arXiv subjects

A. D. Mirlin

Publications and source records attributed to A. D. Mirlin.

At least 19 recordsLinked to original sources

arXiv2021

Resistance of 2D superconducting films

We consider the problem of finite resistance $R$ in superconducting films with geometry of a strip of width $W$ near zero temperature. The resistance is generated by vortex configurations of the phase field. In the first type of process, quantum phase slip, the vortex worldline in 2+1 dimensional space-time is space-like (i.e., the superconducting phase winds in time and space). In the second type, vortex tunneling, the worldline is time-like (i.e., the phase winds in the two spatial directions) and connects opposite edges of the film. For moderately disordered samples, processes of second type favor a train of vortices, each of which tunnels only across a fraction of the sample. Optimization with respect to the number of vortices yields a tunneling distance of the order of the coherence length $ξ$, and the train of vortices becomes equivalent to a quantum phase slip. Based on this theory, we find the resistance $\ln R \sim -g W/ξ$, where $g$ is the dimensionless normal-state conductance. Incorporation of quantum fluctuations indicates a quantum phase transition to an insulating state for $g \lesssim 1$.

cond-mat.supr-con↗

arXiv2021

Multifractally-enhanced superconductivity in thin films

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

cond-mat.mes-hall↗

arXiv2021

Entanglement entropy and particle number cumulants of disordered fermions

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

cond-mat.mes-hall↗

arXiv2021

From Anderson localization on Random Regular Graphs to Many-Body localization

The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the "most long-range" interaction. Central themes -- which are common to the RRG and MBL problems -- include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

cond-mat.dis-nn↗

arXiv2021

Anomalous Hydrodynamics in One Dimensional Electronic Fluid

We construct multi-mode viscous hydrodynamics for one dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In a four-mode regime, all modes are ballistic and acquire KPZ-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to $ω^{-1/3}$ scaling of its real part. In a three-mode regime, the system is in the universality class of classical viscous fluid[9,24]. Self-interaction of the sound modes results in KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to $ω^{-1/3}$ scaling of heat conductivity.

cond-mat.mes-hall↗

arXiv2019

Asymmetry of non-local dissipation: From drift-diffusion to hydrodynamics

We study dissipation in inhomogeneous two-dimensional electron systems. We predict a relatively strong current-induced spatial asymmetry in the heating of the electron and phonon systems -- even if the inhomogeneity responsible for the electrical resistance is symmetric with respect to the current direction. We also show that the heat distributions in the hydrodynamic and impurity-dominated limits are essentially different. In particular, within a wide, experimentally relevant interval of driving fields, the dissipation profile in the hydrodynamic limit turns out to be asymmetric, and the characteristic spatial scale of the temperature distribution can be controlled by the driving field. By contrast, in the same range of parameters, impurity-dominated heating is almost symmetric, with the size of the dissipation region being independent of the field. This allows one to distinguish experimentally the hydrodynamic and impurity-dominated limits. Our results are consistent with recent experimental findings on transport and dissipation in narrow constrictions and quantum point contacts.

cond-mat.mes-hall↗

arXiv2019

From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation

We analyze theoretically the conductivity of Weyl semimetals within the self-consistent Born approximation (SCBA) in the full range of disorder strength, from weak to strong disorder. In the range of intermediate disorder, we find a critical regime which separates the semimetal and diffusion regimes. While the numerical values of the critical exponents are not expected to be exact within the SCBA, the approach allows us to calculate functional dependences of various observables (density of states, quasiparticle broadening, conductivity) in a closed form. This sheds more light on the qualitative behavior of the conductivity and its universal features in disordered Weyl semimetals. In particular, we have found that the vertex corrections in the Kubo formula are of crucial importance in the regime of strong disorder and lead to saturation of the dc conductivity with increasing disorder strength. We have also analyzed the evolution of the optical conductivity with increasing disorder strength, including its scaling properties in the critical regime.

cond-mat.dis-nn↗

arXiv2019

Thermal Transport in One Dimensional Electronic Fluid

We study thermal conductivity for one-dimensional electronic fluid. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than bosonic Umklapp time, the momentum of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to $T / iω$. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by L{é}vy flights of low-momentum bosons that lead to a fractional scaling, $ω^{-\frac{1}{3}}$ and $L^{1/3}$, of heat conductivity with the frequency $ω$ and system size $L$ respectively.

