arXiv subjects

Johannes Mitscherling

Publications and source records attributed to Johannes Mitscherling.

17 recordsLinked to original sources

arXiv2026

Orbital Wigner functions and quantum transport in multiband systems

Traditional theories of electron transport in crystals are based on the Boltzmann equation and do not capture physics arising from quantum coherence. We introduce a transport formalism based on orbital Wigner functions, which accurately captures quantum coherent physics in multiband fermionic systems. We illustrate the power of this approach compared with traditional semiclassical transport theory by testing it numerically against microscopic simulations of one-dimensional, noninteracting, two-band systems---the simplest systems capable of exhibiting interorbital coherence. We show that orbital Wigner functions accurately capture strongly nonequilibrium features of electron dynamics that lie beyond conventional Boltzmann theory, such as the ballistic transport of a relative phase between microscopic orbitals and topological Thouless pumping of charge, both at nonzero temperature and away from the adiabatic limit. Our approach is motivated in part by modern ultracold atom experiments that can prepare and measure far-from-equilibrium charge transport and phase coherence in multiband fermionic systems, calling for correspondingly precise theories of transport. The quantitative accuracy exhibited by our approach, together with its capacity to capture nontrivial physics even at the ballistic scale, establishes orbital Wigner functions as an ideal starting point for developing a fully systematic theory of transport in crystals.

cond-mat.quant-gas↗

arXiv2026

Tracking real-space quantum state breathing through Floquet-projector geometry

Periodic driving of spatially periodic quantum systems generates band structures that are absent in static crystals. We present a quantum geometric theory to characterize the Floquet-Bloch states at stroboscopic times and during micromotion on equal footing. Our framework builds upon time-evolved Floquet projectors that connect static quantum geometry, micromotion-operator geometry, and Floquet topology. To illustrate the formalism, we introduce the Floquet-projector quantum metric, which we employ to characterize the real-space breathing of localized states in a driven chiral-symmetric integrable spin chain. The Floquet-projector quantum metric, integrated over the Brillouin zone, captures the oscillatory variance during micromotion and, at symmetry-selected times, is bounded below by Floquet topological invariants. We further describe how the Floquet projector geometry enables a systematic investigation of micromotion dynamics in periodically driven lattice systems.

quant-ph↗

arXiv2026

Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect

We decompose the intrinsic second-order nonlinear Hall effect (NLHE) of a generic multiband system into its quantum-geometric contributions within a fully quantum-mechanical, projector-based formalism. By expanding the nonlinear conductivity in powers of the quasiparticle lifetime $τ$, we recover the established Berry curvature dipole at order $τ$ and clarify discrepancies in previous literature concerning the (interband) quantum metric dipole (or Berry curvature polarizability) contribution at order $τ^0\textrm{.}$ Crucially, our method reveals an additional contribution at order $τ^0$, determined by the {\it intraband} quantum metric dipole (intraQMD), arising from additional virtual interband transitions captured within the fully quantum-mechanical treatment. The intraQMD contribution is generically nonzero in systems with broken time-reversal symmetry and can be distinguished from other geometric contributions by symmetry. Analytical results for low-energy models of topological band crossings, which are hotspots of quantum geometry, demonstrate how band topology influences each contribution. In particular, the intraQMD contribution is especially large in gapped Dirac cones in antiferromagnets. Through a comprehensive symmetry classification of all magnetic space groups, we identify several candidate materials that are expected to exhibit large intrinsic NLHE, including the topological antiferromagnets Yb$_3$Pt$_4$, CuMnAs, and CoNb$_3$S$_6$, as well as the nodal-plane material MnNb$_3$S$_6$.

cond-mat.mes-hall↗

arXiv2026

Microscopic origin of $p$-wave magnetism

$P$-, $f$-, or $h$-wave antialtermagnets yield large non-relativistic spin splitting with out-of-plane spin polarization in momentum space perpendicular to the coplanar non-collinear local magnetic moments. We provide a microscopic explanation of this unconventional spin polarization by linking it to a previously overlooked site-compensated spin density that orders antiparallel when projected onto opposite momenta. We verify this result both by model derivation of the out-of-plane momentum-space spin polarization being proportional to the direct-space cross product of the coplanar non-collinear spin order, as well as by ab initio calculations in the material candidate CeNiAsO. By providing a general classification and analytic expression for the spin polarization of all spinful two-site tight-binding Hamiltonians, we reveal the momentum-resolved spin polarization as a probe of the Bloch-state geometry arising from spin-site coupling. Furthermore, our approach allows for geometric distinction between ferro-, alter-, and antialtermagnets. Our results provide a quantitative guidance for quantized out-of-plane momentum-space spin polarization and large spin splitting, and construction principles for antialtermagnets.

