arXiv subjects

Johannes Hofmann

Publications and source records attributed to Johannes Hofmann.

At least 19 recordsLinked to original sources

arXiv2026

Magnetotransport of tomographic electrons in a Corbino disk

In clean electron gases at low-to-moderate temperatures, odd-parity modes of the Fermi surface are anomalously long-lived due to Pauli blocking, giving rise to ``tomographic transport'' that is not captured by a hydrodynamic model. Here we show that tomographic flow in a Corbino disk induces an extended boundary layer near electrodes with superballistic transport and enhanced slip velocity, which leads to a parametric enhancement of the quadratic magnetoresistance coefficient. The enhancement depends explicitly on the electrode curvature, allowing its strength to be controlled by the device geometry. The magnetoresistance coefficient reveals three distinct regimes as a function of magnetic field: a tomographic regime at weak fields; a hydrodynamic regime at intermediate fields, reached when the cyclotron radius becomes comparable to a large odd-mode mean free path; and a conventional Ohmic regime at large fields, reached when the cyclotron radius becomes comparable to the short even-mode mean free path. The tomographic regime is characterized by an anomalous dependence of the magnetoresistance on temperature and density, which may account for recent experimentally observed anomalous scaling of the electron viscosity.

cond-mat.mes-hall↗

arXiv2026

Tomographic collective modes in a magnetic field

Two-dimensional Fermi liquids at low temperatures have been theoretically established to exhibit an odd-even effect in the collective quasiparticle relaxation rates where even-parity deformations of the Fermi surface decay at a much faster rate than odd-parity ones. A predicted consequence of this effect is a new tomographic transport regime that mixes hydrodynamic and collisionless transport. In the presence of a magnetic field, however, the tomographic regime is expected to evolve towards conventional transport regimes as soon as the cyclotron radius becomes smaller than the dominant odd-parity mean-free path. In this work, we examine this transition from the point of view of collective modes, using a numerically exact solution of the linearized Boltzmann equation within a generalized relaxation time approximation for the odd-parity and even-parity modes. In the absence of a magnetic field, the transverse conductivity exhibits two diffusive tomographic collective modes, and we find that at a critical magnetic field one of these two tomographic modes disappears. Which tomographic mode persists depends on the Landau parameters, and becomes increasingly dominated by hydrodynamic modes at high fields. We corroborate our analysis using a variational approach for the Fermi surface deformation that captures the angular structure of the deformation and the critical magnetic field strength. The collective modes discussed here can in principle be observed by examining the damping of longitudinal and transverse current responses in finite magnetic fields.

cond-mat.str-el↗

arXiv2026

Odd relaxation in three-dimensional Fermi liquids

Recent theoretical works predict a hierarchy of long-lived, non-hydrodynamic modes in two-dimensional Fermi liquids arising from the feature$-$supposedly unique to two dimensions$-$that relaxation by head-on scattering is not efficient in the presence of Pauli blocking. This leads to a parity-based separation of scattering rates, with odd-parity modes relaxing much more slowly than even-parity ones. In this work, we establish that a similar effect exists in isotropic three-dimensional (3D) Fermi liquids, even though relaxation does not proceed solely by head-on scattering. We show that while the relaxation rates of even and odd modes in 3D share the same leading-order $\sim T^2$ low-temperature scaling typical of Fermi liquids, their magnitudes differ, with odd-parity modes relaxing more slowly than even ones for a broad class of interactions. We find a relative difference between odd-parity and even-parity relaxation rates as large as $40\%$ just by Pauli blocking alone, with a strong additional dependence on the scattering potential, such that the odd-even staggering is further enhanced by interactions that favor large-angle scattering. We identify signatures of these odd-parity relaxation rates in the static transverse conductivity as well as the transverse collective mode structure. Our results establish the unexpected existence of a tomographic like regime in higher-dimensional Fermi liquids and suggest experimental probes via transport measurements.

cond-mat.mes-hall↗

arXiv2026

Instanton theory and fluctuation corrections to the thermal nucleation rate of a ferromagnetic superfluid

