arXiv subjects

Ioannis Matthaiakakis

Publications and source records attributed to Ioannis Matthaiakakis.

15 recordsLinked to original sources

arXiv2026

Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations

This work focuses on the non-dissipative, parity-odd spin transport of $(2+1)$-dimensional relativistic electrons, generated by torsion, and the torsional Hall viscosity $ζ_{\rm H}$. We first determine $ζ_{\rm H}$ for massive Dirac fermions in the presence of a constant electromagnetic field. We predict that the magnetic field induces a contribution to $ζ_{\rm H}$ competing with the one originating from the Dirac mass. Moreover, we quantify the impact on $ζ_{\rm H}$ originating from the band structure deformation quadratic in momentum terms that was proposed by Bernevig-Hughes-Zhang (BHZ). We find that the BHZ deformation substantially enhances $ζ_{\rm H}$ in magnitude as measured in a domain wall configuration, when compared to the free Dirac fermion result. Nevertheless, the torsional Hall viscosity still discriminates between topologically trivial and non-trivial regimes. Our results, hence, pave the way for a deeper understanding of hydrodynamic spin transport and its possible verification in experiments.

cond-mat.mes-hall↗

arXiv2026

The physical meaning of the Belinfante-Rosenfeld ambiguity

Current literature lacks consensus on how to theoretically describe spin polarization and its transport in matter. The underlying reason is the presence of the Belinfante-Rosenfeld (BR) ambiguity in the form of the energy-momentum and spin tensors. I re-examine the BR ambiguity in Einstein-Cartan spacetimes, using the bi-form formalism in a manner applicable to any conserved current and its corresponding gauge field. This allows us to physically interpret the BR ambiguity as the choice of splitting a conserved current into its matter and gauge field contributions.

hep-th↗

arXiv2024

The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries

There exists a long-standing debate regarding the torsion contribution to the 4d chiral anomaly of a Dirac fermion. Central to this debate is the Nieh-Yan anomaly, which has been considered ill-defined and a regularization artifact. Using a heat-kernel approach, we examine the relationship between the Dirac operator index, the Nieh-Yan invariant and the torsional anomaly. We show the Nieh-Yan invariant vanishes on spacetimes without boundaries, if the Dirac index is well-defined. In the known examples of non-vanishing Nieh--Yan invariant on manifolds without boundaries, the heat kernel expansion breaks down, making the index ill-defined. Finally, for finite boundaries we identify several finite bulk and boundary anomaly terms, alongside bulk and boundary Nieh-Yan terms. We construct explicit counterterms that cancel the Nieh-Yan terms and argue that the boundary terms give rise to a torsional anomalous Hall effect. Our results emphasize the importance of renormalization conditions, as these can affect the non-thermal Nieh-Yan anomaly coefficients. In addition, we demonstrate that anomalous torsional transport may arise even without relying on the Nieh-Yan invariant.

hep-th↗

arXiv2024

Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity

General relativity (GR) as described in terms of curvature by the Einstein-Hilbert action is dynamically equivalent to theories of gravity formulated in terms of spacetime torsion or non-metricity. This forms what is called the geometrical trinity of gravity. The theories corresponding to this trinity are, apart from GR, the teleparallel (TEGR) and symmetric teleparallel (STEGR) equivalent theories of general relativity, respectively, and their actions are equivalent to GR up to boundary terms $B$. We investigate how the Gibbons-Hawking-York (GHY) boundary term of GR changes under the transition to TEGR and STEGR within the framework of metric-affine gravity. We show that $B$ is the difference between the GHY term of GR and that of metric-affine gravity. Moreover, we show that the GHY term for both TEGR and STEGR must vanish for consistency of the variational problem. Furthermore, our approach allows to extend the equivalence between GR, TEGR and STEGR beyond the Einstein-Hilbert action to any action built out of the curvature two-form, thus establishing the generalized geometrical trinity of gravity. We argue that these results will be particularly useful in view of studying gauge/gravity duality for theories with torsion and non-metricity.

hep-th↗

arXiv2024

Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory

We consider as a model of Weyl semimetal thermoelectric transport a $(3+1)$-dimensional charged, relativistic and relaxed fluid with a $U(1)_{V} \times U(1)_{A}$ chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature opening the path to experimental verification.

hep-th↗

arXiv2023

Leading order magnetic field dependence of conductivities in anomalous hydrodynamics

We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on $(3+1)$-dimensional hydrodynamics in the presence of a constant ${\cal O}(\partial)$ magnetic field with a $U(1)$ chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. In particular, magnetic field dependent terms that were previously found in the literature only enter the non-zero frequency thermoelectric conductivities through explicitly frame dependent pieces indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid's equilibrium state.

hep-th↗

arXiv2023

Restoring time-reversal covariance in relaxed hydrodynamics

In hydrodynamics, for generic relaxations, the stress tensor and $U(1)$ charge current two-point functions are not time-reversal covariant. This remains true even if the Martin-Kadanoff procedure happens to yield Onsager reciprocal correlators. We consider linearised relativistic hydrodynamics on Minkowski space in the presence of energy, $U(1)$ charge and momentum relaxation. We then show how one can find the minimal relaxed hydrodynamic framework that does yield two-point functions consistent with time-reversal covariance. We claim the same approach naturally applies to boost agnostic hydrodynamics and its limits (e.g. Carrollian, Galilean and Lifshitz fluids).

