Quantum Hall Research Articles

Photon-assisted extrinsic Weyl orbits and three-dimensional quantum Hall effect in surface-doped topological Dirac semimetals

Photon-assisted extrinsic Weyl orbits and three-dimensional quantum Hall effect in surface-doped topological Dirac semimetals

Aharonov-Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene.

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a fractional charge and show fractional statistics as they interchange positions. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, fractional statistics is most notable through quantum interference. Here we study fractional statistics in a bilayer graphene Fabry-Pérot interferometer. We tune the interferometer from the Coulomb-dominated regime to the Aharonov-Bohm regime, both for integer and fractional quantum Hall states. Focusing on the fractional quantum Hall state with a filling factor ν = 1/3, we follow the evolution of the Aharonov-Bohm interference of quasiparticles while varying the magnetic flux through an interference loop and the charge density within the loop independently. When their combined variation is such that the Landau filling remains 1/3, the charge density in the loop varies continuously. We then observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as expected for quasiparticles of one-third of the electron charge. Yet, when the combined variation leads to discrete events of quasiparticle addition or removal, phase jumps emerge and alter the phase evolution. Notably, across all cases with discrete and continuous charge variation, the average phase consistently increases by 2π with each addition of one electron to the loop, as expected for quasiparticles, obeying fractional statistics.

Anticipation of Large Intrinsic Spin Hall Conductivity in Mercury Chalcogenides: A First‐Principles Study

AbstractThe report carried out detailed first‐principle calculations of Mercury chalcogenides (HgX; X = Te, Se and S) using density functional theory, verifying the bulk band inversion property with different exchange‐correlation functionals. The Wannier function method is used to study the non‐trivial topology of HgX systems, spin Berry curvature, and intrinsic spin Hall conductivity. Quantized intrinsic spin Hall conductivity is observed in the HgX systems. Large intrinsic spin Hall conductivity is found in the systems due to a strong spin Berry curvature accumulation near the triply degenerate points in the Brillouin zone. Calculation shows that the intrinsic spin Hall conductivity for all three HgX systems has stable plateaus, with Mercury Telluride having a maximum width of up to 1.05 eV. The maximum intrinsic spin Hall conductivity of –931/e () is obtained in mercury sulfide, higher than the reported values for spin Hall conductivity and the plateau width in typical topological insulators such as , , and as well as in transition metal pnictides (TaX, X = As, P and N) and transition metal iridates.

Unusual Quasiparticles and Tunneling Conductance in Quantum Point Contacts in ν=2/3 Fractional Quantum Hall Systems.

Understanding topological matter in the fractional quantum Hall (FQH) effect requires identifying the nature of edge state quasiparticles. FQH edge state at the filling factor ν=2/3 in the spin-polarized and unpolarized phases is represented by the two modes of composite fermions (CF) with the parallel or opposite spins described by the chiral Luttinger liquids. Tunneling through a quantum point contact (QPC) between different or similar spin phases is solved exactly. With the increase of the applied voltage, the QPC conductance grows from zero and saturates at e^{2}/2h while a weak electron tunneling between the edge modes with the same spin transforms into a backscattering carried by the charge q=e/2 quasiparticles. These unusual quasiparticles and conductance plateau emerge when one or two CF spin-polarized modes in the QPC tunnel into a single mode. We propose experiments on the applied voltage and temperature dependence of the QPC conductance and noise that can shed light on the nature of edge states and FQH transport.

Noncommutative gauge symmetry in the fractional quantum Hall effect

We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}μ in such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}0 of the probe field is coupled to the projected density operator, the spatial components A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}i are best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call “baby noncommutative” gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms. By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.

Topological Thermal Hall Conductance of Even-Denominator Fractional States.

The even-denominator fractional quantum Hall (FQH) states ν=5/2 and ν=7/2 have been long predicted to host non-Abelian quasiparticles. Their present energy-carrying neutral modes are hidden from customary conductance measurements and thus motivate thermal transport measurements, which are sensitive to all energy-carrying modes. While past "two-terminal" thermal conductance (k_{2t}T) measurements already proved the non-Abelian nature of the ν=5/2 FQH state, they might have been prone to a lack of thermal equilibration among the counterpropagating edge modes. Here, we report a novel thermal Hall conductance measurement of the ν=5/2 and ν=7/2 states, being insensitive to equilibration among edge modes. We verify the state's non-Abelian nature, with both states supporting a single upstream Majorana edge mode (hence, a particle-hole Pfaffian order). While current numerical works predict a different topological order, this contribution should motivate further theoretical work.