cond-mat.mes-hall↗

arXiv2025

Orbital magnetization from parallel transport of Bloch states

Quantum geometric formulations of linear and nonlinear responses can be constructed from a single building block in the form of a gauge-invariant interband transition operator. Here, we identify a second building block for quantum geometry: a band-resolved adiabatic connection operator that captures the noncommutativity between band projectors and their momentum derivatives. The band-resolved adiabatic connection operator, first introduced in the theory of adiabatic driving, serves as a generalized angular momentum within the state manifold of single bands, and we employ it to reformulate expressions for the band-resolved orbital magnetic moment. This form provides a complementary geometric interpretation alongside the multiband separation between energetic- and quantum-state properties by the two-state Berry curvature. Our formalism allows us to present formulas valid for both nondegenerate and degenerate bands, thereby removing the limitations of the common Bloch-state formula. We illustrate our theory by calculating a large orbital magnetization emerging without spin-orbit coupling in a spin-compensated, noncoplanar anomalous Hall magnet with degenerate bands.

cond-mat.mes-hall↗

arXiv2025

Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals

The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry emerge in properties linking multiple bands, such as optical responses. In the companion work [arXiv:2409.16358], we identified novel multi-state geometrical invariants using an explicitly gauge-invariant formalism based on projection operators, which we used to clarify the relation between the shift current and the theory of electronic polarization among other advancements for second-order non-linear optics. Here, we provide considerably more detail on the projector formalism and the geometrical invariants arising in the vicinity of a specific value of crystal momentum. We combine the introduction to multi-state quantum geometry with broadly relevant algebraic relationships and detailed example calculations, enabling extensions toward future applications to topological and geometrical properties of insulators and metals.

cond-mat.str-el↗

arXiv2025

The multi-state geometry of shift current and polarization

The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state geometry is necessary to explain properties involving Bloch states of multiple bands, such as optical transitions. To this end, we employ quantum state projectors to develop an explicitly gauge-invariant formalism and demonstrate its power with applications to non-linear optics and the theory of electronic polarization. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization, clarifies the treatment of band degeneracies, and reveals its decomposition into the sum of the skewness of the occupied states and intrinsically multi-state geometry. The projector approach is applied to calculate non-linear optical properties of transition metal dichalcogenides (TMDs) layers, using previously calculated minimal tight-binding models, and demonstrated analytically on a three-band generalization of the Rice-Mele chain to elucidate the different contributions. We close with comments on further applications of the projector operator approach to multi-state geometry.

cond-mat.str-el↗

arXiv2025

Drude weight of an interacting flat-band metal

Flatband systems form a new class of materials that challenge the conventional wisdom of transport. The intrinsically strong electronic correlations combined with the vanishing kinetic energy scale suggest a sensitive dependence of transport properties on the flat band states and make interacting flat bands promising candidates for exotic quantum transport. Utilizing the Drude weight, we investigate the low-frequency spectral properties of the electrical conductivity within a controlled analytic treatment of the many-body response at temperatures above the bandwidth and the interaction strength and below the bandgap. Focusing on this new transport regime, we demonstrate the potential of a quantum geometric approach for interacting systems and intermediate temperatures. The derived spectral weight yields unexplored four-point geometric contributions unrelated to the quantum metric, which questions the previously proposed projection methods. For long-ranged interactions, we show that the low-frequency spectral weight reduces to the variance of the Berry curvature.

cond-mat.str-el↗

arXiv2025

Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level

Two common difficulties in the design of topological quantum materials are that the desired features lie too far from the Fermi level and are spread over a too-large energy range. Doping-induced states at the Fermi level provide a solution, where nontrivial topological properties are enforced by the doping-reduced symmetry. To show this, we consider a regular placement of dopants in a lattice of space group (SG) 176 ($P6\text{}_3/m$), which reduces the symmetry to SG 143 ($P3$). Our two- and four-band models feature double Weyl points, Chern bands, Van Hove singularities, nontrivial multiband quantum geometry due to mixed orbital character, and singular flat bands. We relate these features to density-functional theory (DFT) calculations for dopant and vacancy bands of lead apatite Pb$_{10}($PO$_4)_6$O and Pb$_{10}($PO$_4)_6($OH$)_2$, the van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$, the semiconductor SiC, and the 2D dichalcogenide MoS$_2$.