We provide a field-theoretical description of thermal nucleation in a one-dimensional ferromagnetic superfluid, a quantum-gas analogue of false-vacuum decay. The rate at which ground-state domains nucleate follows an Arrhenius law, with an exponential factor determined by a saddle-point of the energy functional -- the critical droplet or instanton -- and a magnitude fixed by small fluctuations about this configuration. We evaluate both contributions over the full parameter space, using a Gel'fand-Yaglom approach to reduce the calculation of the fluctuation spectrum to an initial-value problem. In addition, we obtain a closed-form expression for critical droplets close to the coexistence line, and use it to formulate an effective theory of domain nucleation and growth as a Kramers escape problem for the droplet size. Our results determine the parametric dependence of the nucleation rate and predict its signature in experimental images of a nucleating gas, increasing the rigor of comparisons between nucleation theory and experiment.

cond-mat.quant-gas↗

arXiv2025

Fermi liquid theory of $d$-wave altermagnets: demon modes and Fano-demon states

We develop a Fermi liquid theory of $d$-wave altermagnets and apply it to describe their collective excitation spectrum. We predict that in addition to a conventional undamped plasmon mode, where both spin components oscillate in phase, there is an acoustic plasmon (or {\em demon}) mode with out-of-phase spin dynamics. By analyzing the dynamical structure factor, we reveal a strong dependence of the demon's frequency and spectral weight both on the Landau parameters and on the direction of propagation. Notably, as a function of the propagation angle, we show that the acoustic mode evolves from a {\em hidden state}, which has zero spectral weight in the density excitation spectrum, to a weakly damped propagating demon mode and then (below a critical interaction parameter) to a {\em Fano-demon mixed state}, which is marked by a strong hybridization with particle-hole excitations and a corresponding asymmetric line shape in the structure factor. Our Letter paves the way for applications of altermagnetic materials in optospintronics by harnessing collective electron spin oscillations beyond traditional magnon spin waves.

cond-mat.mes-hall↗

arXiv2025

Wafer-Scale Single-Crystalline Monolayer Graphene

Producing large-area single-crystalline graphene is key to realizing its full potential in advanced applications, including twistronics. Yet, controlling graphene growth kinetics to avoid grain boundaries or multilayer growth remains challenging. Here, we demonstrate single-crystalline graphene free from multilayer domains via one-step delamination of epitaxial graphene from silicon carbide (SiC). This is enabled by a specific surface reconstruction of 4H-SiC(0001) achieved in our growth conditions. High crystalline quality is confirmed by the observation of the half-integer quantum Hall effect -- the hallmark of monolayer graphene -- in near cm-sized crystals. The scalability of our process, explored with 4''-wafers, represents an advance toward large-scale integration of high-performance graphene applications.

cond-mat.mes-hall↗

arXiv2025

Nonequilibrium Relaxation and Odd-Even Effect in Finite-Temperature Electron Gases

Pauli blocking in Fermi liquids imposes strong phase-space constraints on quasiparticle lifetimes, leading to a well-known quadratic-in-temperature decay rate of quasiparticle modes at low temperatures. In two-dimensional systems, however, even longer-lived modes are predicted (dubbed ``odd-parity'' modes) that involve a collective deformation of the Fermi distribution. Here, we present an efficient method to evaluate the full spectrum of relaxational eigenmodes of a Fermi liquid within kinetic theory. We employ this method to study the experimentally relevant case of a Fermi liquid with screened Coulomb interactions and map out the decay rates of quasiparticle modes beyond the asymptotic low-temperature limit up to the Fermi temperature, thus covering the entire temperature range of typical experiments. We confirm the existence of anomalously long-lived odd-parity modes and provide a comprehensive classification and detailed analysis of the relaxation spectrum. In particular, we find that (i) the odd-parity effect in the decay rates extends to temperatures as large as $T=0.15T_F$, (ii) there is only a small number of long-lived odd-parity modes, with an infinite number of remaining modes that show standard Fermi-liquid scaling, and (iii) the ratio between the odd- and even-parity lifetimes is tunable with the Coulomb interaction strength, in addition to temperature, which reflects a difference in the microscopic relaxation mechanism of the modes. Our findings provide a comprehensive description of the nonequilibrium relaxation behavior of two-dimensional electron gases and bridge a significant gap in our understanding of these systems.

