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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

Abrams, Erez [Princeton University, Massachusetts ↗
DOE OSTI2022

Selective control of conductance modes in multi-terminal Josephson junctions

The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of a multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work, we employ a quantum point contact geometry in three-terminal Josephson devices to demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presence of superconducting coupling. These results establish a full platform on which to realize tunable Andreev bound state spectra in multi-terminal Josephson junctions.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Ordering the topological order in the fractional quantum Hall effect

Here, we discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically, the one-form global symmetry and its anomaly are presented as the organizing principle of these systems. This information is powerful enough to lead to a unique minimal topological order (or a small number of minimal topological orders). Almost all of the known experimentally discovered topological orders are these minimal theories. Since this work is interdisciplinary, we made a special effort to relate to researchers with different backgrounds by providing translations between different perspectives.

Anyons↗
DOE OSTI2022

Unconventional self-similar Hofstadter superconductivity from repulsive interactions

Abstract Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number $${{{{{{{\mathcal{C}}}}}}}}=\pm 6$$ C = ± 6 . The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moiré heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Codimension-2 defects and higher symmetries in (3+1)D topological phases

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6 A 6 gauge theory.

Barkeshli, Maissam↗
DOE OSTI2025

Solving the Bernstein-Vazirani problem using Majorana-based topological quantum algorithms

Executing quantum algorithms using Majorana zero modes—a major milestone for the field of topological quantum computing—requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of a Majorana-based, fault-tolerant quantum algorithm to solve the Bernstein-Vazirani problem in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes’ topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Anti-site defect-induced disorder in compensated topological magnet MnBi2-xSbxTe4

Abstract The gapped Dirac-like surface states of compensated magnetic topological insulator MnBi 2-x Sb x Te 4 (MBST) are a promising host for exotic quantum phenomena such as the quantum anomalous Hall effect and axion insulating state. However, it has become clear that atomic defects undermine the stabilization of such quantum phases as they lead to spatial variations in the surface state gap and doping levels. The large number of possible defect configurations in MBST make studying the influence of individual defects virtually impossible. Here, we present a statistical analysis of the nanoscale effect of defects in MBST with x =0.64, by scanning tunnelling microscopy/spectroscopy. We identify (Bi,Sb) Mn anti-site defects to be the main source of the observed doping fluctuations, leading towards the formation of nanoscale charge puddles and effectively closing the transport gap. Our findings will guide further optimization of this material system via defect engineering, to enable exploitation of its promising properties.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Tuning Electronic Properties of 2D Materials Using Metal Adsorbates: Cu at WTe 2 Edges

Two-dimensional materials exhibit properties promising for novel applications. Topologically protected states at their edges can be harnessed for use in quantum devices. We use ab initio simulations to examine properties of edges in 1T'-WTe 2 monolayers, known to exhibit topological order, and their interactions with Cu atoms. Comparison of (010)-oriented edges that have the same composition but different terminations shows that, as the number of Cu atoms increases, their thermodynamically-preferred arrangement depends on the details of the edge structure. Cu atoms aggregate into a cluster at the most stable edge; while the cluster is non-magnetic, it spin-polarizes the W atoms along the edge, which removes the topological protection. At the metastable edge, Cu atoms form a chain incorporated into the WTe 2 lattice; the topological state is preserved in spite of the dramatic edge restructuring. This suggests that exploiting interactions of metal species with metastable edge terminations can provide a path towards non-invasive interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Filling-enforced obstructed atomic insulators

Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial insulators at the Fermi level. In this paper, we show that, remarkably, for a subset of the topologically trivial insulators, knowing only their electron number and the Wyckoff positions of the atoms we can separate them into two groups: the obstructed atomic insulator (OAI) and the atomic insulator (AI). The interesting group, the OAI, have a center of charge not localized on the atoms. Using the theory of topological quantum chemistry, in this work we first derive the necessary and sufficient conditions for a topologically trivial insulator to be a filling enforced obstructed atomic insulator (feOAI) in the 1651 Shubnikov space groups. Remarkably, the filling enforced criteria enable the identification of obstructed atomic bands without knowing the representations of the band structures. Hence, no calculations are needed for the filling enforced criteria, although they are needed to obtain the band gaps. With the help of the Topological Quantum Chemistry website, we have performed a high-throughput search for feOAIs and have found that 957 ICSD entries (638 unique materials) are paramagnetic feOAIs, among which 738 (475) materials have an indirect gap. The metallic obstructed surface states of feOAIs are also showcased by several material examples. Published by the American Physical Society 2024

