arXiv subjects

A. D. Mirlin

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

At least 37 records · Page 2Linked to original sources

arXiv2017

Transmission through a potential barrier in Luttinger liquids with a topological spin gap

We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy Luttinger liquid theory is gapped by interaction. This phase is of particular interest since it exhibits non-trivial interaction-induced topological properties. Using bosonization and an expansion in the tunneling strength, we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping the fractional spin the edge states can absorb or emit spinons and thus enable single electron tunneling across the impurity even though the bulk spectrum for these excitations is gapped. This results in a finite LDOS below the bulk gap and in a non-monotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase---which combines features of a topological spin insulator and a topological charge metal---in which the topology can be probed by measuring transport properties.

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arXiv2017

Transversal magnetoresistance and Shubnikov-de Haas oscillations in Weyl semimetals

We explore theoretically the magnetoresistance of Weyl semimetals in transversal magnetic fields away from charge neutrality. The analysis within the self-consistent Born approximation is done for the two different models of disorder: (i) short-range impurties and (ii) charged (Coulomb) impurities. For these models of disorder, we calculate the conductivity away from charge neutrality point as well as the Hall conductivity, and analyze the transversal magnetoresistance (TMR) and Shubnikov-de Haas oscillations for both types of disorder. We further consider a model with Weyl nodes shifted in energy with respect to each other (as found in various materials) with the chemical potential corresponding to the total charge neutrality. In the experimentally most relevant case of Coulomb impurities, we find in this model a large TMR in a broad range of quantizing magnetic fields. More specifically, in the ultra-quantum limit, where only the zeroth Landau level is effective, the TMR is linear in magnetic field. In the regime of moderate (but still quantizing) magnetic fields, where the higher Landau levels are relevant, the rapidly growing TMR is supplemented by strong Shubnikov-de Haas oscillations, consistent with experimental observations.

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arXiv2017

Mesoscopic fluctuations of the local density of states in interacting electron systems

We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron-electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to Anderson-Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron-electron attraction. In both cases strong mesoscopic fluctuations of the local density of states exist.

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arXiv2017

Hydrodynamic approach to electronic transport in graphene

The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. In this paper we briefly review the recent advances, both theoretical and experimental, in the hydrodynamic approach to electronic transport in graphene, focusing on viscous phenomena, Coulomb drag, non-local transport measurements, and possibilities for observing nonlinear effects.

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arXiv2017

Transport in a disordered $ν=2/3$ fractional quantum Hall junction

Electric and thermal transport properties of a $ν=2/3$ fractional quantum Hall junction are analyzed. We investigate the evolution of the electric and thermal two-terminal conductances, $G$ and $G^Q$, with system size $L$ and temperature $T$. This is done both for the case of strong interaction between the 1 and 1/ 3 modes (when the low-temperature physics of the interacting segment of the device is controlled by the vicinity of the strong-disorder Kane-Fisher-Polchinski fixed point) and for relatively weak interaction, for which the disorder is irrelevant at $T=0$ in the renormalization-group sense. The transport properties in both cases are similar in several respects. In particular, $G(L)$ is close to 4/3 (in units of $e^2/h$) and $G^Q$ to 2 (in units of $πT / 6 \hbar$) for small $L$, independently of the interaction strength. For large $L$ the system is in an incoherent regime, with $G$ given by 2/3 and $G^Q$ showing the Ohmic scaling, $G^Q\propto 1/L$, again for any interaction strength. The hallmark of the strong-disorder fixed point is the emergence of an intermediate range of $L$, in which the electric conductance shows strong mesoscopic fluctuations and the thermal conductance is $G^Q=1$. The analysis is extended also to a device with floating 1/3 mode, as studied in a recent experiment [A. Grivnin et al, Phys. Rev. Lett. 113, 266803 (2014)].

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arXiv2017

Spectral diffusion and scaling of many-body delocalization transitions

We analyze the role of spectral diffusion in the problem of many-body delocalization in quantum dots and in extended systems. The spectral diffusion parametrically enhances delocalization, modifying the scaling of the delocalization threshold with the interaction coupling constant.

