Coupled-wire constructions have been widely applied to quantum Hall systems and symmetry-protected topological (SPT) phases. In this Letter, we use the coupled one-dimensional nonchiral Luttinger liquids with domain-wall structured mass terms as quantum wires to construct the crystalline higher-order topological superconductors (HOTSC) in two-dimensional interacting fermionic systems by two representative examples: $D_4$-symmetric class-D HOTSC and $C_4$-symmetric class-BD\1 HOTSC, with Majorana corner modes on the edge. Furthermore, based on the coupled-wire constructions, the quantum phase transition between different phases of 2D HOTSC by tuning the inter-wire couplings is investigated in a straightforward way.
We study the effects of e-e interaction in a 3D Crystalline Topological Insulator by adding on-site repulsion to the single-particle Hamiltonian and solving the many-body problem within Cluster Perturbation Theory. The goal is to clarify how many body effects modify the topological phase that stems from the crystal symmetries. Tuning the strength of the on-site interaction we show that band inversion disappears in the bulk and surface states loose their metallic character.
The phase diagram of FeSi1-xGex, obtained from magnetic, thermal and transport measurements on single crystals, shows a first-order transition from a correlated electron semiconductor to a ferromagnetic metal at a critical concentration, x ~ 0.25. The gap of the insulating phase strongly decreases with x. The specific heat coefficient appears to track the density of states of a Kondo insulator. The phase diagram is consistent with a correlation induced insulator-metal transition in conjunction with disorder on the Si/Ge ligand site.
We explore in detail the electronic phases of a system consisting of three non-colinear arrays of coupled quantum wires, each rotated 120 degrees with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a $s$-wave or $d \pm id$ superconductor, a charge density wave insulator, a two-dimensional Fermi liquid, and a 2D Luttinger liquid (also known as smectic metal or sliding Luttinger liquid). The model provides an effective description of electronic interactions in small-angle twisted bilayer graphene and we discuss its im…
We present a detailed study of the electronic transport properties on a single crystalline specimen of the moderately disordered heavy fermion system URh$_2$Ge$_2$. For this material, we find glassy electronic transport in a single crystalline compound. We derive the temperature dependence of the electrical conductivity and establish metallicity by means of optical conductivity and Hall effect measurements. The overall behavior of the electronic transport properties closely resembles that of metallic glasses, with at low temperatures an additional minor spin disorder contribution. We argue tha…
We study theoretically the electron transport in a 1D conductor adiabatically connected to a superconducting and normal metal leads. In the case of non-interacting we show that ac voltage applied along with dc voltage modifies I-V curve resembling a regime of photon-assisted tunneling. We obtain in the limit of low voltages, that the electron-electron interaction affects electronic transport resulting in a decrease of conductance and features in the frequency dependence of the impedance.
We present a theoretical study of correlated atomic wires deposited on substrates in two parts. In this first part, we propose lattice models for a one-dimensional quantum wire on a three-dimensional substrate and map them onto effective two-dimensional lattices using the Lanczos algorithm. We then discuss the approximation of these two-dimensional lattices by narrow ladder models that can be investigated with well-established methods for one-dimensional correlated quantum systems, such as the density-matrix renormalization group or bosonization. The validity of this approach is studied first …
SmB6 was recently proposed to be both a strong topological insulator and a topological crystalline insulator. For this and related cubic topological Kondo insulators, we prove the existence of four different topological phases, distinguished by the sign of mirror Chern numbers. We characterize these phases in terms of simple observables, and we provide concrete tight-binding models for each phase. Based on theoretical and experimental results for SmB6 we conclude that it realizes the phase with C^+_{k_z=0}=+2, C^+_{k_z=pi}=+1, C^+_{k_x=k_y}=-1, and we propose a corresponding minimal model.