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 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. Published by the American Physical Society 2024

Topological properties of C4zT-symmetric semimetals

Two-dimensional topological semimetals are typically characterized by the vorticity of gapless points, and can be classified according to the band representations. However, the topological properties involving the distribution of the Berry curvature in the entire Brillouin zone are often overlooked. In this study, we investigate a two-band two-dimensional topological semimetal protected by C4zT magnetic symmetry, exhibiting a two-fold band degeneracy at the Γ(0, 0) and M(π, π) points. Due to the presence of C4zT symmetry, the Brillouin zone is divided into two patches characterized by half-quantized Berry curvature fluxes with opposite signs. In multi-band case, the half-quantization deviates, indicating the fragile nature. The semimetal presents counter-propagating half-edge channels, accompanied by power-law decaying and oscillating edge currents. The band topology leads to unconventional Landau levels featuring anisotropic edge modes. Each massless Dirac cone, associated with the half-quantized Berry curvature flux, exhibits an integer quantum Hall conductance. Additionally, we calculate the local orbital magnetization with open boundary conditions in both the x and y directions. This reveals isolated magnetization islands, highlighting an experimentally observable magnetic phenomenon in this topological semimetal.

Half-quantum mirror Hall effect

We predict a half-quantized mirror Hall effect induced by mirror symmetry in strong topological insulator films. These films are known to host a pair of gapless Dirac cones in the first Brillouin zone associated with surface electrons. Our findings reveal that mirror symmetry assigns a unique mirror parity to each Dirac cone, resulting in a half-quantized Hall conductance of ±e22h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm \\! \\frac{{e}^{2}}{2h}$$\\end{document} for each cone. Despite the total electrical Hall conductance being null due to time-reversal invariance, the difference in the Hall conductance between the two cones yields a quantized Hall conductance of e2h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{e}^{2}}{h}$$\\end{document} for the difference in mirror currents. The effect of helical edge mirror current - a crucial feature of this quantum effect - may, in principle, be determined by means of electrical measurements. The half-quantum mirror Hall effect reveals a type of mirror-symmetry induced quantum anomaly in a time-reversal invariant lattice system, giving rise to a topological metallic state of matter with time-reversal invariance.

A novel method to solve analytically the non-linear Poisson equation in the inversion layer of a MOSFET

Abstract Despite the enormous importance that the metal oxide semiconductors (MOS) and the field effect transistors (MOSFETs) have in the actual semiconductor technology, the task of finding the analytical solution of the Poisson equation in the inversion layer was not fully accomplished for more than half a century. It is a well-known fact that due to the non-linear nature of this equation, the attempts to solve it got stuck after the first integration. Nevertheless, experimental and applied researchers found ways to characterize, control, and develop MOSFET devices based on approximate models, and numerical calculations. Here I present a new method to analytically solve the nonlinear Poisson equation, in principle, for any charge distribution in the inversion layer of a MOS, and for the charge density of the original Shockley model, in particular. To this purpose, a physical argument related to the charge and field energies in the transient population-inversion process is introduced and a new nonlinear but solvable second order differential equation is obtained, whose solution also solves the original Poisson equation. The analytical results presented here allow us to derive explicit expressions for the electrical potential distribution and, very importantly, for the charge distribution, the inversion layer width and the effective impurity concentration in the depletion layer. The quantum Hall effect and other physical phenomena were discovered in the inversion layer of a MOS. The Hall effect was explained under the assumption that the charge distribution is a two-dimensional electron gas, we show here however that the 2D limit is reached only at high gate voltages. When applied to MOSFET structures, we obtain new expressions for the drain currents in the inversion and depletion layers, as functions of the impurity concentration and the gate voltage for single and double-gate MOSFETs, and we give an insight for multi-gate MOSFETs.

Conflux of spin Nernst and spin Hall effect in ZnCu2SnSe4 Topological Insulator

A comprehensive exploration of the intriguing phenomena known as the spin Nernst effect (SNE) and the spin Hall effect (SHE) within the context of nonmagnetic strong topological insulatorZnCu2SnSe4, has been carried out employing first-principles calculations. Our theoretical calculations unveil significantly large intrinsic spin Nernst conductivity (SNC) and spin Hall conductivity (SHC) in the bulk topological insulatorZnCu2SnSe4. Delving deeper into the intricacies of our findings, we elucidate how the inverted band order in the topological materials drastically influences the spin Berry curvature, consequently exerting a profound impact on SHC and SNC. Detailed analyses reveal that the contribution from the bulk to the generation of pure spin current in a topological insulator is comparable to that of a surface. This underscores the potential role of topological insulators in the development of spin-switching devices. We present compelling evidence thatZnCu2SnSe4holds immense promise as an optimal candidate for the generation of pure spin currents, achieved through the application of both thermal gradients and electric fields. This, in turn, opens up exciting avenues for its utilization in the realms of spin-caloritronics, spin-orbitronics, and spintronics.

