arXiv subjects

Herbert Schoeller

Publications and source records attributed to Herbert Schoeller.

At least 19 recordsLinked to original sources

arXiv2026

Instabilities of Fermi Liquids with Arbitrary Forward Scattering: Exact Approach

In this work, we consider $N$-fold degenerate $D$-dimensional electron gas with spherical Fermi surface and arbitrary forward-scattering density-density interaction transferring small momentum compared to the Fermi momentum $k_{\mathrm{F}}$. The dimensional reduction that is mathematically equivalent to the Haldane patch construction and similar multidimensional bosonization techniques, provides a natural map of two-point $D$-dimensional correlation functions (fermion Green function, susceptibilities etc.) onto effective one-dimensional (1D) correlators with the same diagrammatic structure, which can be evaluated exactly within a 1D bosonizable (Gaussian) theory. We then apply this formalism to evaluate the fermion Green function, pair and charge/flavor susceptibilities, as well as the composite correlation functions for the case of a finite-range interaction, where the interaction range $R_{\mathrm{s}} \gg 1/k_{\mathrm{F}}$ is large compared to the Fermi wavelength. First, we find that the single-particle spectral function remains Fermi-liquid-like which is fully consistent with the previous research. In contrast to the single-particle sector, the many-body channels are efficiently dressed by finite-range interactions, and this dressing is fully equivalent to the one-loop renormalization group (RG), which is also in line with previous multidimensional bosonization results. Within the forward-scattering model, stable long-range order is not possible, and relevant susceptibilities demonstrate singular power-law scaling with temperature $T$ at $T \to 0$. The rest of the abstract is in the PDF.

cond-mat.str-el↗

arXiv2025

High-Temperature Superconductivity from Finite-Range Attractive Interaction

In this letter we consider $D$-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range $R_s$ that is much greater than the Fermi wavelength $λ_F$ breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature $T_c$ versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal $T_c^* \sim 0.1 E_F$ on the interaction range at $R_s \gg λ_F$, $E_F$ is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.

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arXiv2024

Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids

We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting $D$-dimensional Fermi liquid. Our model consists of a $D$-dimensional electron gas subject to an instantaneous electron-electron interaction of a finite range exceeding the average inter-particle distance. Pair, charge and spin susceptibilities are evaluated via the one-loop renormalization group theory and via the bosonization approach, giving identical results. In case of a repulsive interaction, we identify an intrinsic Fermi liquid instability towards insulating spin/charge density wave order when the interaction coupling strength reaches a universal critical value. If both electron and hole pockets of the same size are present, the ground state is an excitonic insulator at arbitrarily small repulsive interaction. If the interaction is attractive, the ground state is a singlet non-BCS superconductor with a uniform condensate. In case if both electron and hole Fermi surfaces are present, we predict an instability towards the inter-pocket pair-density-wave ordering at the critical coupling. This prediction lends strong theoretical support to the pair-density-wave scenario of superconductivity in cuprate materials. Due to its simple and universal nature, presented microscopic mechanism of intrinsic instabilities of interacting $D$-dimensional Fermi liquids constitutes a solid theoretical ground for understanding quantum phase transitions in a variety of quantum materials, from ultraclean semiconductor quantum wells to high-temperature superconductors.

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arXiv2023

RKKY interaction in one-dimensional flat-band lattices

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two classical magnetic impurities in one-dimensional lattice models with flat bands. As two representative examples, we pick the stub lattice and the diamond lattice at half filling. We first calculate the exact RKKY interaction numerically and then compare our data to results obtained via different analytical techniques. In both our examples, we find that the RKKY interaction exhibits peculiar features that can directly be traced back to the presence of a flat band in the energy spectrum. Importantly, these features are not captured by the conventional RKKY approximation based on non-degenerate perturbation theory. Instead, we find that degenerate perturbation theory correctly reproduces our exact results if there is an energy gap between the flat and the dispersive bands, while a non-perturbative approach becomes necessary in the absence of a gap.

cond-mat.mes-hall↗

arXiv2023

Second-order topology and supersymmetry in two-dimensional topological insulators

We unravel a fundamental connection between supersymmetry and a wide class of two dimensional second-order topological insulators (SOTI). This particular supersymmetry is induced by applying a half-integer Aharonov-Bohm flux $f=Φ/Φ_0=1/2$ through a hole in the system. Here, three symmetries are essential to establish this fundamental link: chiral symmetry, inversion symmetry, and mirror symmetry. At such a flux of half-integer value the mirror symmetry anticommutes with the inversion symmetry leading to a nontrivial $n=1$-SUSY representation for the absolute value of the Hamiltonian in each chiral sector, separately. This implies that a unique zero-energy state and an exact twofold degeneracy of all eigenstates with non-zero energy is found even at finite system size. For arbitrary smooth surfaces the link between 2D-SOTI and SUSY can be described within a universal low-energy theory in terms of an effective surface Hamiltonian which encompasses the whole class of supersymmetric periodic Witten models. Applying this general link to the prototypical example of a Bernevig-Hughes-Zhang(BHZ)-model with an in-plane Zeeman field, we analyze the entire phase diagram and identify a gapless Weyl phase separating the topological from the non-topological gapped phase. Surprisingly, we find that topological states localized at the outer surface remain in the Weyl phase, whereas topological hole states move to the outer surface and change their spatial symmetry upon approaching the Weyl phase. Therefore, the topological hole states can be tuned in a versatile manner opening up a route towards magnetic-field-induced topological engineering in multi-hole systems. Finally, we demonstrate the stability of localized states against deviation from half-integer flux, flux penetration into the sample, surface distortions, and random impurities for impurity strengths up to the order of the surface gap.