In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. A…
Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as $(i)$ a tool for revealing the nature of correlated insulators and $(ii)$ a platform for Majorana-based topological qubits. In particular, we show that the band structure of a gate-defined wire immersed in an `inter-valley coherent' correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the …
One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to …
The electronic structures of two mixed valence insulators YbB$_6$ and YbB$_12$ are studied by using the local density approximation (LDA) supplemented with the Gutzwiller method and dynamic mean field theory (DMFT). YbB$_6$ is found to be a moderately correlated Z$_2$ topological insulator, similar to SmB$_6$ but having much larger bulk band gap. Notably, YbB$_12$ is revealed to be in a new novel quantum state, strongly correlated topological crystalline Kondo insulator, which is characterized by its non-zero mirror Chern number. The surface calculations find odd (three) and even (four) number…
We study theoretically electronic transport through a contact of a quantum wire with 2D or 3D leads and find that if the contact is not smooth and adiabatic then the conduction is strongly suppressed below a threshold voltage $V_T$, while above $V_T$ the dc current $\bar I$ is accompanied by coherent oscillations of frequency $f=\bar I / e$. The effect is related to interelectronic repulsion and interaction of dc current with the Friedel oscillations near a sharp contact. In short conducting channels of length $L < L_0 \simeq \hbar v_F/eV_T$ and at high temperatures $T > T_0 \simeq eV_T/k_B$ t…
We develop a method to extract the universal conductance of junctions of multiple quantum wires, a property of systems connected to reservoirs, from static ground-state computations in closed finite systems. The method is based on a key relationship, derived within the framework of boundary conformal field theory, between the conductance tensor and certain ground state correlation functions. Our results provide a systematic way of studying quantum transport in the presence of strong electron-electron interactions using efficient numerical techniques such as the standard time-independent densit…
We propose a method to detect a signature of non-abelian statistics in a 1D superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase, and a total of 4 Majorana particles. We show that an appropriately timed "pulse" in the coupling between the two middle Majoranas leads to a coherent rotation of the two q-bits associated with the pairs of Majoranas in the two TSC segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be u…
Using interlayer interaction to control functional heterostructures with atomic-scale designs has become one of the most effective interface-engineering strategies nowadays. Here, we demonstrate the effect of a crystalline LaFeO3 buffer layer on amorphous and crystalline LaAlO3/SrTiO3 heterostructures. The LaFeO3 buffer layer acts as an energetically favored electron acceptor in both LaAlO3/SrTiO3 systems, resulting in modulation of interfacial carrier density and hence metal-to-insulator transition. For amorphous and crystalline LaAlO3/SrTiO3 heterostructures, the metal-to-insulator transitio…
Analyses of thermal diffusivity data on complex insulators and on strongly correlated electron systems hosted in similar complex crystal structures suggest that quantum chaos is a good description for thermalization processes in these systems, particularly in the high temperature regime where the many phonon bands and their interactions dominate the thermal transport. Here we observe that for these systems diffusive thermal transport is controlled by a universal Planckian time scale $τ\sim \hbar/k_BT$, and a unique velocity $v_E$. Specifically, $v_E \approx v_{ph} $ for complex insulators, and…
Since the discovery of superconductivity and correlated insulator at fractional electron fillings in the twisted bilayer graphene, most theoretical efforts have been focused on describing this system in terms of an effective extended Hubbard model. However, it was recognized that an exact tight binding model on the Moiré superlattice which captures all the subtleties of the bands can be exceedingly complicated. Here we pursue an alternative coupled wire description of the system based on the observation that the lattice relaxation effect is strong at small twist angle, which substantially enla…
Phase-change memory (PCM), a promising candidate for next-generation non-volatile memories, exploits quenched glassy and thermodynamically stable crystalline states as reversibly switchable state variables. We demonstrate PCM functions emerging from a charge-configuration degree of freedom in strongly correlated electron systems. Non-volatile reversible switching between a high-resistivity charge-crystalline (or charge-ordered) state and a low-resistivity quenched state, charge glass, is achieved experimentally via heat pulses supplied by optical or electrical means in organic conductors $θ$-(…
We show that a tetragonal lattice of weakly interacting cavities with uniaxial electromagnetic response is the photonic counterpart of topological crystalline insulators, a new topological phase of atomic band insulators. Namely, the frequency band structure stemming from the interaction of resonant modes of the individual cavities exhibits an omnidirectional band gap within which gapless surface states emerge for finite slabs of the lattice. Due to the equivalence of a topological crystalline insulator with its photonic-crystal analog, the frequency band structure of the latter can be charact…
The alkali hyperoxide KO$_2$ is a molecular analog of strongly-correlated systems, comprising of orbitally degenerate magnetic O$_2^-$ ions. Using first-principles electronic structure calculations, we set up an effective spin-orbital model for the low-energy \textit{molecular} orbitals and argue that many anomalous properties of KO$_2$ replicate the status of its orbital system in various temperature regimes.