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arXiv2016

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

We explore thermodynamics of a quantum membrane, with a particular application to suspended graphene membrane and with a particular focus on the thermal expansion coefficient. We show that an interplay between quantum and classical anharmonicity-controlled fluctuations leads to unusual elastic properties of the membrane. The effect of quantum fluctuations is governed by the dimensionless coupling constant, $g_0 \ll 1$, which vanishes in the classical limit ($\hbar \to 0$) and is equal to $\simeq 0.05$ for graphene. We demonstrate that the thermal expansion coefficient $α_T$ of the membrane is negative and remains nearly constant down to extremely low temperatures, $T_0\propto \exp (-2/g_0)$. We also find that $α_T$ diverges in the classical limit: $α_T \propto - \ln(1/g_0)$ for $g_0 \to 0$. For graphene parameters, we estimate the value of the thermal expansion coefficient as $α_T \simeq - 0.23\:{\rm eV}^{-1}$, which applies below the temperature $T_{\rm uv} \sim g_0 \varkappa_0 \sim 500$\:K (where $\varkappa_0 \sim 1$\:eV is the bending rigidity) down to $T_0 \sim 10^{-14}$\:K. For $T<T_0$, the thermal expansion coefficient slowly (logarithmically) approaches zero with decreasing temperature. This behavior is surprising since typically the thermal expansion coefficient goes to zero as a power-law function. We discuss possible experimental consequences of this anomaly. We also evaluate classical and quantum contributions to the specific heat of the membrane and investigate the behavior of the Grüneisen parameter.

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arXiv2016

Absence of many-body localization in a continuum

We show that many-body localization, which exists in tight-binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many-body localization does not survive the unbounded growth of the single-particle localization length with increasing energy that is characteristic of the continuum limit. The system remains delocalized down to arbitrarily small temperature $T$, although its dynamics slows down as $T$ decreases. Remarkably, the conductivity vanishes with decreasing $T$ faster than in the Arrhenius law. The system can be characterized by an effective $T$-dependent single-particle mobility edge which diverges in the limit of $T\to 0$. Delocalization is driven by interactions between hot electrons above the mobility edge and the "bath" of thermal electrons in the vicinity of the Fermi level.

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arXiv2016

Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary

We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally tree-like structure without a boundary (random regular graph) where extended wavefunctions are ergodic.

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arXiv2016

Anomalous Hooke's law in disordered graphene

The discovery of graphene, a single monolayer of graphite, has closed the discussion on stability of 2D crystals. Although thermal fluctuations of such crystals tend to destroy the long-range order in the system, the crystal can be stabilized by strong anharmonicity effects. This competition is the central issue of the crumpling transition, i.e., a transition between flat and crumpled phases. We show that anharmonicity-controlled fluctuations of a graphene membrane around equilibrium flat phase lead to unusual elastic properties. In particular, we demonstrate that stretching $ξ$ of a flake of graphene is a nonlinear function of the applied tension at small tension: ${ξ\proptoσ^{η/(2-η)}}$ and ${ξ\proptoσ^{η/(8-η)}}$ for clean and strongly disordered graphene, respectively. Conventional linear Hooke's law, ${ξ\proptoσ}$ is realized at sufficiently large tensions: ${σ\ggσ_*},$ where $σ_*$ depends both on temperature and on the disorder strength.

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arXiv2016

Lévy flights due to anisotropic disorder in graphene

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed back-scattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent $T$-matrix approximation.

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arXiv2016

Energy transport in the Anderson insulator

We study the heat conductivity in Anderson insulators in the presence of power-law interaction. Particle-hole excitations built on localized electron states are viewed as two-level systems randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport through this network and evaluate the thermal conductivity. For physically relevant cases of 2D and 3D spin systems with $1/r^3$ dipole-dipole interaction (originating from the conventional $1/r$ Coulomb interaction between electrons), the found thermal conductivity $κ$ scales with temperature as $κ\propto T^3 $ and $κ\propto T^{4/3}$, respectively. Our results may be of relevance also to other realizations of random spin Hamiltonians with long-range interactions.

