arXiv subjects

J. Nissinen

Publications and source records attributed to J. Nissinen.

12 recordsLinked to original sources

arXiv2021

Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates

Relativistic gravitational anomalies lead to anomalous transport coefficients that can be activated at finite temperature in condensed matter systems with gapless fermions. The chiral vortical effect (CVE) is an anomalous chiral current along a rotation axis, expressed in terms of a gravimagnetic field and a gravitational anomaly. Another one, the chiral torsional effect (CTE), arises from hydrodynamically independent frame fields and connection. We discuss the relation of CVE, CTE and gravitational anomalies for relativistic fermions from the perspective of torsion and the Nieh-Yan anomaly. The DC transport coefficients of the two anomalies are found to be closely related depending whether or not torsion is non-zero in the hydrodynamics. The relativistic anomaly from torsion is well defined if instead of an ultraviolet divergent term, the chemical potential or temperature enter. The anomaly term is 2nd order in gradients and contributes in linear response for CTE, implying also the same for CVE. As an example, we consider chiral $p+ip$ Weyl superfluids/conductors. At low-energies, the system is effectively relativistic along a special anisotropy axis. The hydrodynamics is governed by two velocities, normal velocity $\boldsymbol{v}_n$ and superfluid velocity $\boldsymbol{v}_s$. The two anomalies follow from the normal component rotation and the dependence of the momentum density on the superfluid velocity (order parameter). In the CVE the chiral current is produced by solid body rotation of the normal component with (angular) velocity $\boldsymbol{v}_n= \boldsymbolΩ\times \boldsymbol{r}$. In the CTE, a chiral current is produced the vorticity $\nabla \times \boldsymbol{v}_s$, which in the low-energy effective theory is torsion. In equilibrium, $\langle\langle \nabla \times \boldsymbol{v_s}\rangle\rangle= 2\boldsymbolΩ$ on average and the two anomaly currents cancel.

cond-mat.supr-con↗

arXiv2020

Topological polarization, dual invariants, and surface flat band in crystalline insulators

We describe a three-dimensional crystalline topological insulator (TI) phase of matter that exhibits spontaneous polarization. This polarization results from the presence of (approximately) flat bands on the surface of such TIs. These flat bands are a consequence of the bulk-boundary correspondence of polarized topological media, and contrary to related nodal line semimetal phases also containing surface flat bands, they span the entire surface Brillouin zone. We also present an example Hamiltonian exhibiting a Lifshitz transition from the nodal line phase to the TI phase with polarization. Utilizing elasticity tetrads, we show a complete classification of 3D crystalline TI phases and invariants. The phase with polarization naturally arises from this classification as a dual to the previously better-known 3D TI phase exhibiting quantum (spin) Hall effect. Besides polarization, another implication of the large surface flat band is the susceptibility to interaction effects such as superconductivity: the mean-field critical temperature is proportional to the size of the flat bands, and this type of systems may hence exhibit superconductivity with a very high critical temperature.

cond-mat.mtrl-sci↗

arXiv2020

On thermal Nieh-Yan anomaly in Weyl superfluids

We discuss the possibility of the torsional Nieh-Yan anomaly of the type $μ(ej^μ_5) =γT^2({\cal T}^a \wedge {\cal T}_a)$ in Weyl superfluids, where $T$ is temperature and ${\cal T}^a$ is the effective or emergent torsion from the superfluid order parameter. As distinct from the dimensionful ultraviolet (UV) parameter $Λ^2$ in the conventional torsional Nieh-Yan anomaly, the parameter $γ$ is dimensionless in canonical units. This suggests that such dimensionless parameter may be fundamental, being determined by the geometry, topology and number of chiral quantum fields in the system. By comparing this to a Weyl superfluid with low-temperature corrections, $T\llΔ_0$, we show that such a term does exist in the hydrodynamics of a chiral $p$-wave superfluid, such as $^3$He-A, or a chiral superconductor. We also discuss and show how other $T^2$ terms of similar form and of the same order in gradients, coming from e.g. Fermi-liquid corrections and the chiral chemical potential, can also be expressed in terms of dimensionless fundamental parameters with emergent low-energy relativistic fields. Lastly, we discuss our results in comparison to relativistic Weyl fermions and the connection of the torsional gravitational anomalies to thermal transport in Weyl systems.

