It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, in this work, we demonstrate that Hall-like currents can occur in second-order response to ...external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals.
We argue that static nonlinear Hall conductivity can always be represented as a vector in two dimensions and as a pseudotensor in three dimensions independent of its microscopic origin. In a ...single-band model with a constant relaxation rate, this vector or tensor is proportional to the Berry curvature dipole I. Sodemann and L. Fu, Phys. Rev. Lett 115, 216806 (2015). Here, we develop a quantum Boltzmann formalism to second order in electric fields. We find that in addition to the Berry curvature dipole term, there exist additional disorder-mediated corrections to the nonlinear Hall tensor that have the same scaling in the impurity scattering rate. These can be thought of as the nonlinear counterparts to the side-jump and skew-scattering corrections to the Hall conductivity in the linear regime. We illustrate our formalism by computing the different contributions to the nonlinear Hall conductivity of two-dimensional tilted Dirac fermions.
Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 K. A number of recent ...experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators-a composite exciton Fermi liquid-hosts a three dimensional Fermi surface of a neutral fermion, that we name the "composite exciton." We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi liquids and make comparison to experiments in SmB
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We investigate rectified currents in response to oscillating electric fields in systems lacking inversion and time-reversal symmetries. These currents, in second-order perturbation theory, are ...inversely proportional to the relaxation rate, and, therefore, naively diverge in the ideal clean limit. Employing a combination of the nonequilibrium Green function technique and Floquet theory, we show that this is an artifact of perturbation theory, and that there is a well-defined periodic steady state akin to Rabi oscillations leading to finite rectified currents in the limit of weak coupling to a thermal bath. In this Rabi regime the rectified current scales as the square root of the radiation intensity, in contrast with the linear scaling of the perturbative regime, allowing us to readily diagnose it in experiments. More generally, our description provides a smooth interpolation from the ideal periodic Gibbs ensemble describing the Rabi oscillations of a closed system to the perturbative regime of rapid relaxation due to strong coupling to a thermal bath.
A major obstacle to identify exotic quantum phases of matter featuring spin-charge separation above one-dimension is the lack of tailored probes allowing to establish their presence in correlated ...materials. Here we propose an optoelectronic response that could allow to pinpoint the presence of certain spin-charge separated states with emergent neutral gapless fermions in two and three-dimensional materials. We show that even though these states behave like insulators under static electric fields, they can display clear cyclotron resonance peaks in their light absorption spectrum under static magnetic fields, but typically the principal Kohn mode will be missing in comparison to ordinary metals. This distinctive phenomenon could be tested in materials such as triangular lattice organics, three-dimensional mixed valence insulators YbB12 and SmB6, and transition metal dichalcogenides 1T-TaS2 and 1T-TaSe2.
Transitions between topologically distinct electronic states have been predicted in different classes of materials and observed in some. A major goal is the identification of measurable properties ...that directly expose the topological nature of such transitions. Here, we focus on the giant Rashba material bismuth tellurium iodine which exhibits a pressure-driven phase transition between topological and trivial insulators in three dimensions. We demonstrate that this transition, which proceeds through an intermediate Weyl semimetallic state, is accompanied by a giant enhancement of the Berry curvature dipole which can be probed in transport and optoelectronic experiments. From first-principles calculations, we show that the Berry dipole-a vector along the polar axis of this material-has opposite orientations in the trivial and topological insulating phases and peaks at the insulator-to-Weyl critical points, at which the nonlinear Hall conductivity can increase by over 2 orders of magnitude.
We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static (ω → 0) limit for wavevectors q in the regime ...\({l}_{\text{mfp}}^{-1}\ll q\ll {p}_{\text{F}}\), where l mfp is the mean free path and p F is the Fermi momentum. This value is \(({e}^{2}/h){\mathcal{R}}_{\text{FS}}/q\) in two dimensions (2D), where \({\mathcal{R}}_{\text{FS}}\) measures the local radius of curvature of the Fermi surface (FS) in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon FS have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy (NV) center in diamond, placed at a distance z above of the 2D metal or spin liquid. Specifically the magnetic noise is given by \(C\omega {\mathcal{P}}_{\text{FS}}/z\), where \({\mathcal{P}}_{\text{FS}}\) is the perimeter of the FS in momentum space and C is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the FS and are independent of kinematic details of the quasi-particles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the FS of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon FS in two-dimensional systems. We estimate that this universal regime is within reach of current NV center spectroscopic techniques for several spinon FS candidate materials.
SO(5) symmetry in the quantum Hall effect in graphene Wu, Fengcheng; Sodemann, Inti; Araki, Yasufumi ...
Physical review. B, Condensed matter and materials physics,
12/2014, Letnik:
90, Številka:
23
Journal Article
Recenzirano
Odprti dostop
Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions, ...which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants g sub(z) and gbottom. In this paper, we demonstrate that when g sub(z) = -gbottom, an exact SO(5) symmetry survives which unifies the Neel spin order parameter of the antiferromagnetic state and the XY valley order parameter of the Kekule distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at v = 0 to an ideal SO(5) symmetric quantum Hall state remains an open experimental question. We illustrate the physics associated with this SO(5) symmetry by studying the multiplet structure and collective dynamics of filling factor v = 0 quantum Hall states based on exact-diagonalization and low-energy effective theory approaches. This allows to illustrate how manifestations of the SO(5) symmetry would survive even when it is weakly broken.
We study broken symmetry states at integer Landau-level fillings in multivalley quantum Hall systems whose low-energy dispersions are anisotropic. When the Fermi surface of individual pockets lacks ...twofold rotational symmetry, like in bismuth (111) Feldman et al. , Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth, Science 354, 316 (2016) and in Sn1−xPbxSe (001) Dziawa et al., Topological Crystalline Insulator States in Pb1−xSnxSe , Nat. Mater. 11, 1023 (2012) surfaces, interactions tend to drive the formation of quantum Hall ferroelectric states. We demonstrate that the dipole moment in these states has an intimate relation to the Fermi surface geometry of the parent metal. In quantum Hall nematic states, like those arising in AlAs quantum wells, we demonstrate the existence of unusually robust Skyrmion quasiparticles.
We study Z_{2} topologically ordered states enriched by translational symmetry by employing a recently developed two-dimensional (2D) bosonization approach that implements an exact Z_{2} charge-flux ...attachment in the lattice. Such states can display “weak symmetry breaking” of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is “broken” by its anyon quasiparticles, in the sense that its action maps them into a different superselection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of one-dimensional Kitaev wires, leading to the amusing property that there is no local operator that can transport the π-flux quasiparticle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand in hand with other previously identified peculiar features such as ground-state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain Z_{2} topologically ordered states. Moreover, by extending the Z_{2} charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the Z×(Z_{2})^{3} classification of 2D BdG Hamiltonians (class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserve translational symmetry.
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