cond-mat.mes-hall↗

arXiv2022

Nontrivial quantum geometry of degenerate flat bands

The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and nondegenerate bands can be naturally described via the geometry of different Grassmannian manifolds, specific to the band degeneracies. Contrary to the (Abelian) Berry curvature, the quantum metric of a degenerate band resulting from the collapse of a collection of bands is not simply the sum of the individual quantum metrics. We provide a physical interpretation of this phenomenon in terms of transition dipole matrix elements between two bands. By considering a toy model, we show that the quantum metric gets enhanced, reduced, or remains unaffected depending on which bands collapse. The dc longitudinal conductivity and the superfluid stiffness are known to be proportional to the quantum metric for flat-band systems, which makes them suitable candidates for the observation of this phenomenon.

cond-mat.mes-hall↗

arXiv2022

Bound on resistivity in flat-band materials due to the quantum metric

The quantum metric is a central quantity of band theory but has so far not been related to many response coefficients due to its nonclassical origin. However, within a newly developed Kubo formalism for fast relaxation, the decomposition of the dc electrical conductivity into both classical (intraband) and quantum (interband) contributions recently revealed that the interband part is proportional to the quantum metric. Here, we show that interband effects due to the quantum metric can be significantly enhanced and even dominate the conductivity for semimetals at charge neutrality and for systems with highly quenched bandwidth. This is true in particular for topological flat-band materials of nonzero Chern number, where for intermediate relaxation rates an upper bound exists for the resistivity due to the common geometrical origin of quantum metric and Berry curvature. We suggest to search for these effects in highly tunable rhombohedral trilayer graphene flakes.

cond-mat.mes-hall↗

arXiv2021

Non-Hermitian band topology from momentum-dependent relaxation in two-dimensional metals with spiral magnetism

We study the emergence of non-Hermitian band topology in a two-dimensional metal with planar spiral magnetism due to a momentum-dependent relaxation rate. A sufficiently strong momentum dependence of the relaxation rate leads to exceptional points in the Brillouin zone, where the Hamiltonian is nondiagonalizable. The exceptional points appear in pairs with opposite topological charges and are connected by arc-shaped branch cuts. We show that exceptional points inside hole and electron pockets, which are generally present in a spiral magnetic state with a small magnetic gap, can cause a drastic change of the Fermi surface topology by merging those pockets at isolated points in the Brillouin zone. We derive simple rules for the evolution of the eigenstates under semiclassical motion through these crossing points, which yield geometric phases depending only on the Fermi surface topology. The spectral function observed in photoemission exhibits Fermi arcs. Its momentum dependence is smooth -- despite of the nonanalyticities in the complex quasiparticle band structure.

cond-mat.str-el↗

arXiv2021

Electrical Conductivity in Quantum Materials

In recent years, there is an increasing interest in transport phenomena that are fundamentally linked to the presence of multiple bands. In this thesis, we develop, discuss, and apply a theory of the electrical conductivity that includes interband contributions within a microscopic approach. We derive formulas of the conductivity tensor $σ^{αβ}$ and the Hall conductivity tensor $σ^{αβη}_\text{H}$ for a general two-band model. This minimal model of a multiband system captures a broad variety of very different physical phenomena ranging from spiral spin density waves to Chern insulators. We motivate and derive a unique and physically transparent decomposition of the conductivity tensors by identifying intra- and interband contributions as well as symmetric and antisymmetric contributions under the exchange of the current and the electric field directions. Using these criteria, we find that the symmetric interband contribution of $σ^{αβ}$ is connected to the quantum metric, whereas the antisymmetric part involves the Berry curvature and captures the intrinsic anomalous Hall effect. We include a phenomenological relaxation rate $Γ$ of arbitrary size to study the relevance of the interband contributions systematically. Our conductivity formulas are applied to models and experiments of recent interest. We identify typical scaling behaviors of the conductivities with respect to $Γ$ in agreement with theoretical and experimental results. Recent experiments on hole-doped cuprates under very high magnetic fields show a drastic change of the Hall number when entering the pseudogap regime, which is shown to be consistent with the onset of spiral magnetic order. We analyze the experimental results with our formulas of the longitudinal and the Hall conductivity and clarify the validity of the broadly used Boltzmann-like conductivity formulas.

