution of the surface states in the case, when rotational symmetry is broken, and as a result, Dirac points are gapped. We find, that in this case, special role is played by mirror symmetry relative to the plane connecting Dirac points. When it is present, the resulting gapped state is a topological crystalline insulator, which surface spectrum can contain either one or three Dirac poi…
We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.
Bloch theory describes the electronic states in crystals whose energies are distributed as bands over the Brillouin zone. The electronic states corresponding to a (few) isolated energy band(s) thus constitute a vector bundle. The topological properties of these vector bundles provide new characteristics of the corresponding electronic phases. We review some of these properties in the case of (topological) insulators and semi-metals.
The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields the quantized charge Hall effect ($\s_{xy}=(2n+1)e^2/h$) will coexist with spin Hall effect.
We propose a platform for flat Chern band by subjecting two-dimensional Dirac materials -- such as graphene and topological insulator thin films -- to a periodic magnetic field, which can be created by the vortex lattice of a type-II superconductor. As a generalization of the $n=0$ Landau level, the flat band of Dirac fermion under a nonuniform magnetic field remains at zero energy, exactly dispersionless and topologically protected, while its local density of states is spatially modulated due to the magnetic field variation. In the presence of short-range repulsion, we find fractional Chern i…
We explore the ultrafast reflectivity response from photo-generated coupled phonon-surface Dirac plasmons in Sb$_2$Te$_3$ topological insulators several quintuple layers thick. The transient coherent phonon spectra obtained at different time frames exhibit a Fano-like asymmetric line shape of the $A^2_{1g}$ mode, which is attributed to quantum interference between continuum-like coherent Dirac-plasmons and phonons. By analyzing the time-dependent asymmetric line shape using the two-temperature model (TTM), it was determined that a Fano-like resonance persisted up to $\approx$1 ps after photo-e…
Real and complex Clifford bundles and Dirac operators defined on them are considered. By using the index theorems of Dirac operators, table of topological invariants is constructed from the Clifford chessboard. Through the relations between K-theory groups, Grothendieck groups and symmetric spaces, the periodic table of topological insulators and superconductors is obtained. This gives the result that the periodic table of real and complex topological phases is originated from the Clifford chessboard and index theorems.
Graphene, the atomic-thin layer of carbon atoms, was first isolated on an insulating substrate in 2004 by two groups in Manchester University [1, 2] and Columbia [3]. Those milestone experiments established the Dirac nature of the charge carriers in graphene. The same year, C.L. Kane and E.G. Mele predicted that intrinsic spin-orbit coupling in graphene, if strong enough, would lead to a novel state of electronic matter called the Quantum Spin Hall (QSH) state [4, 5]. The QSH state is characterized by conducting gapless edge states circulating around an insulating bulk. Those edge states are p…
The metal-insulator transition has been a subject of intense research since Nevil Mott has first proposed that the metallic behavior of interacting electrons could turn to the insulating one as electron correlations increase. Here, we consider electrons with massless Dirac-like dispersion in two spatial dimensions, described by the Hubbard models on two geometrically different lattices, and perform numerically exact calculations on unprecedentedly large systems that, combined with a careful finite size scaling analysis, allow us to explore the quantum critical behavior in the vicinity of the i…
Dirac metals (gapless semi-conductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the existence of Weyl fermions in three dimensions. Applying magnetic fields near the topological phase transition from a topological insulator to a band insulator in Bi1-xSbx, we observe not only the weak anti-localization phenomenon in magnetoconductivity near zero magnetic fields (B < 0.4 T) but also its upturn above 0.4 T only for E // B. This incompatible coexi…
Topological insulators in the presence of strong Coulomb interaction constitute novel phases of matter. Transitions between these phases can be driven by single-particle or many-body effects. On the basis of {\it ab-initio} calculations, we identify a concrete material, {\it i.e.} Ca$_{2}$PtO$_{4}$, that turns out to be a hole-doped weak topological insulator. Interestingly, the Pt-$d$ orbitals in this material are relevant for the band inversion that gives rise to the topological phase. Therefore, Coulomb interaction should be of importance in Ca$_{2}$PtO$_{4}$. To study the influence of inte…
Dirac semimetal is a class of semi-metallic phase protected by certain types of crystalline symmetries, and its low-energy effective Hamiltonian is described by Dirac equations in three dimensions (3D). Despite of various theoretical studies, theories that describe the topological nature of Dirac semimetals have not been well established. In this work, we define a topological invariant for 3D Dirac semimetals by establishing a mapping between a 3D Dirac semimetal and a topological crystalline insulator in four dimension (4D). We demonstrate this scheme by constructing a tight-binding model for…