Materials Science↗
DOE OSTI2022

Electric control of a canted-antiferromagnetic Chern insulator

Abstract The interplay between band topology and magnetism can give rise to exotic states of matter. For example, magnetically doped topological insulators can realize a Chern insulator that exhibits quantized Hall resistance at zero magnetic field. While prior works have focused on ferromagnetic systems, little is known about band topology and its manipulation in antiferromagnets. Here, we report that MnBi 2 Te 4 is a rare platform for realizing a canted-antiferromagnetic (cAFM) Chern insulator with electrical control. We show that the Chern insulator state with Chern number C = 1 appears as the AFM to canted-AFM phase transition happens. The Chern insulator state is further confirmed by observing the unusual transition of the C = 1 state in the cAFM phase to the C = 2 orbital quantum Hall states in the magnetic field induced ferromagnetic phase. Near the cAFM-AFM phase boundary, we show that the dissipationless chiral edge transport can be toggled on and off by applying an electric field alone. We attribute this switching effect to the electrical field tuning of the exchange gap alignment between the top and bottom surfaces. Our work paves the way for future studies on topological cAFM spintronics and facilitates the development of proof-of-concept Chern insulator devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Bending effects and optical properties of WSe 2 nanoribbons of topological phase

A WSe 2 monolayer of 1T' phase is a large band gap quantum spin Hall insulator, supporting dissipationless charge and spin transports through the topologically protected edge states. Here, in this work, we explore the nanoribbon forms of 1T' phase WSe 2 by first-principles density functional calculations and the many-body perturbation GW and Bethe-Salpeter equation method. We found that the 1T' WSe 2 nanoribbon can show topological edge states with a ribbon width of ~4-6 nm. Those edge bands show crossing through the Fermi level an odd number of times, with one kind of spin-polarization connecting the valence band continuum and conduction band continuum. The topological features of the edge bands hold even under small and medium bending in the nanoribbon, while large bending induces large band splitting, resulting in a topological switch-off in the edge bands. The semiconducting 1T' WSe2 nanoribbon shows a large tunability with bending in optical absorption spectra and exciton states. The lowest-energy exciton is changed from optically dark in the flat nanoribbon to bright in the bent nanoribbons. These properties in the 1T' WSe 2 nanoribbons suggest potential applications in controllable quantum electronics and exciton-based quantum information processes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Signatures of fractional quantum anomalous Hall states in twisted MoTe 2

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism. In the presence of strong electron–electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge. These states could host fractional excitations, including non-Abelian anyons—crucial building blocks for topological quantum computation9. Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe 2 ) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v = −2/3 and v = −3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of ${\sigma }_{xy}=-\,\frac{2}{3}\frac{{e}^{2}}{h}$ and ${\sigma }_{xy}=-\,\frac{3}{5}\frac{{e}^{2}}{h}$ , respectively. Moreover, the v = −1 state exhibits a dispersion corresponding to Chern number −1, consistent with the predicted QAH state. In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe 2 moiré superlattices as a platform for exploring fractional excitations.

Quantum Hall↗
DOE OSTI2021

Cobalt-based magnetic Weyl semimetals with high-thermodynamic stabilities

Abstract Recent experiments identified Co 3 Sn 2 S 2 as the first magnetic Weyl semimetal (MWSM). Using first-principles calculation with a global optimization approach, we explore the structural stabilities and topological electronic properties of cobalt (Co)-based shandite and alloys, Co 3 MM’X 2 (M/M’ = Ge, Sn, Pb, X = S, Se, Te), and identify stable structures with different Weyl phases. Using a tight-binding model, for the first time, we reveal that the physical origin of the nodal lines of a Co-based shandite structure is the interlayer coupling between Co atoms in different Kagome layers, while the number of Weyl points and their types are mainly governed by the interaction between Co and the metal atoms, Sn, Ge, and Pb. The Co 3 SnPbS 2 alloy exhibits two distinguished topological phases, depending on the relative positions of the Sn and Pb atoms: a three-dimensional quantum anomalous Hall metal, and a MWSM phase with anomalous Hall conductivity (~1290 Ω −1 cm −1 ) that is larger than that of Co 2 Sn 2 S 2 . Our work reveals the physical mechanism of the origination of Weyl fermions in Co-based shandite structures and proposes topological quantum states with high thermal stability.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Extracting the Quantum Hall Conductance from a Single Bulk Wave Function

In this work, we propose a new formula that extracts the quantum Hall conductance from a single (2+1)⁢ D gapped wave function. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow, i.e., unitary dynamics generated from the entanglement structure of the wave function. The formula is shown to satisfy all formal properties of the Hall conductance: it is odd under time reversal and reflection, even under charge conjugation, universal and topologically rigid in the thermodynamic limit. Further evidence for relating the formula to the Hall conductance is obtained from conformal field theory arguments. Finally, we numerically check the formula by applying it to a noninteracting Chern band where excellent agreement is obtained.