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arXiv2022

Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus

We propose a realization of a quantum Hall effect (QHE) in a second-order topological insulator (SOTI) in three dimensions (3D), which is mediated by hinge states on a torus surface. It results from the nontrivial interplay of the material structure, Zeeman effect, and the surface curvature. In contrast to the conventional 2D- and 3D-QHE, we show that the 3D-SOTI QHE is not affected by orbital effects of the applied magnetic field and exists in the presence of a Zeeman term only, induced e.g. by magnetic doping. To explain the 3D-SOTI QHE, we analyze the boundary charge for a 3D-SOTI and establish its universal dependence on the Aharonov-Bohm flux threading through the torus hole. Exploiting the fundamental relation between the boundary charge and the Hall conductance, we demonstrate the universal quantization of the latter, as well as its stability against random disorder potentials and continuous deformations of the torus surface.

cond-mat.mes-hall↗

arXiv2022

Floquet Renormalization Group Approach to the Periodically Driven Kondo Model

We study the interplay of strong correlations and coherent driving by considering the strong-coupling Kondo model driven by a time-periodic bias voltage. Combining a recent nonequilibrium renormalization group method with Floquet theory, we find that by the coherent dressing of the driving field side-replicas of the Kondo resonance emerge in the conductance, which are not completely washed out by the decoherence induced by the driving. We show that to accurately capture the interplay of driving and strong correlations one needs to go beyond simple phenomenological pictures, which underestimate decoherence, or adiabatic approximations, highlighting the relevance of non-Markovian memory effects. Within our method the differential conductance shows good quantitative agreement with experimental data in the full crossover regime from weak to strong driving. We analyze memory effects in detail based on the response to short voltage pulses.

cond-mat.mes-hall↗

arXiv2022

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance $x_φ\in[0, L]$ is given by a perfectly linear function of $x_φ$ plus an integer-valued topological invariant $I$ -- the so called boundary invariant. For systems with weak potential amplitudes, we additionally develop Green's function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation.

cond-mat.mes-hall↗

arXiv2022

Quantum dot coupled to topological insulators: The role of edge states

We investigate a system consisting of one or two topological-insulator leads which are tunnel coupled to a single dot level. The leads are described by the one-dimensional Su-Schrieffer-Heeger model. We show that (topological) edge states cause characteristic features in the dot spectral function, the dot occupation, and the finite-bias current across the dot. As the kinetic energy is quenched in the dot region, local two-particle interactions are of particular relevance there. This motivates us to test whether the aforementioned edge-state features are robust against such interactions; we report here that they are either robust or even enhanced. We conclude that the characteristic features can be used to determine if the leads are in their topologically non-trivial or trivial phase.

cond-mat.mes-hall↗

arXiv2021

Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors $ν=1/(2l+1)$, where $l$ is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has $2l+1$ different branches that cannot be connected adiabatically, reflecting the $(2l+1)$-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.

cond-mat.mes-hall↗

arXiv2021

Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property, that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values $0$ and $-1$ [Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation and fixes the mod(1) ambiguity appearing in the Modern Theory of Polarization. In the present work we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from $-N_c$ to $0$, where $N_c$ is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so called nearsightedness principle formulated by W. Kohn [Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models.

cond-mat.mes-hall↗

arXiv2021

Universal properties of boundary and interface charges in continuum models of one-dimensional insulators

We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single region of dislocations and/or impurity potentials breaking translational invariance (the interface model). We investigate the universal properties of excess charges accumulated near the boundary and the interface, respectively. We find a rigorous analytic proof for the earlier observed linear dependence of the boundary charge on the phase of the periodic potential modulation as well as extend these results to the interface model. The linear dependence on the phase shows a universal value for the slope, and is intersected by discontinuous jumps by plus or minus one electron charge at the phase points where localized states enter or leave a band of extended states. Both contributions add up such that the periodicity of the excess charge in the phase over a $2π$-cycle is maintained. While in the boundary model this property is usually associated with the bulk-boundary correspondence, in the interface model a correspondence of scattering state and localized state contributions to the total interface charge is unveiled on the basis of the so-called nearsightedness principle.