We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization group analysis reveals three fixed points that are Lorentz invariant, rotationally invariant, and $O_h$ invariant. Among them, the Lorentz- and $O_h$-invariant fixed points are stable in the low-energy limit while the rotationally invariant fixed point is unstable. The existence of a stable $O_h$-invariant fixed point of Dirac fermions with finite velocity ani…
Multilayer (TiO$_2$)$_m$/(VO$_2$)$_n$ nanostructures ($d^1$ - $d^0$ interfaces with no polar discontinuity) show a metal-insulator transition with respect to the VO$_2$ layer thickness in first principles calculations. For $n$ $\geq$ 5 layers, the system becomes metallic, while being insulating for $n$ = 1 and 2. The metal-insulator transition occurs through a semi-Dirac point phase for $n$ = 3 and 4, in which the Fermi surface is point-like and the electrons behave as massless along the zone diagonal in k-space and as massive fermions along the perpendicular direction. We provide an analysis …
We study a Haldane model with nearest neighbor interactions. We find one-dimensional like collective modes arising due to the interplay of pseudo-spin and valley degrees of freedom. In the large band gap or moderate interaction limit, these excitations are low energy modes lying in the band gap. The dispersion relations are qualitatively different in trivial insulator phase and Chern insulator phase, thus can be used to identify the topology of the Haldane model with the bulk property. We also discuss how to detect these modes in cold atom systems. An abelian gauge theory will emerge when a ph…
The kinetic features of holes (electrons) in the Hubbard model are studied using a variational Monte Carlo method. In doped Mott insulators (U>U_co), holes are classified, in the sense of conduction, into two categories: (i) The holes appearing in doublon-holon pairs are localized, encourage singlet pair formation, and gain the energy to induce a superconducting transition. (ii) The doped holes become carriers, make the system itinerant (superconducting or metallic), but lose the energy in the transition. These two roles are distinguished in correlated superconductivity. This feature is common…
A thin film of ferromagnetically ordered material proximate to the surface of a three-dimensional topological insulator explicitly breaks the time-reversal symmetry of the surface states. For an out-of-plane ferromagnetic order parameter on the surface, the parity is also broken, since the Dirac fermions become massive. This leads in turn to the generation of a topological Chern-Simons term by quantum fluctuations. On the other hand, for an in-plane magnetization the surface states remain gapless for the non-interacting Dirac fermions. In this work we study the possibility of spontaneous break…
We use Dirac quantization of flux to study fractional charges and axion angles θin interacting topological insulators with gapless surface modes protected by time-reversal symmetry. In interacting topological insulators, there are two types of fractional axion angle due to conventional odd and nontrivial even flux quantization at the boundary. On even flux quantization in a gapped time reversal invariant system, we show that there is a halved quarter fractional quantum Hall effect on the surface with Hall conductance of p/4q e2/2h with p and q odd integers. The gapless surface modes can be cha…
We study the extended Bose-Hubbard model on the square lattice at half filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a two-parameter family of wave-functions based on the parton construction which can describe both topological and broken symmetry phases on equal footing. In addition, our wave-functions resolve long standing issues with more conventional short-range Jastrow wave-functions. Using this variational ansatz, we show that a spontaneous time-reversal symmetry breaking frac…
We use high-resolution, tunable angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to study the electronic properties of single crystals of MnBi2Te4, a material that was predicted to be the first intrinsic antiferromagnetic (AFM) topological insulator. We observe both bulk and surface bands in the electronic spectra, in reasonable agreement with the DFT calculations results. In striking contrast to the earlier literatures showing a full gap opening between two surface band manifolds along (0001) direction, we observed a gapless Dirac cone remain …
Heavy fermion systems contain not only strong electron correlations, which promote a rich set of quantum phases, but also a large spin-orbit coupling, which tends to endow the electronic states a topological character. Kondo insulators are understood in terms of a lattice of local moments coupled to conduction electrons in a half-filled band, i.e., with a dense population of about one electron per unit cell. Here, we propose that a new class of Kondo insulator arises when the conduction-electron band is nearly empty ( or, equivalently, full ) . We demonstrated the effect through a honeycomb An…