cond-mat.str-el↗

arXiv2020

Longitudinal and anomalous Hall conductivity of a general two-band model

We derive and analyze the longitudinal and the anomalous Hall conductivity for a general momentum-block-diagonal two-band model. This model captures a broad spectrum of physically very different systems including Néel antiferromagnetic and spiral spin density waves as well as models that involve spin-orbit interaction and are known to show topological properties. We present a complete microscopic derivation for finite temperature and constant scattering rate $Γ$ that is diagonal and equal, but arbitrarily large for both bands. We identify two criteria that allow for a unique and physically motivated decomposition of the conductivities. On the one hand, we distinguish intraband and interband contributions that are defined by the involved quasiparticle spectral functions. On the other hand, we distinguish symmetric and antisymmetric contributions that are defined by the symmetry under the exchange of the current and the electric field directions. The (symmetric) intraband contributions generalize the formula of standard Boltzmann transport theory, which is valid only in the clean limit (small $Γ$), whereas the interband contributions capture interband coherence effects beyond independent quasiparticles. We show that the symmetric interband contribution is a correction only present for finite $Γ$ and is controlled by the quantum metric. The antisymmetric interband contributions generalize the formula of the anomalous Hall conductivity in terms of the Berry curvature to finite $Γ$. We study the clean (small $Γ$) and dirty (large $Γ$) limit analytically. The connection between the presented derivation and the Bastin and Streda formalism is given. We apply our results to a Chern insulator, a ferromagnetic multi-d-orbital, and a spiral spin density wave model.

cond-mat.str-el↗

arXiv2020

Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model

We show that antiferromagnetic spin-density wave order in the two-dimensional Hubbard model yields a drop of the charge carrier density as observed in recent transport measurements for cuprate superconductors in high magnetic fields upon entering the pseudogap regime. The amplitude and the (generally incommensurate) wave vector of the spin-density wave is obtained from dynamical mean-field theory (DMFT). An extrapolation of the finite temperature results to zero temperature yields an approximately linear doping dependence of the magnetic gap $Δ(p) \propto p^*-p$ in a broad doping range below the critical doping $p^*$. The magnetic order leads to a Fermi surface reconstruction with electron and hole pockets, where electron pockets exist only in a restricted doping range below $p^*$. DC charge transport properties are computed by combining the renormalized band structure as obtained from the DMFT with a doping-independent phenomenological scattering rate. A pronounced drop of the longitudinal conductivity and the Hall number in a narrow doping range below $p^*$ is obtained.

cond-mat.str-el↗

arXiv2018

Longitudinal conductivity and Hall coefficient in two-dimensional metals with spiral magnetic order

We compute the longitudinal dc conductivity and the Hall conductivity in a two-dimensional metal with spiral magnetic order. Scattering processes are modeled by a momentum-independent relaxation rate $Γ$. We derive expressions for the conductivities, which are valid for arbitrary values of $Γ$. Both intraband and interband contributions are fully taken into account. For small $Γ$, the ratio of interband and intraband contributions is of order $Γ^2$. In the limit $Γ\to 0$, the conductivity formulas assume a simple quasiparticle form, as derived by Voruganti et. al. [Phys. Rev. B 45, 13945 (1992)]. Using the complete expressions, we can show that relaxation rates in the regime of recent transport experiments for cuprate superconductors in high magnetic fields are sufficiently small to justify the application of these simplified formulas. The longitudinal conductivity exhibits a pronounced nematicity in the spiral state. The drop of the Hall number as a function of doping observed recently in several cuprate compounds can be described with a suitable phenomenological ansatz for the magnetic order parameter.

cond-mat.str-el↗

arXiv2018

Non-linear conductance in mesoscopic weakly disordered wires -- Interaction and magnetic field asymmetry

We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_φ\ll L$, where $L_φ$ is the phase coherence length, we get $\mathcal{G}\sim(L_φ/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_φ/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_φ\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_φ/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_φ/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

cond-mat.mes-hall↗