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The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi_{2}Se_{3} and Bi_{2}Te_{3}. Topological insulators feature gapless surface states and, moreover, magnetic doping and resultant ferromagnetic ordering break time-reversal symmetry to realize quantum anomalous Hall and Chern insulators. Here, we focus on the bulk and investigate the mutual coupling of electronic and magnetic properties of Dirac electrons. Without carrier doping, spiral magnetic orders cause a ferroelectric polarization through the spin-orbit coupling. In a doped metallic state, the anisotropic magnetoresistance arises without uniform magnetization. We find that electric current induces uniform magnetization and conversely an oscillating magnetic order induces electric current. Our model provides a coherent and unified description of all those phenomena. The mutual control of electric and magnetic properties demonstrates implementations of antiferromagnetic spintronics. We also discuss the stoichiometric magnetic topological insulator MnBi_{2}Te_{4}.
RESUMEN
Graphene-based samples have shown a plethora of exotic characteristics and these properties may help the realization of a new generation of fast electronic devices. However, graphene's centrosymmetry prohibits second-order electronic transport. Here, we show giant second-order nonlinear transports in graphene moiré superlattices at zero magnetic field, both longitudinal and transverse to the applied current direction. High carrier mobility and inversion symmetry breaking by hexagonal boron nitride lead to nonlinear conductivities five orders of magnitude larger than those in WTe2. The nonlinear conductivity strongly depends on the gate voltage as well as on the stacking configuration, with a giant enhancement originating from the moiré bands. Longitudinal nonlinear conductivity cannot originate from Berry curvature dipoles. Our theoretical modelling highlights skew scattering of chiral Bloch electrons as the physical origin. With these results, we demonstrate nonlinear charge transport due to valley-contrasting chirality, which constitutes an alternative means to induce second-order transports in van der Waals heterostructures. Our approach is promising for applications in frequency-doubling and energy harvesting via rectification.
RESUMEN
The nonlinear Hall effect due to Berry curvature dipole (BCD) induces frequency doubling, which was recently observed in time-reversal-invariant materials. Here we report novel electric frequency doubling in the absence of BCD on a surface of the topological insulator Bi2Se3 under zero magnetic field. We observe that the frequency-doubling voltage transverse to the applied ac current shows a threefold rotational symmetry, whereas it forbids BCD. One of the mechanisms compatible with the symmetry is skew scattering, arising from the inherent chirality of the topological surface state. We introduce the Berry curvature triple, a high-order moment of the Berry curvature, to explain skew scattering under the threefold rotational symmetry. Our work paves the way to obtain a giant second-order nonlinear electric effect in high mobility quantum materials, as the skew scattering surpasses other mechanisms in the clean limit.
RESUMEN
When a strongly correlated system supports well-defined quasiparticles, it allows for an elegant one-body effective description within the non-Hermitian topological theory. While the microscopic many-body Hamiltonian of a closed system remains Hermitian, the one-body quasiparticle Hamiltonian is non-Hermitian due to the finite quasiparticle lifetime. We use such a non-Hermitian description in the heavy-fermion two-dimensional systems with the momentum-dependent hybridization to reveal a fascinating phenomenon which can be directly probed by the spectroscopic measurements, the bulk "Fermi arcs." Starting from a simple two-band model, we first combine the phenomenological approach with the perturbation theory to show the existence of the Fermi arcs and reveal their connection to the topological exceptional points, special points in the Brillouin zone where the Hamiltonian is nondiagonalizable. The appearance of such points necessarily requires that the electrons belonging to different orbitals have different lifetimes. This requirement is naturally satisfied in the heavy-fermion systems, where the itinerant c electrons experience much weaker interaction than the localized f electrons. We then utilize the dynamical mean field theory to numerically calculate the spectral function and confirm our findings. We show that the concept of the exceptional points in the non-Hermitian quasiparticle Hamiltonians is a powerful tool for predicting new phenomena in strongly correlated electron systems.
RESUMEN
Rectification is a process that converts electromagnetic fields into a direct current. Such a process underlies a wide range of technologies such as wireless communication, wireless charging, energy harvesting, and infrared detection. Existing rectifiers are mostly based on semiconductor diodes, with limited applicability to small-voltage or high-frequency inputs. Here, we present an alternative approach to current rectification that uses the intrinsic electronic properties of quantum crystals without using semiconductor junctions. We identify a previously unknown mechanism for rectification from skew scattering due to the inherent chirality of itinerant electrons in time-reversal invariant but inversion-breaking materials. Our calculations reveal large, tunable rectification effects in graphene multilayers and transition metal dichalcogenides. Our work demonstrates the possibility of realizing high-frequency rectifiers by rational material design and quantum wave function engineering.
RESUMEN
The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space. We introduce a new type of van Hove singularity in two dimensions, resulting from high-order saddle points and exhibiting power-law divergent density of states. We show that high-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. Correlation effects from high-order van Hove singularity near Fermi level are also discussed.
RESUMEN
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum l=+1 are energetically favored for filling ν=1/2+1/2 and 1/4+1/4. The degeneracy between states with ±l is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.
RESUMEN
Weyl fermions with tilted linear dispersions characterized by several different velocities appear in some systems including the quasi-two-dimensional organic semiconductor α-(BEDT-TTF)_{2}I_{3} and three-dimensional WTe_{2}. The Coulomb interaction between electrons modifies the velocities in an essential way in the low-energy limit, where the logarithmic corrections dominate. Taking into account the coupling to both the transverse and longitudinal electromagnetic fields, we derive the renormalization group equations for the velocities of the tilted Weyl fermions in two dimensions, and found that they increase as the energy decreases and eventually hit the speed of light c to result in the Cherenkov radiation. Especially, the system restores the isotropic Weyl cone even when the bare Weyl cone is strongly tilted and the velocity of electrons becomes negative in certain directions.
RESUMEN
We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as ZâE^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Zâ(|logE|)^{-b} with universal b=3/2.
RESUMEN
We construct a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable metallic phase between the normal and topological insulators, it is shown that a direct topological phase transition between two insulators is also possible when an accidental band crossing occurs along directions with high crystalline symmetry. At the quantum critical point, the energy dispersion becomes quadratic along one direction while the dispersions along the other two orthogonal directions are linear, which manifests the zero chirality of the band touching point. Because of the anisotropic dispersion at quantum critical point, various thermodynamic and transport properties show unusual temperature dependence and anisotropic behaviors.