Topological Mott insulator by block spin phenomenology

Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

Recent theory and experiment have revealed that strong spin-orbit coupling can have dramatic qualitative effects on the band structure of weakly interacting solids. Indeed, it leads to a distinct phase of matter, the topological band insulator. In this paper, we consider the combined effects of spin-orbit coupling and strong electron correlation, and show that the former has both quantitative and qualitative effects upon the correlation-driven Mott transition. As a specific example we take Ir-based pyrochlores, where the subsystem of Ir 5d electrons is known to undergo a Mott transition. At weak electron-electron interaction, we predict that Ir electrons are in a metallic phase at weak spin-orbit interaction, and in a topological band insulator phase at strong spin-orbit interaction. Very generally, we show that with increasing strength of the electron-electron interaction, the effective spin-orbit coupling is enhanced, increasing the domain of the topological band insulator. Furthermore, in our model, we argue that with increasing interactions, the topological band insulator is transformed into a "topological Mott insulator" phase, which is characterized by gapless surface spin-only excitations. The full phase diagram also includes a narrow region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron-electron interaction.

We show that for magic-angle twisted bilayer graphene (TBG) away from charge neutrality, although quantum Monte Carlo (QMC) simulations suffer from the sign problem, the computational complexity is at most polynomial at certain integer fillings. For even integer fillings, this polynomial complexity survives even if an extra inter-valley attractive interaction is introduced, on top of Coulomb repulsions. This observation allows us to simulate magic-angle twisted bilayer graphene and to obtain accurate phase diagram and dynamical properties. At the chiral limit and filling $\nu=1$, the simulations reveal a thermodynamic transition separating metallic state and a $C=1$ correlated Chern insulator -- topological Mott insulator (TMI) -- and the pseudogap spectrum slightly above the transition temperature. The ground state excitation spectra of the TMI exhibit a spin-valley U(4) Goldstone mode and a time reversal restoring excitonic gap smaller than the single particle gap. These results are qualitatively consistent with the recent experimental findings at zero-field and $\nu=1$ filling in $h$-BN nonaligned TBG.

In this paper, we study a one-dimensional boson system in a superlattice potential. This system is experimentally feasible by using ultracold atomic gases, and attracts much attention these days. It is expected that the system has a topological phase called a topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with a non-vanishing integer Chern number. Compared to the hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization, we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., the topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefore the Chern number is to be observed in feasible experiments.

We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the 2nd nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fermionic systems. Our fRG results hint at a strong suppression of the scattering processes stabilizing the topological Mott insulator. From analyzing the effects of fermionic fluctuations, we obtain a phase diagram which is the result of the competition of various charge ordering instabilities.

Topological insulators are a new class of materials characterized by fully spin-polarized surface states, a linear dispersion, imperviousness to external non-magnetic perturbations, and a helical character arising out of the perpendicular spin-momentum locking. This article answers in a pedagogical way the distinction between a topological and normal insulator, the role of topology in band theory of solids, and the origin of these surface states. Numerical techniques including diagonalization of the TI Hamiltonians are described to quantitatively evaluate the behaviour of topological insulator states. The Hamiltonians based on continuum and tight binding approaches are contrasted. The application of TIs as components of a fast switching environment or channel material for transistors is examined through I-V curves. The potential pitfall of such devices is presented along with techniques that could potentially circumvent the problem. Additionally, it is demonstrated that a strong internal electric field can also induce topological insulator behaviour with wurtzite nitride quantum wells as representative materials.

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.

A new class of three-dimensional topological insulator, ternary rare earth chalcogenides, is theoretically investigated with ab initio calculations. Based on both bulk band structure analysis and the direct calculation of topological surface states, we demonstrate that LaBiTe3 is a topological insulator. La can be substituted by other rare earth elements, which provide candidates for novel topological states such as quantum anomalous Hall insulator, axionic insulator and topological Kondo insulator. Moreover, YBiTe3 and YSbTe3 are found to be normal insulators. They can be used as protecting barrier materials for both LaBiTe3 and Bi2Te3 families of topological insulators for their well matched lattice constants and chemical composition.

The electronic structure at the interface between a topological band insulator and a Mott insulator is studied within layer dynamical mean field theory. To represent the bulk phases of these systems, we use the generalized Bernevig-Hughes-Zhang model that incorporates the Hubbard-like onsite Coulomb energy U in addition to the spin-orbit coupling term that causes band inversion. The topological and Mott insulating phases are realized by appropriately choosing smaller and larger values of U, respectively. As expected, the interface is found to be metallic because of the localized edge state. When the Coulomb energy in the Mott insulator is close to the critical value, however, this edge state exhibits its largest amplitude deep within the Mott insulator rather than at the interface. This finding corresponds to a new type of proximity effect induced by the neighboring topological band insulator and demonstrates that, as a result of spin-orbit coupling within the Mott insulator, several layers near the interface convert from the Mott insulating phase to a topological insulating phase. Moreover, we argue that the ordinary proximity effect, whereby a Kondo peak is induced in a Mott insulator by neighboring metallic states, is accompanied by an additional reverse proximity effect, by which the Kondo peak gives rise to an enhancement of the density of states in the neighboring metallic layer.