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated hopping processes that break chiral invariance, but preserve both inversion and time-reversal symmetries. In this way, we show that our one-dimensional model gives rise to an interacting second-order topological insulating phase that supports gapped edge states. The topological nature of such interacting phase turns out to be revealed by both long-range order of …
Quantum wires with spin-orbit coupling provide a unique opportunity to simultaneously control the coupling strength and the screened Coulomb interactions where new exotic phases of matter can be explored. Here we report on the observation of an exotic spin-orbit density wave in Pb-atomic wires on Si(557) surfaces by mapping out the evolution of the modulated spin-texture at various conditions with spin- and angle-resolved photoelectron spectroscopy. The results are independently quantified by surface transport measurements. The spin polarization, coherence length, spin dephasing rate, and the …
We study the transport of electrons through a long quantum wire connecting two bulk leads. As the electron density in the wire is lowered, the Coulomb interactions lead to short-range crystalline ordering of electrons. In this Wigner crystal state the spins of electrons form an antiferromagnetic Heisenberg spin chain with exponentially small exchange coupling J. Inhomogeneity of the electron density due to the coupling of the wire to the leads results in violation of spin-charge separation in the device. As a result the spins affect the conductance of the wire. At zero temperature the low-ener…
In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in 1D and 2D. These non-trivial phases require interactions for their existence and, in the cases we consider, the free-fermion classification yields only a trivial phase. Similar to the interpretation of the Kitaev Majorana wire as a mean-field p-wave superconductor Hamiltonian arising from an interacting model with quartic interactions, we show that our systems can be interpreted as "mean-field" char…
Transition metal oxides have been extensively studied and utilized as efficient catalysts. However, the strongly correlated behavior which often results in intriguing emergent phenomena in these materials has been mostly overlooked in understanding the electrochemical activities. Here, we demonstrate a close correlation between the phase transitions and oxygen evolution reaction (OER) in a strongly correlated SrRuO3. By systematically introducing Ru-O vacancies into the single-crystalline SrRuO3 epitaxial thin films, we induced phase transition in crystalline symmetry which resulted in corresp…
Correlated states emerge in low-dimensional systems owing to enhanced Coulomb interactions. Elucidating these states requires atomic scale characterization and delicate control capabilities. In this study, spectroscopic imaging-scanning tunneling microscopy was employed to investigate the correlated states residing in the one-dimensional electrons of the monolayer and bilayer MoSe2 mirror twin boundary (MTB). The Coulomb energies, determined by the wire length, drive the MTB into two types of ground states with distinct respective out-of-phase and in-phase charge orders. The two ground states …
It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realisation of this soft quantum matter physics in an ultra-cold gas. It uses optical lattices and dipolar interactions to realise a particularly simple model. Our analysis reveals a rich phase diagram featuring a meta-nematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes); and a crystalline, `checkerboard' phase.
Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in…
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly-correlated regime without breaking the spin or any other symmetry. In particular, it shows "bumps" (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly-correlated systems. Here we illustrate this approach for the study of both…
We investigate the spectral properties of an open interacting system by solving the Generalized Kadanoff-Baym Ansatz (GKBA) master equation for the single-particle density matrix, namely the time-diagonal lesser Green's function. To benchmark its validity, we compare the solution obtained within the GKBA with the solution of the Dyson equation (equivalently the full Kadanoff-Baym equations). In both approaches, we treat the interaction within the self-consistent second-order Born approximation, whereas the GKBA still retains the retarded propagator calculated at the Hartree-Fock level. We cons…
We investigate the low-energy collective charge excitations (plasmons, holons) in metallic atomic wires deposited on semiconducting substrates. These systems are described by two-dimensional correlated models representing strongly anisotropic lattices or weakly coupled chains. Well-established theoretical approaches and results are used to study their properties: random phase approximation for anisotropic Fermi liquids and bosonization for coupled Tomonaga-Luttinger liquids as well as Bethe Ansatz and density-matrix renormalization group methods for ladder models. We show that the Fermi and To…
We study correlated quantum wires subject to harmonic modulation of the onsite-potential concentrating on the limit of large times, where the response of the system has synchronized with the drive. We identify the ratio $Δε/Ω$ of the driving amplitude $Δε$ and the frequency of driving $Ω$ as the scale determining the crossover from a modified Luttinger liquid picture to a system that behaves effectively like a higher dimensional one. We exemplify this crossover by studying the frequency dependency of the boundary density of state $ρ_{\rm B}(ω)$ as well as the temperature dependency of the line…
We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons or fermions. We show that these exotic quantum phases should be realizable under current experimental conditions in finite-size confining potentials.
A new scattering approach for correlated one-dimensional systems is developed. The adiabatic contact to charge reservoirs is encoded in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation, is expressed through a dynamic scattering matrix. It is shown that the dc conductance is equal to e^2/h for any model with conserved total left- and right-moving charges. The ac conductance matrix is explicitly computated for the interacting Tomonaga-Luttinger model.