cond-mat.str-el↗

arXiv2019

On thermal Nieh-Yan anomaly in topological Weyl materials

We discuss the possibility of a gravitional Nieh-Yan anomaly of the type $\partial_μj^μ_5 =γT^2{\cal T}^a\wedge {\cal T}_a$ in topological Weyl materials, where $T$ is temperature and ${\cal T}^a$ is the effective or emergent torsion. As distinct from the non-universal parameter $Λ$ in the conventional (zero temperature) Nieh-Yan anomaly -- with canonical dimensions of momentum -- the parameter $γ$ is dimensionless. This suggests that the dimensionless parameter is fundamental, being determined by the geometry, topology and number of the number of chiral quantum fields without any explicit non-universal UV scales. This conforms with previous results in the literature, as well as spectral flow calculations using torsional magnetic field at finite temperature.

cond-mat.str-el↗

arXiv2019

Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect

For two-dimensional topological insulators, the integer and intrinsic (without external magnetic field) quantum Hall effect is described by the gauge anomalous (2+1)-dimensional [2+1d] Chern-Simons (CS) response for the background gauge potential of the electromagnetic U(1) field. The Hall conductance is given by the quantized prefactor of the CS term, which is a momentum-space topological invariant. Here, we show that three-dimensional crystalline topological insulators with no other symmetries are described by a topological (3+1)-dimensional [3+1d] mixed CS term. In addition to the electromagnetic U(1) gauge field, this term contains elasticity tetrad fields $E^{\ a}_μ({\bf r},t) = \partial_μX^a(\mathbf{r},t)$ which are gradients of crystalline U(1) phase fields $X^a(\mathbf{r},t)$ and describe the deformations of the crystal. For a crystal in three spatial dimensions $a=1,2,3$ and the mixed axial-gravitational response contains three parameters protected by crystalline symmetries: the weak momentum-space topological invariants. The response of the Hall conductance to the deformations of the crystal is quantized in terms of these invariants. In the presence of dislocations, the anomalous 3+1d CS term describes the Callan-Harvey anomaly inflow mechanism. The response can be extended to all odd spatial dimensions. The elasticity tetrads, being the gradients of the lattice U(1) fields, have canonical dimension of inverse length. Similarly, if such tetrad fields enter general relativity, the metric becomes dimensionful, but the physical parameters, such as Newton's constant, the cosmological constant, and masses of particles, become dimensionless.

cond-mat.mes-hall↗

arXiv2018

Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid $^3$He

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid $^3$He, we show that half-quantum vortices (HQVs) -- linear topological defects carrying half quantum of circulation -- survive transitions from the polar phase to other superfluid phases with polar distortion. In the polar-distorted A phase, HQV cores in 2D systems should harbor non-Abelian Majorana modes. In the polar-distorted B phase, HQVs form composite defects -- walls bounded by strings hypothesized decades ago in cosmology. Our experiments establish the superfluid phases of $^3$He in nanostructured confinement as a promising topological media for further investigations ranging from topological quantum computing to cosmology and grand unification scenarios.

cond-mat.other↗

arXiv2018

Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions

Theory of elasticity in topological insulators has many common features with relativistic quantum fields interacting with gravitational field in the tetrad form. Here we discuss several issues in the effective topological (pseudo)electromagnetic response in three-dimensional weak crystalline topological insulators with no time-reversal symmetry that feature elasticity tetrads, including a mixed "axial-gravitational" anomaly. This response has some resemblance to "quasitopological" terms proposed for massless Weyl quasiparticles with separate, emergent fermion tetrads. As an example, we discuss the chiral/axial anomaly in superfluid 3He-A. We demonstrate the principal difference between the elasticity tetrads and the Weyl fermion tetrads in the construction of the topological terms in the action. In particular, the topological action expressed in terms of the elasticity tetrads, cannot be expressed in terms of the Weyl fermion tetrads since in this case the gauge invariance is lost.

