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Results for “Symmetry protected topological phases”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Hofstadter Topology: Noncrystalline Topological Materials at High Flux

he Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ~10 4 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane–Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Multiple Dirac nodes and symmetry protected Dirac nodal line in orthorhombic α-RhSi

Exotic multifold topological excitations have been predicted and were recently observed in transition metal silicides like β-RhSi. Herein, we report that interesting topological features of RhSi are also observed in its orthorhombic α phase, which displays multiple types of Dirac nodes very close to the Fermi level ε F . Here, we discuss the symmetry analysis, band connectivity along high-symmetry lines using group representations, band structure, the nature of the Dirac points and of a nodal line occurring near ε F which is protected by the crystalline symmetry. The de Haas–van Alphen effect indicates a Fermi surface in agreement with the calculations. We find an elliptically shaped nodal line very close to ε F around and near the S point on the k y -k z plane that results from the intersection of two upside-down Dirac cones. Both Dirac points of the participating Kramers degenerate bands are only 5 meV apart; hence, an accessible magnetic field might induce a crossing between the spin-up partner of the upper Dirac cone and the spin-down partner of the lower Dirac cone, possibly explaining the anomalies observed in the magnetic torque. α-RhSi is a unique system since all bands crossing ε F emerge from Dirac nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Anomaly inflow, dualities, and quantum simulation of Abelian lattice gauge theories induced by measurements

Previous work [] has demonstrated that quantum simulation of Abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their noninvertibility are also presented. Published by the American Physical Society 2024

Okuda, Takuya↗
DOE OSTI2020

Topological surface states in strained Dirac semimetal thin films

We computationally study the Fermi arc states in a Dirac semimetal, both in a semi-infinite slab and in the thin-film limit. We use Cd 3 As 2 as a model system, and include perturbations that break the C-4 symmetry and inversion symmetry while mirror symmetries remain. The surface states are protected by the mirror symmetries present in the bulk states and thus survive these perturbations. Additionally, the Fermi arc states persist down to very thin films, thinner than presently measured experimentally, but are affected by breaking the symmetry of the Hamiltonian. Recent experimental observations of transport in Cd 3 As 2 films strongly suggest transport by surface states. Our findings are consistent with those observations in that we show that Fermi arc states can survive to rather thin films, and our results also suggest that symmetry-breaking terms that preserve the Fermi arc states nevertheless can have a profound effect in the thin film limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Matrix product states (MPS) and “dressed” ground states of quadratic mean fields (e.g., Gutzwiller projected Slater determinants) are both important classes of variational wave functions. This latter class has played important roles in understanding superconductivity and quantum spin liquids. We present a method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g., determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the S = 1 bilinear-biquadratic quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely, indicating the method is accurate and there is minimal loss due to truncation error. We then present an exploration of the entanglement spectra of projected slave-fermion states, exploring their qualitative features and finding good qualitative agreement with the respective exact ground-state spectra found from density matrix renormalization group.

1-dimensional spin chains↗
DOE OSTI2022

Frustrated mixed-spin ladders: Evidence for a bond-order wave phase between rung-singlet and Haldane phases

In frustrated spin ladders, the interplay of frustration and correlations leads to the familiar Haldane (H) and rung-singlet (RS) phases. The nature of the transition between these two phases is still under debate. In this paper we tackle this issue using tools of quantum information theory. We consider frustrated mixed-spin-(1, 1/2) ladders with antiferromagnetic leg, rung and diagonal couplings, and calculate various quantities, such as the entanglement entropy (EE), the Schmidt gap, and the level degeneracy of the entanglement spectrum (ES). We use two numerical techniques, the infinite time-evolving block decimation (iTEBD) and the density matrix renormalization group (DMRG). We demonstrate that there exists an intermediate phase in which the ES levels do not exhibit the characteristic degeneracies of the H and RS phases. To understand the underlying physics in this phase, here we investigate short-range spin correlations along legs, rungs and diagonals and show that in this intermediate phase long-wavelength modulations occur, akin to bond-order waves.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Non-equilibrium states and interactions in the topological insulator and topological crystalline insulator phases of NaCd4As3

Topological materials are of great interest because they can support metallic edge or surface states that are robust against perturbations, with the potential for technological applications. Here, we experimentally explore the light-induced non-equilibrium properties of two distinct topological phases in NaCd4As3: a topological crystalline insulator (TCI) phase and a topological insulator (TI) phase. This material has surface states that are protected by mirror symmetry in the TCI phase at room temperature, while it undergoes a structural phase transition to a TI phase below 200 K. After exciting the TI phase by an ultrafast laser pulse, we observe a leading band edge shift of >150 meV that slowly builds up and reaches a maximum after ∼0.6 ps and that persists for ∼8 ps. The slow rise time of the excited electron population and electron temperature suggests that the electronic and structural orders are strongly coupled in this TI phase. It also suggests that the directly excited electronic states and the probed electronic states are weakly coupled. Both couplings are likely due to a partial relaxation of the lattice distortion, which is known to be associated with the TI phase. In contrast, no distinct excited state is observed in the TCI phase immediately or after photoexcitation, which we attribute to the low density of states and phase space available near the Fermi level. Our results show how ultrafast laser excitation can reveal the distinct excited states and interactions in phase-rich topological materials.