cond-mat.str-el↗

arXiv2019

Critical behavior at the localization transition on random regular graphs

We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1 = 3$, with a box distribution of disorder and in the middle of the band (energy $E=0$), which is the model most frequently considered in the literature. As a first step, we carry out an accurate determination of the critical disorder, with the result $W_c =18.17\pm 0.01$. After this, we determine the dependence of the correlation volume $N_ξ= m^ξ$ (where $ξ$ is the associated correlation length) on disorder $W$ on the delocalized side of the transition, $W < W_c$, by means of population dynamics. The asymptotic critical behavior is found to be $ξ\propto (W_c-W)^{-1/2}$, in agreement with analytical prediction. We find very pronounced corrections to scaling, in similarity with models in high spatial dimensionality and with many-body localization transitions.

cond-mat.dis-nn↗

arXiv2018

Decay of plasmonic waves in Josephson junction chains

We study the damping of plasma waves in linear Josephson junction chains as well as in two capacitively coupled chains. In the parameter regime where the ground capacitance can be neglected, the theory of the antisymmetric mode in the double chain can be mapped onto the theory of a single chain. We consider two sources of relaxation: the scattering from quantum phase slips (QPS) and the interaction among plasmons related to the nonlinearity of the Josephson potential. The contribution to the relaxation rate $1/τ$ from the nonlinearity scales with the fourth power of frequency $ω$, while the phase-slip contribution behaves as a power law with a non-universal exponent. In the parameter regime where the charging energy related to the junction capacitance is much smaller than the Josephson energy, the amplitude of QPS is strongly suppressed. This makes the relaxation mechanism related to QPS efficient only at very low frequencies. As a result, for chains that are in the infrared limit on the insulating side of the superconductor-insulator transition, the quality factor $ωτ$ shows a strongly non-monotonic dependence on frequency, as was observed in a recent experiment.

cond-mat.supr-con↗

arXiv2018

Statistics of eigenstates near the localization transition on random regular graphs

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes $N$ below the correlation volume $N_ξ$ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length $ξ\sim \log N_ξ$ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast "diffusion" which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. Spectral correlations in the delocalized phase near the transition are characterized by level number variance $Σ_2(ω)$ crossing over, with increasing freqyency $ω$, from ergodic behavior $Σ_2=\left(2/π^2\right)\lnω/Δ$ to $Σ_2\propto ω^2$ at $ω_c\sim (N N_ξ)^{-1/2}$ and finally to Poissonian behavior $Σ_2 = ω/Δ$ at $ω_ξ\sim N_ξ^{-1}$. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate $d\to\infty$ limit of the Anderson model in $d$ spatial dimensions.

cond-mat.dis-nn↗

arXiv2018

Many-body localization transition with power-law interactions: Statistics of eigenstates

We study spectral and wavefunction statistics for many-body localization transition in systems with long-range interactions decaying as $1/r^α$ with an exponent $α$ satisfying $ d \le α\le 2d$, where $d$ is the spatial dimensionality. We refine earlier arguments and show that the system undergoes a localization transition as a function of the rescaled disorder $W^* = W / L^{2d-α} \ln L$, where $W$ is the disorder strength and $L$ the system size. This transition has much in common with that on random regular graphs. We further perform a detailed analysis of the inverse participation ratio (IPR) of many-body wavefunctions, exploring how ergodic behavior in the delocalized phase switches to fractal one at the critical point and on the localized side of the transition. Our analytical results for the scaling of the critical disorder $W$ with the system size $L$ and for the scaling of IPR in the delocalized and localized phases are supported and corroborated by exact diagonalization of spin chains.

cond-mat.dis-nn↗

arXiv2018

Long lifetimes of ultra-hot particles in interacting Fermi systems

The energy dependence of the relaxation rate of hot electrons due to interaction with the Fermi sea is studied. We consider 2D and 3D systems, quasi-1D quantum wires with multiple transverse bands, as well as single-channel 1D wires. Our analysis includes both spinful and spin-polarized setups, with short-range and Coulomb interactions. We show that, quite generally, the relaxation rate is a non-monotonic function of the electron energy and decays as a power-law at high energies. In other words, ultra-hot electrons regain their coherence with increasing energy. Such a behavior was observed in a recent experiment on multi-band quantum wires, J. Reiner et al, Phys. Rev. X {\bf 7}, 021016 (2017).