cond-mat.mes-hall↗

arXiv2025

Probing Fractional Quantum Hall states in weakly interacting Fermi gases

Quantum gases are used to simulate the physics of the lowest Landau level (LLL) with neutral atoms, which in the simplest setup is achieved by rotating the gas at the confining harmonic trap frequency, a requirement that is difficult to achieve in practice. We point out that for weakly interacting Fermi gases, this rapid-rotation limit is not needed to access the LLL: As a direct consequence of first-order perturbation theory, many-body wave functions of states in the LLL remain unchanged at any rotation, and only their energies shift. This implies that even in the absence of rotations or for moderate rotations frequencies, LLL states are present as excited states at finite angular momentum. For fermions with contact interactions, these states are exact eigenstates of a paradigmatic model of Fractional Quantum Hall (FQH) states described by a single Haldane pseudopotential ($V_1$ for spin-polarized and $V_0$ for spinful systems), which realizes exact Laughlin and Haldane wave functions. We suggest that recently developed excitation and imaging techniques for rotating few-fermion systems allow for a detailed experimental investigation of FQH wave functions and to study the crossover to large particle number. We illustrate this for $N = 6$ spin-balanced fermions

cond-mat.quant-gas↗

arXiv2025

Odd-parity effect and scale-dependent viscosity in atomic quantum gases

Two-dimensional electron gases are predicted to possess an anomalous ''tomographic'' transport regime that is marked by an odd-even effect in the relaxation times, with odd-parity deformations of the Fermi surface becoming long-lived in comparison to even-parity ones. In this work, we establish that neutral two-component atomic Fermi gases also exhibit this tomographic effect. By diagonalizing the Fermi liquid collision integral, we identify odd-parity modes with anomalously long lifetimes below temperatures $T\leq 0.15T_F$, which is within reach of cold atom experiments. Furthermore, in contrast to electron gases, we find that the odd-even effect in neutral gases is widely tuneable with interactions along the BCS-BEC crossover and is suppressed on the BEC side. We propose as an experimental signature of the odd-even effect the damping rate of quadrupole oscillations, which is anomalously enhanced due to the presence of long-lived odd-parity modes. Our findings suggest that the dynamics of two-dimensional Fermi gases is richer than previously thought and should include additional long-lived modes.

cond-mat.quant-gas↗

arXiv2025

Magnetic field suppression of tomographic electron transport

Degenerate two-dimensional electron liquids are theoretically established to possess two vastly distinct collisional electron mean free paths, where even-parity deformations of the Fermi surface are hydrodynamic with a short collisional mean free path but odd-parity deformations remain near ballistic (known as the "tomographic" transport regime). Predicted signatures of this regime rely on the scaling of observables with temperature or device dimension, both of which are difficult to establish with certainty. Here, we consider magnetotransport in a minimal model of tomographic electrons and show that even a small magnetic field suppresses tomographic transport signatures and thus acts as a sensitive and unique probe of this regime. Fundamentally, the magnetic field breaks time-reversal invariance, which is a prerequisite for the odd-even parity effect in the collisional relaxation. We analyze in detail the scaling of the transverse conductivity, which has been linked to small-channel conductance of interaction-dominated electrons, and show that a tomographic scaling regime at intermediate wave numbers is quickly suppressed with magnetic field to a hydrodynamic or collisionless form. We confirm that the suppression occurs at relatively small magnetic fields when the cyclotron radius is comparable to the ballistic mean free path of the dominant odd-parity mode. This occurs at a much smaller magnetic field than the magnetic field strength required to suppress hydrodynamic electron transport, which suggests an experimental protocol to extract the odd-parity mean free path.

