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At least 253 records · Page 14
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 OSTI2023

Torus geometry eigenfunctions of an interacting multi-Landau-level Hamiltonian

A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al., Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact many-body eigenfunctions on the disk not just for quasiholes but for all charged and neutral excitations of the entire Jain sequence filling fractions. We extend this to geometries without full rotational symmetry, namely, the torus and cylinder geometries, and present their spectra. Exact diagonalization of the interaction on the torus produces the low-energy spectra at filling fraction v = n/(2⁢pn + 1) that is identical, up to a topological (2⁢pn + 1)-fold multiplicity, to that of the integer quantum Hall spectra at v = n, for the incompressible state as well as all excitations. While the ansatz eigenfunctions in the disk geometry cannot be generalized to closed geometries such as torus or sphere, we show how to extend them to cylinder geometry. Meanwhile, we show eigenfunctions for charged excitations at filling fractions between 1/3 and 2/5 can be written on the torus and the spherical geometries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Hall viscosity of the composite-fermion Fermi seas for fermions and bosons

The Hall viscosity has been proposed as a topological property of incompressible fractional quantum Hall states and can be evaluated as Berry curvature. This paper reports on the Hall viscosities of composite-fermion Fermi seas at ν = 1/m, where m is even for fermions and odd for bosons. A well-defined value for the Hall viscosity is not obtained by viewing the 1/m composite-fermion Fermi seas as the n → ∞ limit of the Jain ν = n/(nm ± 1) states, whose Hall viscosities (±n + m)ℏρ/4 (ρ is the two-dimensional density) approach ±∞ in the limit n → ∞. A direct calculation shows that the Hall viscosities of the composite-fermion Fermi sea states are finite and also relatively stable with system size variation, although they are not topologically quantized in the entire τ space. Here, I find that the ν = 1/2 composite-fermion Fermi sea wave function for a square torus yields a Hall viscosity that is expected from particle-hole symmetry and is also consistent with the orbital spin of 1/2 for Dirac composite fermions. I compare my numerical results with some theoretical conjectures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Superconductivity in a topological lattice model with strong repulsion

The highly tunable nature of synthetic quantum materials-both in the solid-state and cold atom contexts-invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce the "double Hofstadter"model, a minimal 2D lattice model that incorporates exactly these features: Time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. Further, at the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the quantum spin Hall insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be p-wave-reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Density dependence of the excitation gaps in an undoped Si/SiGe double-quantum-well heterostructure

In this work, we report low-temperature magneto-transport measurements of an undoped Si/SiGe asymmetric double quantum well heterostructure. The density in both layers is tuned independently utilizing top and bottom gates, allowing the investigation of quantum wells at both imbalanced and matched densities. Integer quantum Hall states at total filling factor v T =1 and v T =2 are observed in both density regimes, and the evolution of their excitation gaps is reported as a function of the density. The v T =1 gap evolution departs from the behavior generally observed for valley splitting in the single layer regime. Furthermore, by comparing the v T =2 gap to the single particle tunneling energy, Δ SAS , obtained from Schrödinger–Poisson (SP) simulations, evidence for the onset of spontaneous interlayer coherence is observed for a relative filling fraction imbalance smaller than ~50%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A unified realization of electrical quantities from the quantum International System of Units

In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm’s law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development of such a system remains challenging. Here, in this study, we report a unified realization of the volt, ohm and ampere by integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) in a single cryostat. Our system has a quantum voltage output that ranges from 0.24 mV to 6.5 mV with combined relative uncertainties down to 3 μV V −1 . The QAHR provides a realization of the ohm at zero magnetic field with uncertainties near 1 μΩ Ω −1 . We use the QAHR to convert a longitudinal current to a quantized Hall voltage and then directly compare that against the PJVS to realize the ampere. We determine currents in the range of 9.33–252 nA, and our lowest uncertainty is 4.3 μA A −1 at 83.9 nA. For other current values, a systematic error that ranges from −10 μA A −1 to −30 μA A −1 is present due to the imperfect isolation of the PJVS microwave bias.

Quantum metrology↗
DOE OSTI2024

Fingerprints of composite fermion Lambda levels in scanning tunneling microscopy

A composite fermion (CF) is a topological quasiparticle that emerges from a nonperturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to noninteracting fermions that form Landau levels in a magnetic field, CFs can fill analogous “Lambda” levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes the low-energy properties of CFs, we show that high-energy features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the noninteracting CF paradigm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Unconventional Fractional Phases in Multiband Vortexable Systems

We study topological flat bands with distinct features that deviate from conventional Landau level behavior. We show that even in the ideal quantum geometry limit, moiré flat band systems can exhibit physical phenomena fundamentally different from Landau levels without lattices. In particular, we find new fractional quantum Hall states emerging from multiband vortexable systems, where multiple exactly flat bands appear at the Fermi energy. While the set of bands as a whole exhibits ideal quantum geometry, individual bands separately lose vortexability, and thus making them very different from a stack of Landau levels. At certain filling fractions, we find fractional states whose Hall conductivity deviates from the filling factor. Through careful numerical and analytical studies, we rule out all known mechanisms—such as fractional quantum Hall crystals or separate filling of trivial and topological bands—as possible explanations. Leveraging the exact solvability of vortexable systems, we use analytic Bloch wave functions to uncover the origin of these new fractional states, which arises from the commensurability between the moiré unit cell and the magnetic unit cell of an emergent effective magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Composite anyons on a torus

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same “effective” integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Lastly, we obtain from these wave functions, both analytically and numerically, various topological quantities, such as ground-state degeneracy, the Chern number, and the Hall viscosity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Deformed Fredkin model for the ν = 5 / 2 Moore-Read state on thin cylinders