cond-mat.mes-hall↗

arXiv2021

Universality of Abelian and non-Abelian Wannier functions in one dimension

Within a Dirac model in $1+1$ dimensions, a prototypical model to describe low-energy physics for a wide class of lattice models, we propose a field-theoretical version for the representation of Wannier functions, the Zak-Berry connection, and the geometric tensor. In two natural Abelian gauges we present universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase $γ$ of the gap parameter and the charge correlation length $ξ$ in an insulator. The two gauges allow for a universal low-energy formulation of the surface charge and surface fluctuation theorem, relating the boundary charge and its fluctuations to bulk properties. Our analysis describes the universal aspects of Wannier functions for the wide class of one-dimensional generalized Aubry-André-Harper lattice models. In the low-energy regime of small gaps we demonstrate universal scaling of all lattice Wannier functions and their moments in the corresponding Abelian gauges. We also discuss non-Abelian lattice gauges and find that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. Our results present evidence that universal aspects of Wannier functions and of the boundary charge are uniquely related and can be elegantly described within universal low-energy theories.

cond-mat.mes-hall↗

arXiv2021

Universality of Boundary Charge Fluctuations

We establish the quantum fluctuations $ΔQ_B^2$ of the charge $Q_B$ accumulated at the boundary of an insulator as an integral tool to characterize phase transitions where a direct gap closes (and reopens), typically occurring for insulators with topological properties. The power of this characterization lies in its capability to treat different kinds of insulators on equal footing; being applicable to transitions between topological and non-topological band, Anderson, and Mott insulators alike. In the vicinity of the phase transition we find a universal scaling $ΔQ_B^2(E_g)$ as function of the gap size $E_g$ and determine its generic form in various dimensions. For prototypical phase transitions with a massive Dirac-like bulk spectrum we demonstrate a scaling with the inverse gap in one dimension and a logarithmic one in two dimensions.

cond-mat.stat-mech↗

arXiv2020

Multilevel coherences in quantum dots

We study transport through strongly interacting quantum dots with $N$ energy levels that are weakly coupled to generic multi-channel metallic leads. In the regime of coherent sequential tunneling, where level spacing and broadening are of the same order but small compared to temperature, we present a unified, $SU(N)$-invariant form of the kinetic equation for the reduced density matrix of the dot and the tunneling current. This is achieved by introducing the concept of flavor polarization for the dot and the reservoirs, and splitting the kinetic equation in terms of flavor accumulation, anisotropic flavor relaxation, as well as exchange-field- and detuning-induced flavor rotation. In particular, we identify the exchange field as the cause of negative differential conductance at off-resonance bias voltages appearing in generic quantum-dot models. To illustrate the notion of flavor polarization, we analyze the non-linear current through a triple quantum-dot device.

cond-mat.mes-hall↗

arXiv2020

Quadrupole spin polarization as signature of second-order topological superconductors

We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.

cond-mat.mes-hall↗

arXiv2020

Chiral 1D Floquet topological insulators beyond rotating wave approximation

We study one-dimensional (1D) Floquet topological insulators with chiral symmetry going beyond the standard rotating wave approximation. The occurrence of many anticrossings between Floquet replicas leads to a dramatic extension of phase diagram regions with stable topological edge states (TESs). We present an explicit construction of all TESs in terms of a truncated Floquet Hamiltonian in frequency space, prove the bulk-boundary correspondence, and analyze the stability of the TESs in terms of their localization lengths. We propose experimental tests of our predictions in curved bilayer graphene.

cond-mat.mes-hall↗

arXiv2020

Electronic transport in one-dimensional Floquet topological insulators via topological and nontopological edge states

Based on probing electronic transport properties we propose an experimental test for the recently discovered rich topological phase diagram of one-dimensional Floquet topological insulators with Rashba spin-orbit interaction [Kennes \emph{et al.}, Phys. Rev. B {\bf 100}, 041103(R) (2019)]. Using the Keldysh-Floquet formalism we compute electronic transport properties of these nanowires, where we propose to couple the leads in such a way, as to primarily address electronic states with a large weight at one edge of the system. By tuning the Fermi energy of the leads to the center of the topological gap we are able to directly address the topological edge states, granting experimental access to the topological phase diagram. Surprisingly, when tuning the lead Fermi energy to special values in the bulk which coincide with extremal points of the dispersion relation, we find additional peaks of similar magnitude to those caused by the topological edge states. These peaks reveal the presence of continua of states centered around aforementioned extremal points whose wavefunctions are linear combinations of delocalized bulk states and exponentially localized edge states, where the ratio of edge- to bulk-state amplitude is maximal at the extremal point of the dispersion. We discuss the transport properties of these \emph{non-topological edge states}, explain their emergence in terms of an intuitive yet quantitative physical picture and discuss their relationship with Van Hove singularities in the bulk of the system. The mechanism giving rise to these states is not specific to the model we consider here, suggesting that they may be present in a wide class of one-dimensional systems.

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