cond-mat.mes-hall↗

arXiv2025

Magnetotransport of tomographic electrons in a channel

Hydrodynamics is a new paradigm of electron transport in high-mobility devices, where frequent electron collisions give rise to a collective electron flow profile. However, conventional descriptions of these flows, which are based on the fluid equations for a classical gas extended to include impurity scattering, do not account for the distinct collisional relaxation in quantum-mechanical systems. In particular, by dint of Pauli blocking even modes of the distribution function relax over significantly shorter length scales than odd modes (dubbed the ``tomographic'' effect). We establish an analytical description of tomographic electron flow in a channel, and find four new distinguishing features: (i) Non-equilibrium effects from the boundaries penetrate significantly deeper into the flow domain; (ii) an additional velocity slip condition leads to a significant increase in the channel conductance; (iii) bulk rarefaction corrections decrease the curvature of the velocity profile in the channel center; and (iv) all these anomalous transport effects are rapidly suppressed with magnetic fields. The latter effect leads to a non-monotonic magneto-conductance, which can be used to measure both the even- and odd-mode mean free paths. Our asymptotic results unveil the underlying physics of tomographic flows and provide an alternative to numerical solutions of the Fermi-liquid equations.

cond-mat.mes-hall↗

arXiv2025

Tomographic electron flow in confined geometries: Beyond the dual-relaxation time approximation

Hydrodynamic-like electron flows are typically modeled using the Stokes-Ohm equation or a kinetic description that is based on a dual-relaxation time approximation. Such models assume a short intrinsic mean free path $\ell_e$ due to momentum-conserving electronic scattering and a large extrinsic mean free path $\ell_\text{MR}$ due to momentum-relaxing impurity scattering. This assumption, however, is overly simplistic and falls short at low temperatures, where it is known from exact diagonalization studies of the electronic collision integral that another large electronic mean free path $\ell_o$ emerges, which describes long-lived odd electron modes -- this is sometimes known as the tomographic effect. Here, using a matched asymptotic expansion of the Fermi liquid kinetic equation that includes different electron relaxation times, we derive a general asymptotic theory for tomographic flows in arbitrary smooth boundary geometries. Our key results are a set of governing equations for the electron density and electron current, their slip boundary conditions and boundary layer corrections near diffuse edges. We find that the tomographic effect strongly modifies previous hydrodynamic theories for electron flows: In particular, we find that (i) an equilibrium is established in the bulk, where the flow is governed by Stokes-Ohm like equations with significant finite-wavelength corrections, (ii) the velocity slip conditions for these equations are strongly modified from the widely-used hydrodynamic slip-length condition (iii) a large kinetic boundary layer arises near diffuse boundaries of width $\sim\sqrt{\ell_e \ell_o}$, and (iv) all these effects are strongly suppressed by an external magnetic field. We illustrate our findings for electron flow in a channel. The equations derived here represent the fundamental governing equations for tomographic electron flow in arbitrary smooth geometries.

cond-mat.mes-hall↗

arXiv2024

Few-to-many-particle crossover of pair excitations in a superfluid

Motivated by recent advances in the creation of few-body atomic Fermi gases with attractive interactions, we study theoretically the few-to-many-particle crossover of pair excitations, which for large particle numbers evolve into a mode that describes amplitude fluctuations of the superfluid order parameter (the "Higgs" mode). Our analysis is based on the hypothesis that salient aspects of the excitation spectrum are captured by interactions between time-reversed pair states in a harmonic oscillator potential. Microscopically, this assumption leads to a Richardson-type pairing model, which is integrable and thus allows a systematic quantitative study of the few-to-many-particle crossover with only minor numerical effort. We first establish a parity effect in the ground-state energy, i.e., a spectral convexity in the energy of open-shell configurations compared to their closed-shell neighbors, which is quantified by a so-called Matveev-Larkin parameter discussed for mesoscopic superconductors, which generalizes the pairing gap to mesoscopic ensembles and which behaves quantitatively differently in a few-body and a many-body regime. The crossover point for this quantity is widely tunable as a function of interaction strength. We then compute the excitation spectrum and demonstrate that the pair excitation energy shows a minimum that deepens with increasing particle number and shifts to smaller interaction strengths, consistent with the finite-size precursor of a quantum phase transition to a superfluid state. We extract a critical finite-size scaling exponent that characterizes the decrease of the gap with increasing particle number.

cond-mat.quant-gas↗

arXiv2024

Nonlinear thermoelectric probes of anomalous electron lifetimes in topological Fermi liquids