Angle-resolved photoemission spectroscopy↗
DOE OSTI2022

Universal tripartite entanglement signature of ungappable edge states

Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this Letter we argue that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information h(A:B)=S R (A:B)-I(A:B) between two parties, we argue that for A,B being adjacent subregions in the bulk h=$\frac{c+}{3}$ ln 2, where c + is the minimal total central charge of the boundary theory. As evidence, we prove that h=0 for string-net models and numerically verify that h=$\frac{|C|}{3}$ ln 2 for a Chern-C insulator. Our Letter establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Layer-dependent topological phase in a two-dimensional quasicrystal and approximant

The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing “forbidden” symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta 1.6 Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta 21 Te 13 , reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Nonlocal Finite-Depth Circuits for Constructing Symmetry-Protected Topological States and Quantum Cellular Automata

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are . Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with k - gates, i.e., gates that act on no more than k degrees of freedom but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric k -local gates that create symmetry-protected topological (SPT) states from an initial product state. Our construction applies to SPT states protected by global symmetries or subsystem symmetries but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata in any dimension using finite-depth circuits of k -local gates. These results imply that the topological classifications of SPT phases and quantum cellular automata both collapse to a single trivial phase in the presence of k -local interactions. We furthermore argue that SPT phases are fragile to k -local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Broken time-reversal symmetry in the topological superconductor UPt 3

Topological properties of materials are of fundamental as well as practical importance. Of particular interest are unconventional superconductors that break time-reversal symmetry, for which the superconducting state is protected topologically and vortices can host Majorana fermions with potential use in quantum computing. However, in striking contrast to the unconventional A phase of superfluid 3 He where chiral symmetry was directly observed, identification of broken time-reversal symmetry of the superconducting order parameter, a key component of chiral symmetry, has presented a challenge in bulk materials. The two leading candidates for bulk chiral superconductors are UPt 3 and Sr 2 RuO 4 , although evidence for broken time-reversal symmetry comes largely from surface-sensitive measurements. A long-sought demonstration of broken time-reversal symmetry in bulk Sr 2 RuO 4 is the observation of edge currents, which has so far not been successful. The situation for UPt 3 is not much better. In this work, we use vortices to probe the superconducting state in ultraclean crystals of UPt 3 . Using small-angle neutron scattering, a strictly bulk probe, we demonstrate that the vortices possess an internal degree of freedom in one of its three superconducting phases, providing direct evidence for bulk broken time-reversal symmetry in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Symmetry-Protected Moiré Band Engineering and Enhanced Electron–Phonon Coupling in Xe/Bi 2 Se 3 Superlattices: Path to Topological Superconductivity

Observation of superconductivity, magnetism, and correlated insulating phases driven by the moiré potential in twisted graphene bilayer has opened the exciting new field of “twistronics”. Even richer physics is expected if moiré superlattice could be generated on topological insulators; however, until now, experimental studies have been scarce. Here, we demonstrate topological moirés generated by adsorbing a monolayer of noble gas on a topological insulator. By angle-resolved photoemission spectroscopy, we show that the moiré potential replicates the topological surface state and affects it in a way fundamentally different from the trivial states. Replicated Dirac cones generally avoid crossings, except at the time-reversal invariant momenta that remain gapless. This creates van Hove singularities at the moiré Brillouin zone corners, providing the mechanism of enhancing correlations. Indeed, we observe a strong enhancement of the electron–phonon coupling strength that, if properly tuned, might lead to topological superconductivity and Majorana Fermions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Topological electride phase of sodium at high pressures and temperatures

Sodium, a textbook example of a nearly-free-electron metal, exhibits unforeseen pressure-induced behavior including the stabilization of numerous polymorphs—some possessing extremely complex unit cells—as well as a metal-to-insulator transition to the iconic hP4 phase. However, until recently, most of the experimental and theoretical studies on solid sodium have been restricted to the low-temperature regime. In this work, using ab initio evolutionary structure searches coupled with quasiharmonic calculations, we discover seven new phases of sodium that are more stable than the known hP4 phase at pressure-temperature conditions that were recently attained in ramp-compression experiments. From these, our calculations suggest that P6 3 /m Na is the ground state between ≈250 GPa at 710 K and ≈350 GPa at 1900 K. Electronic structure calculations show that this phase is a topological semimetal with a Dirac nodal surface that is protected by a nonsymmorphic symmetry S 2z and an electride owing to its non-nuclear charge localized within one-dimensional honeycomb channels and zero-dimensional cages. Our results highlight the complexity of dense sodium's free-energy landscape and intricate electronic structure that emerges at finite temperatures and conditions where ionic cores overlap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated , also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Role of bath-induced many-body interactions in the dissipative phases of the Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it nonperturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant, which is applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. In conclusion, we also study the effect of on-site staggered potentials on the SSH phase diagram and discuss extensions of our method to higher dimensions.

1-dimensional systems↗
DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗
DOE OSTI2021

An index for two-dimensional SPT states

We define an index for 2D G-invariant invertible states of bosonic lattice systems in the thermodynamic limit for a finite symmetry group G with a unitary action. Furthermore, we show that this index is an invariant of the symmetry protected phase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Topological excitonic insulator with tunable momentum order

Correlated topological materials often maintain a delicate balance among physical symmetries. Many topological orders are symmetry protected, whereas most correlated phenomena arise from spontaneous symmetry breaking. Cases where symmetry breaking induces a non-trivial topological phase are rare. Here we demonstrate the presence of two such phases in Ta 2 Pd 3 Te 5 , where Coulomb interactions form excitons that condense below 100 K, one with zero and the other with finite momentum. We observed a full spectral bulk gap, which stems from exciton condensation. This topological excitonic insulator state spontaneously breaks mirror symmetries but involves a weak structural coupling. Scanning tunnelling microscopy shows gapless boundary modes in the bulk insulating phase. Their magnetic field response, together with theoretical modelling, indicates a topological origin. These observations establish Ta 2 Pd 3 Te 5 as a topological excitonic insulator in a three-dimensional crystal. Finally, our results manifest a unique sequence of topological exciton condensations in a bulk crystal, offering exciting opportunities to study critical behaviour and excitations.

36 MATERIALS SCIENCE↗