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arXiv2016

Anderson localization on random regular graphs

A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from small ($N\ll N_c$) to large ($N\gg N_c$) system, where $N_c$ is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wavefunction statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly non-trivial. Our results support an analytical prediction that states in the delocalized phase (and at $N\gg N_c$) are ergodic in the sense that their inverse participation ratio scales as $1/N$.

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arXiv2016

Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the non-linear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore 2D systems that would be Anderson insulators in the absence of interaction and 2D or 3D systems that undergo Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature $T_c$) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions -- especially, in the regime when $T_c$ is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approaches the SIT.

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arXiv2016

Many-body delocalization transition and relaxation in a quantum dot

We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state", a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.

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arXiv2015

Rippling and crumpling in disordered free-standing graphene

Graphene is a famous realization of elastic crystalline 2D membrane. Thermal fluctuations of a 2D membrane tend to destroy the long-range order in the system. Such fluctuations are stabilized by strong anharmonicity effects, which preserve thermodynamic stability. The anharmonic effects demonstrate critical behaviour on scales larger than the Ginzburg scale. In particular, clean suspended flake of graphene shows a power-law increase of the bending rigidity with the system size, $\varkappa\propto L^η,$ due to anharmonic interaction between in-plane and out-of-plane (flexural) phonon modes. We demonstrate that random fluctuations of membrane curvature caused by static disorder may change dramatically the scaling of the bending rigidity and lead to a non-monotonous dependence of $\varkappa$ on $L.$ We derive coupled RG describing combined flow of $\varkappa$ and effective disorder strength $b$, find a critical curve $b(\varkappa)$ separating flat and crumpled phases, and explore the behavior of disorder in the flat phase. Deep in the flat phase, disorder decays in a power-law way at scales larger than the Ginzburg length which therefore sets a characteristic size for the ripples--static out-of-plane deformations observed experimentally in suspended graphene. We find that in the limit $L \to \infty $ ripples are characterized by anomalous exponent $2η$ in contrast to dynamical fluctuations governed by $η$. For sufficiently strong disorder, there exists an intermediate range of spatial scales where ripples decay much slower, with exponent $η/4$. In the near-critical regime, the membrane shows fractal properties implying a multiple folding starting from a certain length scale $L_1$ and finally flattens at a much larger scale $L_2$ (which diverges at criticality). We conclude the paper by a comparison of our results with available experimental data on graphene ripples.

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arXiv2015

Transversal magnetoresistance in Weyl semimetals

We explore theoretically the magnetoresistvity of three-dimensional Weyl and Dirac semimetals in transversal magnetic fields within two alternative models of disorder: (i) short-range impurities and (ii) charged (Coulomb) impurities. Impurity scattering is treated using the self-consistent Born approximation. We find that an unusual broadening of Landau levels leads to a variety of regimes of the resistivity scaling in the temperature-magnetic field plane. In particular, the magnetoresitance is non-monotonous for the white-noise disorder model. For $H\to 0$ the magnetoresistance for short-range impurities vanishes in a non-analytic way as $H^{1/3}$. In the limits of strongest magnetic fields $H$, the magnetoresistivity vanishes as $1/H$ for pointlike impurities, while it is linear and positive in the model with Coulomb impurities.

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arXiv2015

Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films

We develop a theory for the vortex unbinding transition in homogeneously disordered superconducting films. This theory incorporates the effects of quantum, mesoscopic and thermal fluctuations stemming from length scales ranging from the superconducting coherence length down to the Fermi wavelength. In particular, we extend the renormalization group treatment of the diffusive nonlinear sigma model to the superconducting side of the transition. Furthermore, we explore the mesoscopic fluctuations of parameters in the Ginzburg-Landau functional. Using the developed theory, we determine the dependence of essential observables (including the vortex unbinding temperature, the superconducting density, as well as the temperature-dependent resistivity and thermal conductivity) on microscopic characteristics such as the disorder-induced scattering rate and bare interaction couplings.

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