In two-dimensional Fermi liquids (FLs), odd-parity Fermi surface deformations have anomalously slow relaxation rates that are suppressed as $T^4$ with temperature $T$, distinct from the standard FL $T^2$ scaling. We demonstrate here that these long-lived modes, which are often hidden in linear response, have a significant impact on nonlinear transport by establishing a direct proportionality of nonlinear thermoelectric currents to the anomalously large relaxation time. These currents exist in topological time-reversal invariant FLs, and their magnitude is characterized by topological heat capacitance terms that we refer to as the Berry curvature capacity and the velocity-curvature capacity. We quantify the effect in bismuth telluride, which is an efficient thermoelectric and a topological insulator with a hexagonal Fermi surface. The proposed field-induced thermoelectric currents are well within the range of current experiments. Our findings demonstrate the potential to explore topological and many-body effects in FLs through the nonlinear thermoelectric response, urging further experimental studies.

cond-mat.mes-hall↗

arXiv2024

Universal fragmentation in annihilation reactions with constrained kinetics

In reaction-diffusion models of annihilation reactions in low dimensions, single-particle dynamics provides a bottleneck for reactions, leading to an anomalously slow approach to the empty state. Here, we construct a reaction model with a reciprocal bottleneck on particle dynamics where single-particle motion conserves the center of mass. We show that such a constrained reaction-diffusion dynamics does not approach an empty state but freezes at late times in a state with fragmented particle clusters, and that the late-time dynamics and asymptotic density are universal. Our setup thus constitutes a minimal model for the fragmentation of a one-dimensional lattice into independent particle clusters, and we provide exact results for the final density in the large-reaction rate limit. We suggest that the universal reaction dynamics could be observable in experiments with cold atoms or in the Auger recombination of exciton gases.

cond-mat.stat-mech↗

arXiv2024

Scale and conformal invariance in rotating interacting few-fermion systems

We show that rotating two-dimensional Fermi gases possess a nonrelativistic scale and conformal invariance at weak but nonzero interactions, where the scale invariance of universal short-range interactions is not yet broken by quantum effects. We demonstrate the symmetry in the excitation spectrum of few-fermion ensembles in a harmonic trap obtained by exact diagonalization. The excitation spectrum is shown to split in a set of primary states and derived excited states that consist of breathing modes as well as two different center-of-mass excitations, which describe cyclotron and guiding-center excitations of the total particle cloud. Furthermore, the conformal symmetry is manifest in the many-body wave function, where it dictates the form of the hyperradial component, which we demonstrate using Monte Carlo sampling of few-body wave functions.

cond-mat.quant-gas↗

arXiv2024

Fluctuation corrections to Lifshitz tails in disordered systems

Quenched disorder in semiconductors induces localized electronic states at the band edge, which manifest as an exponential tail in the density of states. For large impurity densities, this tail takes a universal Lifshitz form that is characterized by short-ranged potential fluctuations. We provide both analytical expressions and numerical values for the Lifshitz tail of a parabolic conduction band, including its exact fluctuation prefactor. Our analysis is based on a replica field integral approach, where the leading exponential scaling of the tail is determined by an instanton profile, and fluctuations around the instanton determine the subleading pre-exponential factor. This factor contains the determinant of a fluctuation operator, and we avoid a full computation of its spectrum by using a Gel'fand-Yaglom formalism, which provides a concise general derivation of fluctuation corrections in disorder problems. We provide a revised result for the disorder band tail in two dimensions.

cond-mat.stat-mech↗

arXiv2023

Shear viscosity in interacting two-dimensional Fermi liquids

In interaction-dominated two-dimensional electron gases at intermediate temperatures, electron transport is not diffusive as in the conventional Drude picture but instead hydrodynamic. The relevant transport coefficient in this regime is the shear viscosity. Here, we develop a numerically exact basis expansion to solve the Fermi liquid equation, and apply it to compute the shear viscosity of the electron gas with screened Coulomb interactions. Our calculations are valid at all temperatures and in particular describe the response beyond the asymptotic low-temperature limit, where perturbative approaches exist. We show that even in this low-temperature limit, there is a nonanalytic exchange contribution to the shear viscosity, highlighting the need for a full nonperturbative solution of the Fermi liquid equation. We hope that the techniques developed in this work will serve as a platform to determine the response of interacting Fermi liquids.

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