Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems

Abstract

In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects, so are their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is purely intrinsic, and the second-order thermal Hall noise has both intrinsic and extrinsic contributions. In particular, the intrinsic part of the second-order thermal Hall noise is a manifestation of the quantum fluctuation of quantum geometric tensor, which widely exists as long as Berry curvature is nonzero. These intrinsic thermal Hall noises provide direct measurable means to band geometric information, including Berry curvature related quantities and quantum fluctuation of quantum geometric tensor.

References in corpus (66)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Shot Noise in Mesoscopic Conductors
• Universal Intrinsic Spin-Hall Effect
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Experimental realization of a topological crystalline insulator in SnTe
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Nonlinear Hall Effects
• Geometry and non-adiabatic response in quantum and classical systems
• Time-reversal-symmetry-broken quantum spin Hall effect
• Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Room temperature nonlinear Hall effect and wireless RF rectification in Weyl semimetal TaIrTe4
• Berry curvature memory through electrically driven stacking transitions
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
• Strain-engineering of Berry curvature dipole and valley magnetization in monolayer MoS${}_2$
• Berry curvature dipole current in transition metal dichalcogenides family
• Measuring quantized circular dichroism in ultracold topological matter
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Conductance and noise signatures of Majorana backscattering
• Quantum frequency doubling in the topological insulator Bi2Se3
• Zero-magnetic-field Hall effects in artificially corrugated bilayer graphene
• Extracting the quantum metric tensor through periodic driving
• How to Measure the Quantum Geometry of Bloch Bands
• Nonlinear anomalous Hall effect for Néel vector detection
• Berry Curvature Dipole in Strained Graphene: a Fermi Surface Warping Effect
• Giant $c$-axis nonlinear anomalous Hall effect in T${}_d$-MoTe${}_2$ and WTe${}_2$
• Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Topological currents in black phosphorus with broken inversion symmetry
• Signatures of Majorana Zero Modes in Spin-Resolved Current Correlations
• Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter
• Revealing tensor monopoles through quantum-metric measurements
• Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
• A system for measuring auto- and cross-correlation of current noise at low temperatures
• Berry Curvature and Quantum Metric in $N$-band systems -- an Eigenprojector Approach
• Fluctuation-dissipation relations far from equilibrium
• Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
• Magnus Hall Effect
• Nonlinear I-V Characteristics of a Mesoscopic Conductor
• Electronic heat flow and thermal shot noise in quantum circuits
• Giant shot noise from Majorana zero modes in topological trijunctions
• Shot Noise of a Temperature-Biased Tunnel Junction
• Generalized Wilson Loop Method for Nonlinear Light-Matter Interaction
• Shot noise of spin current
• Shot noise of the edge transport in the inverted band HgTe quantum wells
• Shot Noise Induced by Nonequilibrium Spin Accumulation
• General bounds on electronic shot noise in the absence of currents
• Shot noise in the edge states of 2D topological insulators
• Current noise from a magnetic moment in a helical edge
• Identifying Majorana bound states by tunneling shot-noise tomography
• Noise signatures for determining chiral Majorana fermion modes
• Fluctuation dissipation relations for strongly correlated out-of-equilibrium circuits
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry
• Unrestricted electron bunching at the helical edge
• Quantum third-order nonlinear Hall effect of a four-terminal device with time-reversal symmetry
• Finite frequency backscattering current noise at a helical edge
• Edge States in Lateral p-n Junctions in Inverted Band HgTe Quantum Wells
• Universal Current Correlations Induced by the Majorana and Fermionic Andreev Bound States

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• Tunable moiré materials for probing Berry physics and topology
• Instantaneous response and quantum geometry of insulators
• Local geometry and quantum geometric tensor of mixed states
• Intrinsic gyrotropic magnetic current from Zeeman quantum geometry
• Reentrant topological phases and spin density wave induced by 1D moiré potentials
• Reentrant topological phases and entanglement scalings in moiré-modulated extended Su-Schrieffer-Heeger Model
• Quantum Geometric Tensor for Mixed States Based on the Covariant Derivative
• Orbital anomalous Hall effect in the few-layer Weyl semimetal TaIrTe4
• Quantum nonlinear ac transport theory at low frequency
• Classification of spin Hall effect in two-dimensional systems
• Linear thermal noise induced by Berry curvature dipole in a four-terminal system
• Distinct topological excitonic insulators characterized by quantum geometry