We have performed systematic angle-resolved photoemission spectroscopy of the topological crystalline insulator (TCI) Pb1-xSnxTe to elucidate the evolution of its electronic states across the topological phase transition. As previously reported, the band structure of SnTe (x = 1.0) measured on the (001) surface possesses a pair of Dirac-cone surface states located symmetrically across the Xbar point in the (110) mirror plane. Upon approaching the topological phase transition into the trivial phase at x_c ~ 0.25, we discovered that Dirac cones gradually move toward the Xbar point with its spect…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a fully saturated zero mode will have different behaviors near the boundary according to the sign of the effective mass for Dirac fermions. The Hall conductance is quantized to be n (n is an integer) in the unit of e^2/h for a positive mass, n+1 for a negative mass, and n+1/2 for massless fermions. In topological insulator the massive term to the Dirac fermions ca…
Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic systems exhibit properties which can be well described by the Dirac equation. Such physics is no longer the exclusive domain of quantum field theories and other esoteric mathematical musings; instead, real physics of real systems is governed by such equations, and important materials science and practical implications hinge on our understanding of Dirac particles…
The gapless surface Dirac cone of time reversal invariant topological insulators is protected by time reversal symmetry due to the Kramers' theorem. Spin degree of freedom is usually required since Kramers' theorem only guarantees double degeneracy for spinful fermions, but not for spinless fermions. In this paper, we present an antiferromagnetic spinless model, which breaks time reversal symmetry. Similar to time reversal invariant topological insulators, this model possesses a topologically non-trivial phase with a single surface Dirac cone, which is protected by the combination of time reve…
The non-trivial topology of the three-dimensional (3D) topological insulator (TI) dictates the appearance of gapless Dirac surface states. Intriguingly, when a 3D TI is made into a nanowire, a gap opens at the Dirac point due to the quantum confinement, leading to a peculiar Dirac sub-band structure. This gap is useful for, e.g., future Majorana qubits based on TIs. Furthermore, these Dirac sub-bands can be manipulated by a magnetic flux and are an ideal platform for generating stable Majorana zero modes (MZMs), which play a key role in topological quantum computing. However, direct evidence f…
In the recently discovered topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with a unique set of characteristics. Among the theoretical predictions for TCIs is the possibility of imparting mass to the massless Dirac fermions by breaking crystal symmetry, as well as a Lifshitz transition with a change of Fermi surface topology. Here we report high resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe. We demonstrate the formation of zero mass Dirac fermions protected by crystal symmetry and the mechanism of mass generat…
We study the surface states and chiral hinge states of a 3D second-order topological insulator in the presence of an external magnetic gauge field. Surfaces pierced by flux host Landau levels, while surfaces parallel to the applied field are not significantly affected. The chiral hinge modes mediate spectral flow between neighbouring surfaces. As the magnetic field strength is increased, the surface Landau quantization deviates from that of a massive Dirac cone. Quantitatively, the $n = 0$ Landau level falls inside the surface Dirac gap, and not at the gap edge. The $n \ne 0$ levels exhibit a …
Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by a dual theory, QED3 with a dual Dirac fermion coupled to a gauge field. This duality is established by considering two alternate descriptions of the 3d topological insulator (TI) surface. The first description is the usual Dirac cone surface state. The second description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, w…
The tunability of topological surface states (SS) and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In topological crystalline insulators (TCIs), a spontaneously generated Dirac gap was recently observed, which was ascribed to broken cubic crystal symmetry. However, this structural distortion has not been directly observed so far, and the microscopic mechanism of Dirac gap opening via crystal symmetry breaking remains elusive. In this work, we present scanning tunneling microscopy (STM) measurements of a TCI Pb$_{1-x}$Sn$…
In this paper Chiral Magnetic Effect (CME) in Dirac semimetals is studied by means of lattice Monte Carlo simulation. We measure conductivity of Dirac semimetals as a function of external magnetic field in parallel $σ_{\parallel}$ and perpendicular $σ_{\perp}$ to the external field directions. The simulations are carried out in three regimes: semimetal phase, onset of the insulator phase and deep in the insulator phase. In the semimetal phase $σ_{\parallel}$ grows whereas $σ_{\perp}$ drops with magnetic field. Similar behaviour was observed in the onset of the insulator phase but conductivity …