We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲ 7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on an IBM quantum processor. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Unconventional Hall response in the quantum limit of HfTe 5

Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe 5 , adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Direct observation of a magnetic-field-induced Wigner crystal

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown evidence for Wigner crystals (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Furthermore, analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Composite fermion mass: Experimental measurements in ultrahigh quality two-dimensional electron systems

Composite fermions (CFs), exotic quasiparticles formed by pairing an electron and an even number of magnetic flux quanta, emerge at high magnetic fields in an interacting electron system, and can explain phenomena such as the fractional quantum Hall state (FQHS) and other many-body phases. CFs possess an effective mass (m CF ) whose magnitude is inversely related to the most fundamental property of a FQHS, namely its energy gap. Here we present here experimental measurements of m CF in ultrahigh quality two-dimensional electron systems confined to GaAs quantum wells of varying thickness. An advantage of measuring m CF over gap measurements is that mass values are insensitive to disorder and are therefore ideal for comparison with theoretical calculations, especially for high-order FQHS. Our data reveal that m CF increases with increasing well width, reflecting a decrease in the energy gap as the electron layer becomes thicker and the in-plane Coulomb energy softens. Comparing our measured masses with available theoretical results, we find significant quantitative discrepancies, highlighting that more rigorous and accurate calculations are needed to explain the experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Experimental Characterization and Modeling of High Hole Mobility GeSn Quantum Wells: The Role of Alloy Disorder Scattering

Understanding mechanisms influencing electrical transport in material systems not only provides a scientific explanation for observed behavior but also offers insight into ways to enhance transport in devices. This study reports experimental hole mobility of 8 x 10 4 cm 2 V -1 s -1 in a Ge 0.92 Sn 0.08 , the highest recorded mobility for the GeSn system. A study of the material's quality is presented using structural and electrical characterization techniques, with transport data being supported by simulations using an extensive modeling framework. Quantum Hall measurements further indicate the material's high quality and potential spintronic applications, with extracted values of 0.0689$m$ 0 and 13.6 for the effective mass and effective g‐factor, respectively. It is observed that transport is limited by alloy disorder scattering at cryogenic temperatures. A comparative study between the presented structure and similar quantum well heterostructures revealed that the difference in hole mobilities is captured by a disparity in the reduced nominal alloy disorder scattering potential (Δ U alloy = 0.8 eV), that is lower than the value of a fully random alloy (Δ U alloy = 1.4–1.7 eV) potential. The difference in Δ U alloy suggests that heterostructures with similar geometries and alloy compositions can have different alloy disorder scattering, implying that an underlying mechanism, such as short‐range order, may be responsible and warrants further investigation.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

Signatures of fractional charges via anyon–trions in twisted MoTe 2

Fractionalization of the electron charge e is one of the most striking phenomena arising from strong electron–electron interactions. A celebrated example is the emergence of anyons with fractional charges in fractional quantum Hall effect (FQHE) states. Recently, zero-field fractional Chern insulators (FCIs), lattice analogues of the FQHE states that form without Landau levels, have been realized. FCIs provide a unique platform to investigate anyons, yet their detection remains a challenge. Here we report the observation of anyon–trions, a new type of excitonic complex formed by binding a trion with a fractional charge in twisted MoTe 2 bilayers. Photoluminescence spectroscopy of quantum-confined excitons reveals emergent peaks that appear only within slightly doped FCI states. The new spectral features are red-shifted relative to the trions in undoped FCIs, but share the same electric field, temperature and magnetic field dependence. These observations suggest their origin as trions binding with elementary quasi-particles, that is, anyon–trions. Crucially, the ratio of binding energies between the anyon–trions in the −2/3 and −3/5 FCI states matches the expected fractional charge ratio of e/3 to e/5. This provides strong evidence for fractional charges in FCI—an essential property of anyons. Our results address a fundamental question in FCI physics and establish trion spectroscopy as a powerful probe of fractionally charged excitations, complementary to transport- and tunnelling-based approaches.

Quantum Hall↗
DOE OSTI2021

Exact Landau Level Description of Geometry and Interaction in a Flatband

Flatbands appear in many condensed matter systems, including the two-dimensional electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study metric. The influence of the band geometry on electron-electron interaction is difficult to understand analytically because the geometry is in general nonuniform in momentum space. In this work, we study the topological flatband of Chern number C = 1 with a momentum-dependent but positive definite Berry curvature that fluctuates in sync with Fubini-Study metric. We derive an exact correspondence between such ideal flatbands and Landau levels and show that the band geometry fluctuation gives rise to a new type of interaction in the corresponding Landau levels that depends on the center of mass of two particles. We characterize such interactions by generalizing the usual Haldane pseudopotentials. This mapping gives exact zero-energy ground states for short-ranged repulsive generalized pseudopotentials in flatbands, in analogy to fractional quantum Hall systems. Driving the center-of-mass interactions beyond the repulsive regime leads to a dramatic reconstruction of the ground states towards gapless phases. The generalized pseudopotential could be a useful basis for future numerical studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Possible Spin-Triplet Excitonic Insulator in the Ultraquantum Limit of HfTe 5

More than 50 years ago, excitonic insulators formed by the pairing of electrons and holes due to Coulomb interactions were first predicted [A. N. Kozlov and L. A. Maksimov, Sov. J. Exp. Theor. Phys. 21, 790 (1965); L. V. Keldysh and Y. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965); D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967)]. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moiré superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together, and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet excitonic insulator in the ultra-quantum limit of a three-dimensional topological material HfTe 5 . We observe that the spin-polarized zeroth Landau bands dispersing along the field direction cross each other beyond a characteristic magnetic field in HfTe 5 , forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about 2⁢5⁢0 μ⁢eV when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10–72 T). In conclusion, our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.

36 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↗