arXiv subjects

Alexander Krikun

Publications and source records attributed to Alexander Krikun.

At least 19 recordsLinked to original sources

arXiv2023

Holographic timelike superconductor

We explore the state of matter characterized by the charged timelike vector order parameter. We employ holographic duality in order to construct such a state and study its thermoelectric transport, fermionic spectral function and the sign of the Meissner effect. We uncover the unusual features of this "timelike superconductor": the absence of the gap in the fermionic spectrum and co-existence of Drude peak and supercurrent in the AC transport, which are reminiscent to those of time-reversal-odd and gapless superconductors, correspondingly. We show that this state is dynamically stable and thermodynamically at least metastable. Along the way we develop the holographic model of the charged vector field, which acquires mass due to a variant of the Stueckelberg mechanism with the adjoint Higgs field.

cond-mat.str-el↗

arXiv2023

Nodal-antinodal dichotomy from anisotropic quantum critical continua in holographic models

We demonstrate that the absence of stable quasiparticle excitations on parts of the Fermi surface, similar to the "nodal-antinodal dichotomy" in underdoped cuprate superconductors, can be reproduced in models of strongly correlated electrons defined via a holographic dual. We show analytically that the anisotropy of the quantum critical continuum, which is a feature of these models, may lead to washing out the quasiparticle peak in one direction while leaving it intact in the perpendicular one. The effect relies on the qualitatively different scaling of the self-energy in different directions. Using the explicit example of the anisotropic Q-lattice model, we demonstrate how this effect emerges due to specific features of the near horizon geometry of the black hole in the dual description.

cond-mat.str-el↗

arXiv2022

Thermoelectric transport properties of gapless pinned charge density waves

Quantum strongly correlated matter exhibits properties which are not easily explainable in the conventional framework of Fermi liquids. Universal effective field theory tools are applicable in these cases regardless of the microscopic details of the quantum system, since they are based on symmetries. It is necessary, however, to construct these effective tools in full generality, avoiding restrictions coming from particular microscopic descriptions which may inadequately constrain the coefficients that enter in the effective theory. In this work we demonstrate on explicit examples how the novel hydrodynamic coefficients which have been recently reinstated in the effective theory of pinned charge density waves (CDW) can affect the phenomenology of the thermo-electric transport in strongly correlated quantum matter. Our examples, based on two classes of holographic models with pinned CDW, have microscopics which are conceptually different from Fermi liquids. Therefore, the above novel transport coefficients are nonzero, contrary to the conventional approach. We show how these coefficients allow to take into account the change of sign of the Seebeck coefficient and the low resistivity of the CDW phase of the cuprate high temperature superconductors, without referring to the effects of Fermi surface reconstruction.

cond-mat.str-el↗

arXiv2020

Phase relaxation and pattern formation in holographic gapless charge density waves

We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a "gapless" algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge density wave and observed in holographic homogeneous lattice models. We follow the motion of the quasinormal modes across the dynamical phase transition in models with either periodic inhomogeneous or helical homogeneous spatial structures, showing that the phase relaxation rate is continuous at the critical temperature. Moreover, we find that the qualitative low-energy dynamics of the broken phase is universal, insensitive to the precise pattern of translation symmetry breaking, and therefore applies to homogeneous models as well.

hep-th↗

arXiv2020

Relaxation regimes of the holographic electrons at charge neutrality after a local quench of chemical potential

In this work we study the relaxation of the system of strongly correlated electrons, at charge neutrality, when the chemical potential undergoes a local change. This setup is a model for for the X-ray absorbtion edge study in the half-filled graphene. We use holographic duality to describe the system as a classical Schwarzschild black hole in curved 4-dimensional AdS spacetime. Assuming the amplitude of the quench is small, we neglect the backreaction on the geometry. We numerically study the two relaxation regimes: the adiabatic relaxation when the quench is slow and the relaxation governed by the quasinormal modes of the system, when the quench is fast. We confirm the expectation that the scale of separation between the slow and fast regimes is set by the characteristic frequency of the quasinormal modes.

hep-th↗

arXiv2020

Charge density response and fake plasmons in holographic models with strong translation symmetry breaking

We study the charge density response in holographic models with explicit translation symmetry breaking which is relevant in IR. In particular, we focus on Q-lattices and the Bianchy VII helix. We show that the hydrodynamic sound mode is removed from the spectrum due to the strong momentum relaxation and therefore, the usual treatment of the plasmon as Coulomb-dressed zero sound does not apply. Furthermore, the dominant coherent modes in the longitudinal channel, which control the neutral density-density correlator, are diffusive. We show these modes are strongly suppressed when the boundary Coulomb interaction is turned on. This renders the low frequency charge density response spectrum completely incoherent and featureless. At intermediate frequencies, we observe a broad feature -- the fake plasmon -- in the dressed correlator, which could be confused with an overdamped plasmon. However, its gap is set by the scale of translation symmetry breaking instead of the plasma frequency. This broad feature originates from the non-hydrodynamic sector of the holographic spectrum, and therefore, its behaviour, typical of strongly correlated quantum critical systems with holographic duals, deviates from the standard Fermi-liquid paradigm.

