Fractional Quantum Hall States of the A Phase in the Second Landau Level.

A proposal of the existence of an Anomalous phase (A phase) [Das et al., Phys. Rev. Lett. 131, 056202 (2023)PRLTAO0031-900710.1103/PhysRevLett.131.056202] at the experimental range of moderate Landau-level-mixing strength has recently been made for the 5/2 state. We here report that the gapped A phase is generic to the sequence of spin-polarized fractional quantum Hall states with filling fractions ν=n/(nm-1) and ν=1-n/(nm-1), (n≥1,m≥3), that exhausts almost all the observed states and also predicts some states in the second Landau level for GaAs systems. Our proposed trial wave functions for all these states have remarkably high overlaps with the corresponding exact ground states and can support non-Abelian quasiparticle excitations with charge e/[2(nm-1)]. By analyzing edge modes, we predict experimentally verifiable thermal Hall conductance 2.5(π^{2}k_{B}^{2}T/3h) for all the states in these sequences.

Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength.

A successful probing of the neutral Majorana mode in recent thermal Hall conductivity measurements opines in favor of the particle-hole symmetric Pfaffian (PH-Pf) topological order, contrasting the theoretical predictions of Pfaffian or anti-Pfaffian phases. Here we report a reentrant anomalous quantized phase that is found to be gapped in the thermodynamic limit, distinct from the conventional Pfaffian, anti-Pfaffian, or PH-Pf phases, at an intermediate strength of Landau level mixing. Our proposed wave function consistent with the PH-Pf shift in spherical geometry rightly captures the topological order of this phase, as its overlap with the exact ground state is very high and it reproduces low-lying entanglement spectra. A unique topological order, irrespective of the flux shifts, found for this phase, possibly corroborates the experimentally found topological order.

Superfluid density in conventional superconductors: from clean to strongly disordered.

The highly convergent form of superfluid density in disordered conventional superconductors available in the literature and independently obtained by us following the approach of an earlier paper (Mandal and Ramakrishnan 2020Phys. Rev.B102024514) has been reformulated to separate out the generally used so-called 'dirty-limit' term and an additional term. We use this new expression for making an extensive comparison with previously published experimental data and show that the former, generally used, term isnotsufficient for analyzing these results. We point out that consequently, there is a large regime (disordered superconductors with moderate to no disorder) where theoretical predictions need to be confronted with experiment.

Skyrmions at vanishingly small Dzyaloshinskii-Moriya interaction or zero magnetic field.

By introducing biquadratic together with usual bilinear ferromagnetic nearest neighbor exchange interaction in a square lattice, we find that the energy of the spin-wave mode is minimized at a finite wavevector for a vanishingly small Dzyaloshinskii-Moriya interaction (DMI), supporting a ground state with spin-spiral structure whose pitch length is unusually short as found in some of the experiments. Apart from reproducing the magnetic structures that can be obtained in a canonical model with nearest neighbor exchange interaction only, a numerical simulation of this model with further introduction of magnetic anisotropy and magnetic field predicts many other magnetic structures some of which are already observed in the experiments. Among many observed structures, nanoscale skyrmion even at vanishingly small DMI is found for the first time in a model. The model provides the nanoscale skyrmions of unit topological charge at zero magnetic field as well. We obtain phase diagrams for all the magnetic structures predicted in the model.

Length-scale independent skyrmion and meron Hall angles.

Motivated by the recent observation (Zeissler et al 2020 Nature Commun. 11 428) of enigmatic radius-independent skyrmion Hall angle in chiral magnets, we derive skyrmion Hall angle based on the recent solution of skyrmions characterized by the sole length scale determined with the Dzyaloshinskii-Moriya interaction strength and applied magnetic field. We find that the skyrmion Hall angle is independent of input current density and the length-scale which determines the radius of a skyrmion. This is corroborated with the single length-scale dependent skyrmion profile which is the solution of the Euler equation of polar angle representing magnetization. Although the magnitude of Hall angle may change with the change of profile (shape) of the skyrmion, it remains unchanged for a particular profile. With the application of tunable current along mutually perpendicular directions, this property enables us to propose an experimental setup by which the transverse motion of a skyrmion can be restricted so that the skyrmion can only traverse longitudinally. We further find the length-scale and input-current density independent Hall angles for merons where their transverse motion will be opposite depending on whether the spin at their centers are up or down, in agreement with an experiment.

Generalization of Laughlin's theory for the fractional quantum Hall effect.