Quantum Anomalous Hall Crystal at Fractional Filling of Moiré Superlattices.

We predict the emergence of a state of matter with intertwined ferromagnetism, charge order, and topology in fractionally filled moiré superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling (ν=1/2) at larger twist angles of the twisted semiconductor bilayer tMoTe_{2}.

Non-equilibrium excited-state fractionally quantized Hall effects observed via current bias spectroscopy

Studies of fractional quantum Hall effects (FQHE) across various two-dimensional electronic systems (2DES) have helped to establish the equilibrium FQHE many-body ground states with fractionally charged excitations and composite particles in condensed matter. Then, the question arises whether an FQHE system driven to non-equilibrium can approach a different stationary state from the known equilibrium FQHE states. To investigate this question, we examine FQHE over filling factors, ν, 2 ≥ ν ≥ 1 under non-equilibrium finite bias conditions realized with a supplementary dc-current bias, IDC, in high mobility GaAs/AlGaAs devices. Here, we show that all observable canonical equilibrium FQHE resistance minima at ∣IDC∣ = 0 undergo bimodal splitting vs. IDC, yielding branch-pairs and diamond shapes in color plots of the diagonal resistance, as canonical FQHE are replaced, with increasing IDC, by excited-state fractionally quantized Hall effects at branch intersections. A tunneling model serves to interpret the results.

Quantum Hall resistance standards based on epitaxial graphene with p-type conductivity

In the last decade, quantum resistance metrology has benefited from the application of graphene as the base material for the fabrication of quantum Hall (QH) resistance standards since it allows for the realization of the resistance unit ohm in the revised International System of Units under relaxed experimental conditions. Here, we present a detailed magnetotransport investigation of p-type epitaxial graphene, which was doped by the molecular acceptor F4-TCNQ. High-accuracy measurements of the QH resistance show an excellent quantization and a reproduction of the nominal value, the half of the von Klitzing constant RK/2, within 2 nΩ/Ω. It underlines the universality of the QH effect and shows that p-type epitaxial graphene can also serve as the basis for future resistance standards for operation at relaxed experimental conditions. For the p-type devices, the onset of the QH plateau is observed at about 1 T higher magnetic fields, which can be attributed to an additional disorder or a non-symmetric charge transfer mechanism in the QH regime.

Probing Site-Resolved Current in Strongly Interacting Superconducting Circuit Lattices.

Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerful tools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of insitu particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore nonequilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.

Strongly coupled edge states in a graphene quantum Hall interferometer

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into 2e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{2}}}{{\\boldsymbol{e}}}$$\\end{document} quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between interference phase jumps and AB frequency doubling, unveiling how strong repulsive interaction between edge channels leads to the apparent pairing phenomena. By tuning electron density in-situ from filling factor ν<2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}} \\, < \\, {{\\boldsymbol{2}}}$$\\end{document} to ν>7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}} \\, > \\, {{\\boldsymbol{7}}}$$\\end{document}, we tune the interaction strength and observe periodic interference phase jumps leading to AB frequency doubling. Our observations demonstrate that the combination of repulsive interaction between the spin-split ν=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}}={{\\boldsymbol{2}}}$$\\end{document} edge channels and charge quantization is sufficient to explain the frequency doubling, through a near-perfect charge screening between the localized and extended edge channels. Our results show that interferometers are sensitive probes of microscopic interactions and enable future experiments studying correlated electrons in 1D channels using density-tunable graphene.

Unraveling the dynamics of magnetization in topological insulator-ferromagnet heterostructures via spin-orbit torque

Spin–orbit coupling is a relativistic effect coupling the orbital angular momentum with the spin, which determines the physical properties of condensed matter. For instance, the spin–orbit coupling strongly influences spin dynamics, opening the possibility for promising applications. The topological insulator–ferromagnet heterostructure is a typical example exhibiting spin dynamics driven by current-induced spin–orbit torque. Recent observations of the sign flip of Hall conductivity imply that the spin–orbit torque is strong enough to flip magnetization within this heterostructure. Motivated by this, our study elucidates the conditions governing spin flips by studying the magnetization dynamics. We establish that the interplay between spin-anisotropy and spin–orbit torque plays a crucial role in the magnetization dynamics. Furthermore, we categorize various modes of magnetization dynamics, constructing a comprehensive phase diagram across distinct energy scales, damping constants, and applied frequencies. We also consider the effect of a magnetic field on the magnetization dynamics. This research not only offers insights into controlling spin direction but also charts a new pathway to the practical application of spin–orbit coupled systems.