hep-th↗

arXiv2019

Isolated zeros destroy Fermi surface in holographic models with a lattice

We study the fermionic spectral density in a strongly correlated quantum system described by a gravity dual. In the presence of periodically modulated chemical potential, which models the effect of the ionic lattice, we explore the shapes of the corresponding Fermi surfaces, defined by the location of peaks in the spectral density at the Fermi level. We find that at strong lattice potentials sectors of the Fermi surface are unexpectedly destroyed and the Fermi surface becomes an arc-like disconnected manifold. We explain this phenomenon in terms of a collision of the Fermi surface pole with zeros of the fermionic Green's function, which are explicitly computable in the holographic dual.

hep-th↗

arXiv2019

Anisotropic destruction of the Fermi surface in inhomogeneous holographic lattices

We analyze fermionic response of strongly correlated holographic matter in presence of inhomogeneous periodically modulated potential mimicking the crystal lattice. The modulation is sourced by a scalar operator that explicitly breaks the translational symmetry in one direction. We compute the fermion spectral function and show that it either exhibits a well defined Fermi surface with umklapp gaps opening on the Brillouin zone boundary at small lattice wave vector, or, when the wave vector is large, the Fermi surface is anisotropically deformed and the quasiparticles get significantly broadened in the direction of translation symmetry breaking. Making use of the ability of our model to smoothly extrapolate to the homogeneous Q-lattice like setup, we show that this novel effect is not due to the periodic modulation of the potential and Umklapp physics, but rather due to the anisotropic features of the holographic horizon. That means it encodes novel physics of strongly correlated critical systems which may be relevant for phenomenology of exotic states of electron matter.

hep-th↗

arXiv2019

Anomalous attenuation of plasmons in strange metals and holography

The plasmon is a ubiquitous collective mode in charged liquids. Due to the long-range Coulomb interaction, the massless zero sound mode of the neutral system acquires a finite plasmon frequency in the long-wavelength limit. In the zero-temperature state of conventional metals -- the Fermi liquid -- the plasmon lives infinitely long at long wavelength when the system is (effectively) translationally invariant. In contrast, we will show that in strongly entangled strange metals the protection of zero sound fails at finite frequency and plasmons are always short lived regardless of their wavelength. Computing the explicit plasmon response in holographic strange metals as an example, we show that decay into the quantum critical continuum replaces Landau damping and this happens for any wavelength.

cond-mat.str-el↗

arXiv2019

Isolated zeros in the spectral function as signature of a quantum continuum

We study the observable properties of quantum systems which involve a quantum continuum as a subpart. We show in a very general way that in any system, which consists of at least two isolated states coupled to a continuum, the spectral function of one of the states exhibits an isolated zero at the energy of the other state. Several examples of quantum systems exhibiting such isolated zeros are discussed. Although very general, this phenomenon can be particularly useful as an indirect detection tool for the continuum spectrum in the lab realizations of quantum critical behavior.

cond-mat.str-el↗

arXiv2019

Coherent vs incoherent transport in holographic strange insulators

Holographic strange metals are known to have a power law resistivity rising with temperature, which is reminiscent of the strange metal phases in condensed matter systems. In some holographic models, however, the exponent of the power law in the resistivity can be negative. In this case one encounters phases with diverging resistivity at zero temperature: holographic strange insulators. These states arise as a result of translational symmetry breaking in the system, which can either be strong explicit and relevant in the IR, or spontaneous, but pinned by a small explicit source. In some regards, one can associate these two classes to the normal band insulators due to the strong ionic potential, and Mott insulator due to the commensurate lock in of the charge density wave. We study different features of these classes on the explicit example of a holographic helical model with homogeneous Bianchy VII type translational symmetry breaking, and uncover the main mechanisms underlying transport in these two cases. We find that while transport in the explicit relevant case is governed by the incoherent conductivity, in the pinned spontaneous case the leading contribution comes from the coherent part.

hep-th↗

arXiv2018

Holographic discommensurations

When the system with internal tendency to a spontaneous formation of a spatially periodic state is brought in contact with the external explicit periodic potential, the interesting phenomenon of commensurate lock in can be observed. In case when the explicit potential is strong enough and its period is close to the period of the spontaneous structure, the latter is forced to assume the periodicity of the former and the commensurate state becomes a thermodynamically preferred one. If instead the two periods are significantly different, the incommensurate state is formed. It is characterized by a finite density of solitonic objects -- discommensurations -- on top of the commensurate state. In this note I study the properties of discommensurations in holographic model with inhomogeneous translational symmetry breaking and explain how one can understand the commensurate/incommensurate phase transition as a proliferation of these solitons. Some useful numerical techniques are discussed in the Appendix.

