Nonlinear Hall Effect In Topological Quantum States

Hall effects,as paradigmatic phenomena,have inspired tremendous studies of topological quantum states,which significantly deepened our understanding of symmetry and topology in condensed matter physics.Among these Hall effects,the timereversal symmetry(TRS)is essential to be broken to produce an electric Hall voltage by an external magnetic field or internal magnetic moments.However,the nonlinear Hall effect,by theoretical predictions and experimental observations in recent years,shows that Hall-like currents can emerge in second-order response to external electric fields in a wide class of materials with the TRS but without the inversion symmetry.Such nonlinear Hall effect originates from the Berry curvature dipole of electronic band structures.In other words,it may be realized in topological quantum states with nontrivial topological electronic structures,especially in Weyl semimetals.Thus,we investigate the nonlinear Hall effect in nonmagnetic topological material HgTe with ideal Weyl points and antiferromagnetic(AFM)topological half-Heusler materials.The thesis is organized as follows:In the first two chapters,we introduce the background of topological quantum states and the main research methods.We first introduce the basic concepts and novel characteristics of topological insulators,topological crystalline insulators,Weyl semimetals,Dirac semimetals,and nodal line semimetals.And then we focus on Berry curvature,which is of significance for understanding topological quantum states and nonlinear Hall effect.Chapter two introduces the k·p method and the theory of invariants.In chapter three,we demonstrate the relevant theories and experiments of the nonlinear Hall effect.In the theories,we give an elaborate derivation of the nonlinear Hall coefficient in term of Berry curvature dipole tensor,and discuss the constraints on the nonlinear Hall effect imposed by the crystal point symmetries.In the experiments,we illustrate the former observation of nonlinear Hall effect of bilayer WTe2.In chapter four,we focus on strain-engineered nonlinear Hall effect in HgTe.Considering different topological states including ideal Weyl phase with no coexisting trivial band at the Fermi level emerge in HgTe induced by in-plane strains,we suggest strained HgTe as a promising candidate material to realize the nonlinear Hall effect.Based on numerical calculations of the Berry curvature dipole,we find that the magnitude of nonlinear Hall effect can be simply engineered by in-plane strain.In chapter five,we extend the nonlinear Hall effect to a wide class of magnetic materials with combined time-reversal and fractional translation symmetry.While TRS is broken,the nonlinear Hall effect can still present due to the combined symmetry.We illustrate that the AFM half-Heusler materials reach the symmetry requirements and possess various topological quantum states including Dirac,Weyl,nodal line and triplepoint semimetals.We firstly investigate the forms of the Berry curvature dipole tensor induced by different AFM configurations and corresponding symmetries,and then we find that different AFM orders can be identified by nonlinear Hall response behaviors.Based on the effective model,we explicitly calculate the Berry curvature dipole,which are found to be vanishingly small for the triple-point semimetal phase,and large in the Weyl semimetal phase.We conclude and give some future prospects in chapter six.