cond-mat.str-el↗

arXiv2017

Dimensional crossover of effective orbital dynamics in polar distorted 3He-A: Transitions to anti-spacetime

Topologically protected superfluid phases of $^3$He allow one to simulate many important aspects of relativistic quantum field theories and quantum gravity in condensed matter. Here we discuss a topological Lifshitz transition of the effective quantum vacuum in which the determinant of the tetrad field changes sign through a crossing to a vacuum state with a degenerate fermionic metric. Such a transition is realized in polar distorted superfluid $^3$He-A in terms of the effective tetrad fields emerging in the vicinity of the superfluid gap nodes: the tetrads of the Weyl points in the chiral A-phase of $^3$He and the degenerate tetrad in the vicinity of a Dirac nodal line in the polar phase of $^3$He. The continuous phase transition from the $A$-phase to the polar phase, i.e. in the transition from the Weyl nodes to the Dirac nodal line and back, allows one to follow the behavior of the fermionic and bosonic effective actions when the sign of the tetrad determinant changes, and the effective chiral space-time transforms to anti-chiral "anti-spacetime". This condensed matter realization demonstrates that while the original fermionic action is analytic across the transition, the effective action for the orbital degrees of freedom (pseudo-EM) fields and gravity have non-analytic behavior. In particular, the action for the pseudo-EM field in the vacuum with Weyl fermions (A-phase) contains the modulus of the tetrad determinant. In the vacuum with the degenerate metric (polar phase) the nodal line is effectively a family of $2+1$d Dirac fermion patches, which leads to a non-analytic $(B^2-E^2)^{3/4}$ QED action in the vicinity of the Dirac line.

cond-mat.supr-con↗

arXiv2017

Effective Minkowski to Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar 3He

We discuss the effective metric experienced by the Nambu-Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose-Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid 3He, experimentally observed in uniaxial aerogel 3He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar "ghost" condensate.

cond-mat.other↗

arXiv2017

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green's functions parametrized by a 16 element matrix $e^μ_α$ in an expansion around the Weyl point. The matrix $e^μ_α$ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric $g_{μν}$ governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components $g^{00}$ and $g_{00}$ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for $g^{00}>0$ and respectively $g_{00}>0$ or $g_{00}<0$, we find additional "type-III" and "type-IV" Weyl fermions with instabilities (complex frequencies) for $g^{00}<0$ and $g_{00}>0$ or $g_{00}<0$, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where $g^{00}$ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.

cond-mat.str-el↗

arXiv2012

The quantum Hall curve

We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions needed to describe scaling data arise in a simple and transparent way from the group theory and geometry of these \emph{quantum Hall curves}. The renormalization-group potential therefore emerges naturally in a geometric context that complements the phenomenology found in our companion paper [Phys. Rev. B 85, 155123 (2012)]. We show how the algebraic geometry of elliptic curves is an efficient way to analyze specific scaling data, extract the modular symmetries of the transport coefficients, and use this information to fit the given system into the one-dimensional (real) family of curves that may model all universal properties of quantum Hall systems.

cond-mat.str-el↗

arXiv2012

An RG potential for the quantum Hall effects

The phenomenological analysis of fully spin-polarized quantum Hall systems, based on holomorphic modular symmetries of the renormalization group (RG) flow, is generalized to more complicated situations where the spin or other "flavors" of charge carriers are relevant, and where the symmetry is different. We make the simplest possible ansatz for a family of RG potentials that can interpolate between these symmetries. It is parametrized by a single number $a$ and we show that this suffices to account for almost all scaling data obtained to date. The potential is always symmetric under the main congruence group at level two, and when $a$ takes certain values this symmetry is enhanced to one of the maximal subgroups of the modular group. We compute the covariant RG $β$-function, which is a holomorphic vector field derived from the potential, and compare the geometry of this gradient flow with available temperature driven scaling data. The value of $a$ is determined from experiment by finding the location of a quantum critical point, i.e., an unstable zero of the $β$-function given by a saddle point of the RG potential. The data are consistent with $a \in \mathbb{R}$, which together with the symmetry leads to a generalized semi-circle law.

cond-mat.str-el↗