hep-th↗

arXiv2022

Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

Motivated by establishing holographic renormalization for gravitational theories with non-metricity and torsion, we present a new and efficient general method for calculating Gibbons-Hawking-York (GHY) terms. Our method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in $(n-1)+1$ dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for Lovelock-Chern-Simons and metric-affine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within AdS/CFT.

hep-th↗

arXiv2022

Non-dissipative electrically driven fluids

Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid's chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.

hep-th↗

arXiv2022

Hall viscosity and hydrodynamic inverse Nernst effect in graphene

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a non-linear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.

cond-mat.mes-hall↗

arXiv2022

Destroying superconductivity in thin films with an electric field

In this paper we use a Ginzburg-Landau approach to show that a suitably strong electric field can drive a phase transition from a superconductor to a normal metal. The transition is induced by taking into account corrections to the permittivity due to the superconductive gap and persists even when screening effects are considered. We test the model against recent experimental observations in which a strong electric field has been observed to control the supercurrent in superconducting thin films. We find excellent agreement with the experimental data and are able to explain several observed features. We additionally suggest a way to test our theoretical proposal via superconductor-superconductor electron tunneling.

cond-mat.supr-con↗

arXiv2022

Quantum Complexity as Hydrodynamics

As a new step towards defining complexity for quantum field theories, we map Nielsen operator complexity for $SU(N)$ gates to two-dimensional hydrodynamics. We develop a tractable large $N$ limit that leads to regular geometries on the manifold of unitaries as $N$ is taken to infinity. To achieve this, we introduce a basis of non-commutative plane waves for the $\mathfrak{su}(N)$ algebra and define a metric with polynomial penalty factors. Through the Euler-Arnold approach we identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory of large-qudit operator complexity. For large $N$, our cost function captures two essential properties of holographic complexity measures: ergodicity and conjugate points.

hep-th↗

arXiv2019

Turbulent hydrodynamics in strongly correlated Kagome metals

A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids are not amenable to the perturbative methods of Fermi liquid theory, but can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene, which possesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes of their band structure provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in stoichiometric Scandium (Sc) Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction and hence reflects the strength of the correlations, is enhanced by a factor of about 3.2 as compared to graphene, due to orbital hybridization. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put, for the first time, the turbulent flow regime described by holography within the reach of experiments.

cond-mat.str-el↗

arXiv2019

Functional dependence of the Hall viscosity-induced transverse voltage in two-dimensional Fermi liquids

The breaking of parity and time-reversal symmetry in two-dimensional Fermi liquids gives rise to non-dissipative transport features characterized by the Hall viscosity. In magnetic fields, the Hall viscous force directly competes with the Lorentz force, since both mechanisms contribute to the Hall voltage. In this work, we present a channel geometry that allows us to uniquely distinguish these two contributions and derive, for the first time, their functional dependency on all external parameters. We show that the ratio of the Hall viscous to the Lorentz force contribution is negative and that its modulus decreases with increasing width, slip-length and carrier density, while it increases with the electron-electron mean free path of our channel. In typical materials such as GaAs the Hall viscous contribution can dominate the Lorentz signal up to a few tens of millitesla until the total Hall voltage vanishes and subsequently is overcome by the Lorentz contribution. Moreover, we prove that the total Hall electric field is parabolic due to Lorentz effects, whereas the offset of this parabola is characterized by the Hall viscosity. Hence, our results pave the way to measure and identify the Hall viscosity via both global and local voltage measurements.

cond-mat.mes-hall↗

arXiv2018

Strongly coupled electron fluids in the Poiseuille regime

In the context of describing electrons in solids as a fluid in the hydrodynamic regime, we consider a flow of electrons in a channel of finite width, i.e.~a Poiseuille flow. The electrons are accelerated by a constant electric field. We develop the appropriate relativistic hydrodynamic formalism in 2+1 dimensions and show that the fluid has a finite dc conductivity due to boundary-induced momentum relaxation, even in the absence of impurities. We use methods involving the AdS/CFT correspondence to examine the system in the strong-coupling regime. We calculate and study velocity profiles across the channel, from which we obtain the differential resistance $dV/dI$. We find that $dV/dI$ decreases with increasing current $I$ as expected for a Poiseuille flow, also at strong coupling and in the relativistic velocity regime. Moreover, we vary the coupling strength by varying $η/s$, the ratio of shear viscosity over entropy density. We find that $dV/dI$ decreases when the coupling is increased. We also find that strongly coupled fluids are more likely to become ultra-relativistic and turbulent. These conclusions are insensitive to the presence of impurities. In particular, we predict that in channels which are clearly in the hydrodynamic regime already at small currents, the DC channel resistance strongly depends on $η/s$.

cond-mat.mes-hall↗