Topological quantum states require stringent combination of crystal symmetry and spin–orbit coupling (SOC) strength. Here, we report that the ternary Zintl compound series BaCaX (X = Si, Ge, Sn and Pb, Group IV) in the same crystal structure having eight valence electrons per formula unit can host two different topological quantum phases, controlled by atomic size and SOC strength. BaCaSi is a nodal-line semimetal (NLSM) with band inversion protected by mirror symmetry and hosts a strong topological insulator (TI) state when SOC is turned on, thus, a NLSM-TI phase. Moving to larger atomic sizes and heavier atoms, BaCaGe and BaCaSn are normal insulators (NIs); then, with the strongest SOC in BaCaPb, a different band inversion is induced, giving a strong TI phase without the need of NLSM. Thus, we also predict two types of topological transitions in a phase diagram for BaCaX: (1) NLSM-TI to NI, then to TI by tuning atomic size and SOC strength via alloying, and (2) NI or TI to NLSM-TI via pressure.

[EN]In three-dimensional topological Insulators, the topological protected helical surface conducting states exist along with the bulk insulating states. In a class of topological insulators, namely topological crystalline insulators, the protection role of surface states is taken by crystalline symmetry instead of time-reversal symmetry. These exotic characteristics bring about potential applications in logic devices, thermoelectricity or quantum computers. However, due to some critical challenges (like their compatibility with the existing devices, their fabrication processes as well as their compatibility with topological or quantum behavior under external stimuli, working temperature range, cost efficiency, practical structure and ease of use), topological materials are still lagging in device applications. In this regard, this thesis aims at investigating the fundamental properties of a topological crystalline insulator, 𝑃𝑏0.77𝑆𝑛0.23𝑆𝑒, based on Raman characterization at different temperature ranges and low magnetic fields as well as magneto-transport of its Hall bar devices at low temperatures, albeit with meeting challenges in fabrication and characterization. The Raman response of this material at relaxed conditions confirms the presence of topological surface states. Moreover, temperature-dependent Raman characterizations indicate that both surface states and their bulk counterparts contribute to the Raman response considering the interplay of electrons and phonons. Furthermore, our findings based on magnetic-field dependent Raman characterization demonstrate that the surface states are topologically protected by symmetry. These Raman results are also corroborated with magneto-transport characterizations, revealing the prominent role of an inherent attribute of this material based on strong spin-orbit coupling. Our results pave the way for electron studies in field-effect transistors based on topological phase transitions

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spin-orbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surface originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, non-trivially linked nodal line semimetals and circuit-based quantum simulators.

The interface between topological and normal insulators hosts metallic states that appear due to the change in band topology. While topological states at a surface, i.e., a topological insulator-air/vacuum interface, have been studied intensely, topological states at a solid-solid interface have been less explored. Here we combine experiment and theory to study such embedded topological states (ETSs) in heterostructures of GeTe (normal insulator) and hbox {Sb}_2hbox {Te}_3 (topological insulator). We analyse their dependence on the interface and their confinement characteristics. First, to characterise the heterostructures, we evaluate the GeTe-Sb_2Te_3 band offset using X-ray photoemission spectroscopy, and chart the elemental composition using atom probe tomography. We then use first-principles to independently calculate the band offset and also parametrise the band structure within a four-band continuum model. Our analysis reveals, strikingly, that under realistic conditions, the interfacial topological modes are delocalised over many lattice spacings. In addition, the first-principles calculations indicate that the ETSs are relatively robust to disorder and this may have practical ramifications. Our study provides insights into how to manipulate topological modes in heterostructures and also provides a basis for recent experimental findings [Nguyen et al. Sci. Rep. 6, 27716 (2016)] where ETSs were seen to couple over thick layers.

A topological superconducting state can be induced in the surface state of a topological insulator (TI) by way of proximity coupling to a conventional $s$-wave superconductor ($s\ensuremath{-}\mathrm{SC}$). Planar $s\ensuremath{-}\mathrm{SC}/\mathrm{TI}$ junction structures were proposed as a scalable platform for controlled generation and manipulation of Majorana zero mode (MZM), which holds intriguing promise for fault-tolerant quantum computing. Despite intensive research efforts, the presence of MZM has not been definitively demonstrated in $s\ensuremath{-}\mathrm{SC}/\mathrm{TI}/s\ensuremath{-}\mathrm{SC}$ lateral junctions. A key factor is a lack of direct measurement and quantitative understanding of the proximity coupling between the $s\ensuremath{-}\mathrm{SC}$ and TI. Here we report evidence for strong superconducting proximity effect between a three-dimensional strong TI and Al, a conventional $s\ensuremath{-}\mathrm{SC}$ with minimal intrinsic spin-orbit coupling, in the form of pronounced enhancement of the in-plane critical field (${H}_{c||}$) of the thin Al. Specifically, the ${H}_{c||}$ of a 6-nm-thick Al film deposited on a TI is found to be 2.7 times its Pauli limit and about three times that of a simultaneously deposited reference film on $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_{2}$. The analysis of the ${H}_{c||}$ enhancement within the Maki theory indicates significant induced spin-orbit interaction in the Al due to electronic coupling to the TI. Our results revealed a pathway for producing SC/TI devices of high interfacial electrical transparency conducive for MZM generation and manipulation.

I present a theory of topological heavy-fermion semiconductors based on the large-N symplectic representation for the electron spin. The theory is exact in the limit when the number of spin flavors N=2k is infinite. I find that both weak and strong topological insulating phases exist for k<3. Furthermore, for k>2 the weak topological insulating state fully suppressed while only strong topological and trivial insulator states survive. In addition, using the mean-field theory results, I consider the tunneling into topologically trivial and non-trivial phases of a generic heavy-fermion insulators by calculating the differential tunneling conductance. The implications of the presented results for the existing heavy-fermion semiconductors are discussed.