We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-pr…
We prove theoretically that certain strongly correlated Kondo insulators are topological crystalline insulators with nontrivial topology protected by crystal symmetries. In particular, we find that SmB$_6$ is such a material. In addition to a nontrivial Z$_2$ topological index protected by time reversal symmetry, SmB$_6$ also has nontrival mirror Chern numbers protected by mirror symmetries. On the $(100)$ surface of SmB$_6$, the nontrivial mirror Chern numbers do not generate additional surface states beyond those predicted by the Z$_2$ topological index. However, on the $(110)$ surface, two …
We describe a simple model of fermions in quasi-one dimension that features interaction induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on …
Based on first-principles calculations and symmetry analysis, we propose that a transition metal rutile oxide, in particular $β'$-PtO$_2$, can host a three-dimensional topological Dirac semimetal phase. We find that $β'$-PtO$_2$ possesses a linked nodal rings structure when spin-orbit coupling is neglected. Incorporating spin-orbit coupling gaps the nodal rings, while preserving a single pair of three-dimensional Dirac points protected by a screw rotation symmetry. This Dirac point is created by a band inversion of two $d$ bands, which is a realization of a DSM phase in correlated electron sys…
We investigate the connection between the transport properties and the thermodynamics of electronic systems with a tendency to form broken-symmetry mesophases evocative of the physics of liquid crystals. Through a hydrodynamic approach to the electronic transport in inhomogeneous systems, we develop a perturbative expansion for the macroscopic conductivity to study the transport of two-dimensional smectic and nematic phases. At the fluctuation induced first order phase transition expected for the smectic to isotropic transition, a jump in the macroscopic conductivity is predicted, with a direc…
We study strongly correlated ground and excited states of rotating quasi-2D Fermi gases constituted of a small number of dipole-dipole interacting particles with dipole moments polarized perpendicular to the plane of motion. As the number of atoms grows, the system enters {\it an intermediate regime}, where ground states are subject to a competition between distinct bulk-edge configurations. This effect obscures their description in terms of composite fermions and leads to the appearance of novel composite fermion quasi-hole states. In the presence of dipolar interactions, the principal Laughl…
Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting
Division of Chemistry and Chemical Engineering, California Institute of Technology（加州理工学院化学与化学工程系）；Marcus Center for Theoretical Chemistry, California Institute of Technology（加州理工学院马库斯理论化学中心）；Qingdao Institute for Theoretical and Computational Sciences and Center for Optics Research and Engineering, Shandong University（山东大学青岛理论与计算科学研究所及光学研究与工程中心）；Division of Engineering and Applied Sciences, California Institute of Technology（加州理工学院工程与应用科学系）；Department of Chemistry and Biochemistry, University of Maryland, College Park（马里兰大学帕克分校化学与生物化学系）；Institute for Physical Science and Technology, University of Maryland, College Park（马里兰大学帕克分校物理科学与技术研究所）
Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the low-energy and strong coupling limits, which impose severe constraints on the physical systems where they could be realized. We investigate the microscopic relevance of a class of coupled-wire models and their possible experimental realization in cold-atom experiments. We connect with earlier results and prove the emergence of fractional quantum Hall states in the limit of strong inter-wire tunnel…
High-harmonic generation (HHG) in crystalline solids have been examined so far on the basis of one-body energy-band structures arising from electron itineracy in a periodic potential. Here, we show emergence of HHG signals which are attributed to dynamics of many-body states in a low-dimensional correlated electron system. An interacting fermion model and its effective pseudo-spin model on a one-dimensional dimer-type lattice are analyzed. Observed HHG signals in a spontaneously symmetry-broken state, where charge densities are polarized inside of dimer units, show threshold behavior with resp…
We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of spinless electrons. Explicit results are obtained for thin quantum rings with realistic Coulomb interactions, by calculating this function via a many-body instanton approach.
Excitonic insulator is a coherent electronic phase that results from the formation of a macroscopic population of bound particle-hole pairs - excitons. With only a few candidate materials known, the collective excitonic behavior is challenging to observe, being obscured by crystalline lattice effects. Here we use polarization-resolved Raman spectroscopy to reveal the quadrupolar excitonic mode in the candidate zero-gap semiconductor Ta$_2$NiSe$_5$ disentangling it from the lattice phonons. The excitonic mode pronouncedly softens close to the phase transition, showing its electronic character, …