Motivated by the structure of the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor [Formula: see text] (m odd), I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory, without a priori assumption of the presence of CFs. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for 1/m state. Each of these wave functions is interpreted as expelling an electron into a different Hilbert subspace from the original Hilbert space of the Laughlin condensate while still maintaining its correlation (although changed) with the electrons in the condensate such that the expelled electron behaves as a CF with respect to the electrons in the condensate. With this interpretation, I show that the ground state wavefunctions for general states at filling fractions [Formula: see text], respectively, can be constructed as coherent superposition of n coupled Laughlin condensates and their 'conjugates', formed at different Hilbert subspaces. The corresponding wave functions, specially surprising for [Formula: see text] sequence of states, are identical with those proposed in the theory of noninteracting CFs. The states which were considered as fractional quantum Hall effect of interacting CFs, can also be treated in the same footing as for the prominent sequences of states describing as the coupled condensates among which one is a non-Laughlin condensate in a different Hilbert subspace. Further, I predict that the half filling of the lowest Landau level is a quantum critical point for phase transition between two topologically distinct phases each corresponding to a family of states: one consists of large number of coupled Laughlin condensates of filling factor 1/3 and the other corresponds to large number of coupled conjugate Laughlin condensates of filling factor 1, which may be distinguished, respectively, by the absence and presence of upstream edge modes.

Anomalously low magnetoroton energies of the unconventional fractional quantum Hall States of composite fermions.

We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8 at very low wave vectors with anomalously low energies which do not have any analog to the conventional fractional quantum Hall states. Rather slow decay of the oscillations of the pair-correlation functions in these states is responsible for the low-energy magnetorotons. This is a manifestation of the distinct topology predicted previously for these fractional quantum Hall effect states. Experimental consequences of our theory are also discussed.

Enigmatic 4/11 state: a prototype for unconventional fractional quantum Hall effect.

The origin of the fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that the FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, the FQHE here results from the suppression of pairs with a relative angular momentum of three rather than one, confirming the exotic mechanism proposed by Wójs, Yi, and Quinn [Phys. Rev. B 69, 205322 (2004)]. We predict that the 4/11 state reported a decade ago by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] is a conventional partially spin polarized FQHE of composite fermions, and we estimate the Zeeman energy where a phase transition into the unconventional fully spin polarized state will occur.

Amplitude fluctuations driven by the density of electron pairs within nanosize granular structures inside strongly disordered superconductors: evidence for a shell-like effect.

Motivated by the recent observation of the shell effect in a nanoscale pure superconductor by Bose et al. [Nat. Mater. 9, 550 (2010)], we explore the possible shell-like effect in a strongly disordered superconductor as it is known to produce nanosize superconducting puddles (SPs). We find a remarkable change in the texture of the pairing amplitudes that is responsible for forming the SP, upon monotonic tuning of the average electron density, , and keeping the disorder landscape unaltered. Both the spatially averaged pairing amplitude and the quasiparticle excitation gap oscillate with . This oscillation is due to a rapid change in the low-lying quasiparticle energy spectra and thereby a change in the shapes and positions of the SPs. We establish a correlation between the formation of SPs and the shell-like effect. The experimental consequences of our theory are also discussed.

Possible anti-Pfaffian pairing of composite fermions at ν = 3/8.

We predict that an incompressible fractional quantum Hall state is likely to form at ν = 3/8 as a result of a chiral p-wave pairing of fully spin polarized composite fermions carrying four quantized vortices, and that the pairing is of the anti-Pfaffian kind. Experimental ramifications include quasiparticles with non-Abelian braid statistics and upstream neutral edge modes.

Higher-energy composite fermion levels in the fractional quantum Hall effect.

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect.

Manifestation of helical edge states as zero bias magneto-tunneling-conductance peaks in noncentrosymmetric superconductors.

Helical edge states exist in the mixed spin singlet and triplet phase of a noncentrosymmetric superconductor (NCSS) when the pair amplitude (PA) in the negative helicity band, Δ(-), is smaller than the PA in the positive helicity band, Δ(+), i.e., when the PA in the triplet component is more than the same in the singlet component. We numerically determine energies of these edge states as a function of γ = Δ(-)/Δ(+). The presence of these edge states is reflected in the tunneling process from a normal metal to an NCSS across a bias energy eV. (i) Angle resolved spin conductance (SC) obeying the symmetry g(s)(φ) = -g(s)(-φ) shows peaks when the bias energy equals the available quasiparticle edge state energy provided [Formula: see text]. (ii) The total SC, G(s), is zero but modulates with eV for finite magnetic field H. (iii) The zero bias peaks of G(s) and total charge conductance, G(c), at finite H split into two at finite eV for moderate H. (iv) At zero bias, G(c) and G(s) increase with H and show peaks at |H|∼γH(0), where H(0) is a characteristic field.

Two-dimensional electron system in high magnetic fields: Wigner crystal versus composite-fermion liquid.

The two-dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (<1%) in the energy due to the weak interaction between composite fermions can cause a fundamental change in the nature of the ground state, thus providing insight into the puzzling experimental results.

Relevance of inter-composite-fermion interaction to the edge Tomonaga-Luttinger liquid.

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of noninteracting composite fermions. However, the weak residual interaction between composite fermions is found to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one-dimensional theory.