cond-mat.mes-hall↗

arXiv2018

Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene

We demonstrate that a key elastic parameter of a suspended crystalline membrane---the Poisson ratio (PR) $ν$---is a non-trivial function of the applied stress $σ$ and of the system size $L$, i.e., $ν=ν_L(σ)$. We consider a generic 2D membrane embedded into space of dimensionality $2+d_c$. (The physical situation corresponds to $d_c=1$.) A particularly important application of our results is free-standing graphene. We find that at very low stress, where the membrane exhibits a linear response, the PR $ν_L(0)$ decreases with increasing $L$ and saturates for $ L\to \infty$ at a value which depends on the boundary conditions and is essentially different from the value $ν=-1/3$ previously predicted by the membrane theory within a self-consisted scaling analysis. By increasing $σ$, one drives a membrane into a non-linear regime characterized by a universal value of PR that depends solely on $d_c.$ This universal non-linear PR acquires its minimum value $ν_{\rm min}=-1$ in the limit $d_c\to \infty.$ With the further increase of $σ$, the PR changes sign and finally saturates at a positive non-universal value prescribed by the conventional elasticity theory. We also show that one should distinguish between the absolute and differential PR ($ν$ and $ν^{\rm diff}$, respectively). While coinciding in the limits of very low and very high stresses, they differ in general, $ν\neq ν^{\rm diff}$. In particular, in the non-linear universal regime, $ν^{\rm diff}$ takes a universal value which, similarly to absolute PR, is a function solely of $d_c$ but is different from the universal value of $ν$. In the limit $d_c\to \infty$, the universal value of $ν^{\rm diff}$ tends to $-1/3$, at variance with the limiting value $-1$ of $ν$. Finally, we briefly discuss generalization of these results to a disordered membrane.

cond-mat.mes-hall↗

arXiv2018

Differential Poisson's ratio of a crystalline two-dimensional membrane

We compute the differential Poisson's ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality $d \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the differential Poisson's ratio approaches a universal value determined solely by the spatial dimensionality $d_c$, with a power-law expansion $ν= -1/3 + 0.016/d_c + O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous literature holds only in the limit $d_c\to \infty$.

cond-mat.mes-hall↗

arXiv2017

Multifractality of wave functions on a Cayley tree: From root to leaves

We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree) from the central site ("root") to the boundary ("leaves"). We show that the eigenfunction moments $P_q=N \left<|ψ|^{2q}(i)\right>$ exhibit a multifractal scaling $P_q\propto N^{-τ_q}$ with the volume (number of sites) $N$ at $N\to\infty$. The multifractality spectrum $τ_q$ depends on the strength of disorder and on the parameter $s$ characterizing the position of the observation point $i$ on the lattice. Specifically, $s= r/R$, where $r$ is the distance from the observation point to the root, and $R$ is the "radius" of the lattice. We demonstrate that the exponents $τ_q$ depend linearly on $s$ and determine the evolution of the spectrum with increasing disorder, from delocalized to the localized phase. Analytical results are obtained for the $n$-orbital model with $n \gg 1$ that can be mapped onto a supersymmetric $σ$ model. These results are supported by numerical simulations (exact diagonalization) of the conventional ($n=1$) Anderson tight-binding model.

cond-mat.dis-nn↗

arXiv2017

Superconductor-Insulator Transition in disordered Josephson junction chains

We study the superconductor-insulator quantum phase transition in disordered Josephson junction chains. To this end, we derive the field theory from the lattice model that describes a chain of superconducting islands with a capacitive coupling to the ground ($C_0$) as well as between the islands ($C_1$). We analyze the theory in the short-range ($C_1 \ll C_0$) and in the long-range ($C_1 \gg C_0$) limits. The transition to the insulating state is driven by the proliferation of quantum phase slips. The most important source of disorder originates from trapped charges in the substrate that suppress the coherence of phase slips, thus favoring superconducting correlations. Using the renormalization-group approach, we determine the phase diagram and evaluate the temperature dependence of the dc conductivity and system-size dependence of the resistance around the superconductor-insulator transition. These dependences have in general strongly non-monotonic character, with several distinct regimes reflecting an intricate interplay of superconductivity and disorder.

cond-mat.supr-con↗

arXiv2017

Resonant supercollisions and electron-phonon heat transfer in graphene

We study effects of strong impurities on the heat transfer in a coupled electron-phonon system in disordered graphene. A detailed analysis of the electron-phonon heat exchange assisted by such an impurity through the 'resonant supercollision' mechanism is presented. We further explore the local modification of heat transfer in a weakly disordered graphene due to a resonant scatterer and determine spatial profiles of the phonon and electron temperature around the scatterer under electrical driving. Our results are consistent with recent experimental findings on imaging resonant dissipation from individual atomic defects.

cond-mat.mes-hall↗