hep-th↗

arXiv2018

Doping the holographic Mott insulator

Mott insulators form because of strong electron repulsions, being at the heart of strongly correlated electron physics. Conventionally these are understood as classical "traffic jams" of electrons described by a short-ranged entangled product ground state. Exploiting the holographic duality, which maps the physics of densely entangled matter onto gravitational black hole physics, we show how Mott-insulators can be constructed departing from entangled non-Fermi liquid metallic states, such as the strange metals found in cuprate superconductors. These "entangled Mott insulators" have traits in common with the "classical" Mott insulators, such as the formation of Mott gap in the optical conductivity, super-exchange-like interactions, and form "stripes" when doped. They also exhibit new properties: the ordering wave vectors are detached from the number of electrons in the unit cell, and the DC resistivity diverges algebraically instead of exponentially as function of temperature. These results may shed light on the mysterious ordering phenomena observed in underdoped cuprates.

hep-th↗

arXiv2018

Pinning of longitudinal phonons in holographic spontaneous helices

We consider the spontaneous breaking of translational symmetry and identify the associated Goldstone mode -- a longitudinal phonon -- in a holographic model with Bianchi VII helical symmetry. For the first time in holography, we observe the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of our setup. We study the dispersion relation of the resulting pseudo-Goldstone mode, uncovering how its speed and mass gap depend on the amplitude of the source and temperature. In addition, we extract the optical conductivity as a function of frequency, which reveals a metal-insulator transition as a consequence of the pinning.

hep-th↗

arXiv2018

Numerical Solution of the Boundary Value Problems for Partial Differential Equations. Crash course for holographer

These are the notes for a series of Numerical Study group meetings, held in Lorentz institute in the fall of 2017. The aim of the notes is to provide a non-specialist with the minimal knowledge in numerical methods used in BVP for PDEs, necessary to solve the problems typically arising in applications of holography to condensed matter systems. A graduate level knowledge of Linear Algebra and theory of Differential Equations is assumed. Special attention is payed to the treatment of the boundary conditions of general form. The notes focus on the practical aspects of the implementation leaving aside the theory behind the methods in use. A few simple problems to test the acquired knowledge are included.

hep-th↗

arXiv2017

Commensurate lock-in in holographic non-homogeneous lattices

We consider the spontaneous formation of striped structures in a holographic model which possesses explicit translational symmetry breaking, dual to an ionic lattice with spatially modulated chemical potential. We focus on the perturbative study of the marginal modes which drive the transition to a phase exhibiting spontaneous stripes. We study the wave-vectors of the instabilities with largest critical temperature in a wide range of backgrounds characterized by the period and the amplitude of the chemical potential modulation. We report the first holographic observation of the commensurate lock-in between the spontaneous stripes and the underlying ionic lattice, which takes place when the amplitude of the lattice is large enough. We also observe an incommensurate regime in which the amplitude of the lattice is finite, but the preferred stripe wave-vector is different from that of the lattice.

hep-th↗

arXiv2016

Commensurability effects in holographic homogeneous lattices

An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as "homogeneous holographic lattices." Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to correctly describe momentum relaxation and hence (finite) DC conductivities. However, it is not clear whether they are able to capture other lattice effects which are of interest in condensed matter. In this paper we investigate this question focusing our attention on the phenomenon of commensurability, which arises when the lattice scale is tuned to be equal to (an integer multiple of) another momentum scale in the system. We do so by studying the formation of spatially modulated phases in various models of homogeneous holographic lattices. Our results indicate that the onset of the instability is controlled by the near horizon geometry, which for insulating solutions does carry information about the lattice. However, we observe no sharp connection between the characteristic momentum of the broken phase and the lattice pitch, which calls into question the applicability of these models to the physics of commensurability.

hep-th↗

arXiv2015

Phases of holographic d-wave superconductor

We study different phases in the holographic model of d-wave superconductor. These are described by solutions to the classical equations of motion found in different ansatze. Apart from the known homogeneous d-wave superconducting phase we find three new solutions. Two of them represent two distinct families of the spatially modulated solutions, which realize the charge density wave phases in the dual theory. The third one is the new homogeneous phase with nonzero anapole moment. These phases are relevant to the physics of cuprate high-Tc superconductor in pseudogap region. While the d-wave phase preserves translation, parity and time reversal symmetry, the striped phases break translations spontaneously. Parity and time-reversal are preserved when combined with discrete half-periodic shift of the wave. In anapole phase translation symmetry is preserved, but parity and time reversal are spontaneously broken. All of the considered solutions brake the global $U(1)$. Thermodynamical treatment shows that in the simplest d-wave model the anapole phase is always preferred, while the stripe phases realize the continuous transition in solution space between the normal phase and two homogeneous condensed phases.

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