Dissipative frequency converter: From Lindblad dynamics to non-Hermitian topology

A topological frequency converter represents a dynamical counterpart of the integer quantum Hall effect, where a two-level system enacts a quantized time-averaged power transfer between two driving modes of incommensurate frequency. Here, we investigate as to what extent temporal coherence in the quantum dynamics of the two-level system is important for the topological quantization of the converter. To this end, we consider dissipative channels corresponding to spontaneous decay and dephasing in the instantaneous eigenbasis of the Hamiltonian as well as spontaneous decay in a fixed basis. The dissipation is modelled using both a full Lindblad and an effective non-Hermitian (NH) Hamiltonian description. For all three dissipation channels, we find a transition from the unperturbed dynamics to a quantum watchdog effect, which destroys any power transfer in the strong coupling limit. This is striking because the watchdog effect leads to perfectly adiabatic dynamics in the instantaneous eigenbasis, at first glance similar to the unperturbed case. Furthermore, it is found that dephasing immediately leads to an exponential decay of the power transfer in time due to loss of polarization in the mixed quantum state. Finally, we discuss the appearance in the effective NH trajectory description of nonadiabatic processes, which are suppressed in the full Lindblad dynamics. Published by the American Physical Society 2024

Magnetic field-dependent thermopower: Insights into spin and quantum interactions

This study explores the impact of external magnetic fields on thermoelectric properties, focusing on the interplay of spin and quantum effects. Using gadolinium (Gd) as a case study, we observed anomalous magneto-thermopower trends, with a reduction in thermopower at ∼35 K and an enhancement at TC ≈ 293 K under high magnetic fields. Comprehensive temperature and field-dependent measurements, including specific heat capacity, magnetic susceptibility, and Hall effect, were performed to uncover the underlying mechanisms. We derived a relation for the total thermopower of an uncompensated ferromagnetic metal and calculated multi-band carrier characteristics, such as concentration and mobility, using the maximum entropy principle. Our findings reveal a ∼70 % suppression of the magnetic contribution to specific heat capacity under a 12 T field and a positive magnon-drag contribution to the total thermopower. Field-dependent Hall measurements indicate that the anomalous Hall effect is dominated by intrinsic contributions from Berry curvature. Additionally, transverse magnetoresistance data suggest anisotropic Fermi surfaces, domain movement, suppression of spin-flip effects, and Fermi surface modifications. First-principles calculations based on Density Functional Theory (DFT) further support these findings. These calculations reveal significant Berry curvature contributions, leading to an anomalous Hall conductivity of approximately 1260 S/cm at the Fermi level. The enhancement of thermopower near TC is primarily attributed to the suppression of magnon-drag and the imbalance in carrier mobility and relaxation times, driven by spin and quantum effects. These combined effects result in a ∼50 % increase in thermopower and a ∼150 % improvement in zT at 12 T. The notable peak in zT at cryogenic temperatures highlights a potential pathway for designing efficient thermoelectric materials for cryogenic cooling applications. Our results demonstrate the significance of field-dependent spin and quantum effects in enhancing thermoelectric performance, offering new directions for thermoelectric research and material design.

Molecular beam epitaxy growth and doping modulation of topological semimetal NiTe2

In this study, high-quality thin films of the topological semimetal phase NiTe2 were prepared using the molecular beam epitaxy technique, confirmed through x-ray diffraction with pronounced Laue oscillations. Electrical transport experiments reveal that thick films have properties similar to bulk materials. By employing co-deposition, we introduced either magnetic or non-magnetic elements during the growth of thinner films, significantly altering their electrical properties. Notably, the magnetic element Cr induces long-range ferromagnetic ordering, leading to the observation of a significant anomalous Hall effect in NiTe2 thin films. The Hall conductivity remains nearly constant well below the Curie temperature, indicating the correlation with the intrinsic topological nature of the band structure. Theoretical first principles band calculations support the generation of the Weyl semimetal state in the material through magnetic doping. These findings pave the way for exploring more magnetic Weyl semimetals and related low-dimensional quantum devices based on topological semimetals.