2-dimensional systems↗
DOE OSTI2021

Building Neutron Scattering Infrastructure in Louisiana for Advanced Materials (Final Report)

The main objective of the Louisiana Consortium for Neutron Scattering (LaCNS) is to build a major neutron scattering infrastructure capable of treating both soft and hard materials. The goal is to create a sustainable effort having the quality, breadth, and depth necessary to produce competitive proposals including collaborative and center type proposals. Our scientific aim is to understand the role of coupling in emergent complex materials and its impact on the structure/property relationship and to explore how to tune the key couplings to guide the design of materials with the desired properties. This naturally includes building a base of users of the Spallation Neutron Source (SNS) and the High Flux Isotope Reactor (HFIR) in Louisiana; to train highly talented graduate and post-doctoral students in synthesis, neutron scattering, and simulation and modeling techniques, thereby helping to produce the next generation of scientist who use neutron scattering techniques as a crucial part of their research. The goal of our hard matter program is to understand the interplay between spin, charge, orbital, and lattice degrees of freedom in carefully selected complex materials. We have made considerable progress on number of complex systems including the oxide Sr3(Ru1-xMnx)2O7 where short-range magnetic ordering with anisotropic spin texture is initiated at the metal-insulator transition that clearly indicates a strong spin-charge coupling. Another critical area is in quantum materials. For example, in the topological semimetal BaMnSb2, we found a 3D canted antiferromagnetic Weyl semimetal with a 2D electronic structure and a nontrivial Berry phase. In addition, in the hexagonal chiral Mn1/3NbS2 system, we found soliton/soliton and soliton/antisoliton domain walls where the application of small fields or small currents can be used to control nanoscopic magnetic domains where the control of domain walls is crucially important for information storage. In addition, chemical transformation investigations were performed on the VISION instrument at Spallation Neutron Source (SNS). The soft matter effort was focused on understanding the role of non-covalent interactions on the structure and dynamics of fluid-based soft matter. One key focus was on sequence-defined (SD) amphiphilic peptoid polymers that allow encoding of molecular interactions and thereby systematic investigations of how charge directs the solution self-assembly of amphiphilic polymers in water. Another important area was on the dynamics of lipids self-assembled into membranes for exploring the permeability and mechanical using both neutron spin echo (NSE) spectroscopy and quasielastic neutron scattering (QENS) to distinguished between viscoelasticity and permeability at the molecular scale. Overall, the LaCNS project was quite successful, generating 145 publications and 245 presentations. Our graduate and post-doctoral students were well trained resulting in positions in national laboratories (Oak Ridge National Laboratory (ORNL), Argonne National Laboratory and Los Alamos National Laboratory), major research universities, and industry. We also developed a uniaxial pressure cell along with ORNL for SNS. A critical goal of this project was to establish a foundation for competing nationally in federally funded research programs. To this end, we were quite successful in generating over twenty-two federally and non-federally funded grants including awards from NSF, DOE, and DOD, and two early career awards. Equally important, we were able to secure a key major piece of instrumentation via a large ARO grant for a state-of-the-art electron microscope.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Topological heavy fermions in magnetic field

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e., its total Chern number, our method—based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group— reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Topological aspects of matters and Langlands program

The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string theory, but it has been little studied in low-energy physics. In the framework of the Langlands program, we present a unified description of the integer and fractional quantum Hall effect and the duality found in the fractal nature of the energy spectrum of two-dimensional Bloch electrons, statistical physics, and quantum computation. The new unified view of existing dualism presented in this paper raises the entirely new question of how each theory of physics is connected as a piece of the Langlands program.

Physics↗
DOE OSTI2021

Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling

We consider a class of quantum field theories and quantum mechanics, which we couple to $\mathbb{Z}$ N topological QFTs, in order to classify non-perturbative effects in the original theory. The $\mathbb{Z}$ N TQFT structure arises naturally from turning on a classical background field for a $\mathbb{Z}$ N 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to $\mathbb{Z}$ N TQFT, the non-perturbative expansion parameter is exp[-S I /N] = exp[-8π 2 /g 2 N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T 3 x $S^1_L$ can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $\mathbb{CP}$ 1 model, and mass gap for arbitrary θ in $\mathbb{CP}$ N-1 , N ≥ 3 on $\mathbb{R}$ 2 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