T. Nattermann - Academia.edu (original) (raw)

Papers by T. Nattermann

The zero temperature phase diagram of Cooper pairs exposed to disorder and magnetic field is foun... more The zero temperature phase diagram of Cooper pairs exposed to disorder and magnetic field is found to exhibit four distinct phases: a Bose and a Fermi insulating, a metallic and a superconducting phase, respectively. The results explain the giant negative magneto-resistance found experimentally in In-O, TiN, Bi and high-$T_c$ materials.

Physica A: Statistical Mechanics and its Applications, 2004

The position of an interface (domain wall) in a medium with random pinning defects is not determi... more The position of an interface (domain wall) in a medium with random pinning defects is not determined unambiguously by a current value of the driving force even in average. Based on general theory of the interface motion in a random medium we study this hysteresis, different possible shapes of domain walls and dynamical phase transitions between them. Several principal characteristics of the hysteresis, including the coercive force and the curves of dynamical phase transitions obey scaling laws and display a critical behavior in a vicinity of the mobility threshold. At finite temperature the threshold is smeared and a new range of thermally activated hysteresis appears. At a finite frequency of the driving force there exists a range of the non-adiabatic regime, in which not only the position, but also the average velocity of the domain wall displays hysteresis.

Comptes Rendus de l'Académie des Sciences - Series IV - Physics, 2001

Bose-Einstein condensates confined in traps exhibit unique features which have been the object of... more Bose-Einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. In this paper I will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems.

AIP Conference Proceedings, 2009

ABSTRACT The localization-disorder paradigm is analyzed for a specific system of weakly repulsive... more ABSTRACT The localization-disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that, at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long-range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes non-ergodic at very low density. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose-systems.This article is an extended version of a presentation delivered by one of the authors (V.L.P.) at a Conference on Modern Trends in Theoretical Physics dedicated to the Lev Landau Centenary (Chernogolovka, Russia, June 2008).

Physical Review B, 1992

ABSTRACT

Bulletin of the American Physical Society, 2010

A theory of the hysteresis loop in ferromagnets controlled by the domain wall motion is presented... more A theory of the hysteresis loop in ferromagnets controlled by the domain wall motion is presented. Domain walls are considered as plane or linear interfaces moving in a random medium under the action of the external ac magnetic field H = H0 sin ωt. We introduce important characteristics of the hysteresis loop, such as dynamic threshold fields, reversal field etc. together with well known characteristics as coercive field and hysteresis loop area (HLA) A. We show that all these characteristics are regulated by two dimensionless combinations of the H0 and ω and intrinsic characteristics of the ferromagnet. The moving domain wall can create magnetic bubbles playing the role of pre-existing nuclei of the reversed magnetization. We discuss a simple model of this process. For magnetization reversal determined by domain inflation we predict that HLA scales as A ∝ ω β H α 0 with α = 1/2 and β = 1/2. Numerical simulations confirm this result.

Physical Review B, 2018

An asymptotically exact theory of spectrum and transverse distribution of magnetization in long-w... more An asymptotically exact theory of spectrum and transverse distribution of magnetization in long-wave magnons is presented. It is based on exact analytical solution of linearized Landau-Lifshitz equation in a film. The quantization of the transverse wave vector and role of evanescent waves at different values of parameters and wave vectors is studied.

Zeitschrift f�r Physik B Condensed Matter, 1991

We analyze the influence of thermal and frozen-in disorder on the flux line (FL) density p oc(H-H... more We analyze the influence of thermal and frozen-in disorder on the flux line (FL) density p oc(H-H~)~ close to the lower critical field H~ 1. Arguments which consider the steric repulsion of fluctuating FLs give/7= (d-1)~/ 2(1-~) with ~ the roughness exponent of a single FL and d the space dimensionality. We show by a phenomenological scaling approach and a renormalization group treatment, that this is correct only for d<d~-2/~-1, i.e. for/7< 1. For d > dc the steric FL repulsion at scales more than some critical one is irrelevant and fi= 1. For disordered superconductors d~=2 and /7= 1 for d=2, 3. We also found the melting line for a FL lattice in the presence of frozen-in impurities close to

Series on Directions in Condensed Matter Physics, 1997

A review is given on some recent developments in the theory of the Ising model in a random field.... more A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

Physical Review Letters, 2008

Le Journal de Physique IV, 1999

Physical Review Letters, 1998

Physical Review Letters, 2006

It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects... more It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects as twin or grain boundaries. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher

EPL (Europhysics Letters), 2014

PACS 75.10.-b-General theory and models of magnetic ordering PACS 75.60.-d-Domain effects, magnet... more PACS 75.10.-b-General theory and models of magnetic ordering PACS 75.60.-d-Domain effects, magnetization curves, and hysteresis PACS 75.70.Kw-Domain structure (including magnetic bubbles and vortices) Abstract-Recently completely new types of domain walls (DWs) have been discovered in helical magnets, consisting generically of a regular array of pairs of magnetic vortex lines [1]. Only for special orientations DWs are free of vortices. In this article we calculate their elastic and pinning properties, using the pitch angle θ as a small parameter. In particular we show that vortex free DWs exhibit long range elasticity which makes them very stiff and suppresses their pinning by impurities. Their roughening transition temperature is of the order of the Néel temperature. DWs including vortices (either by orientation or due to step formation above their roughening transition) show short range elasticity and strong pinning by impurities. These results apply both to centro-symmetric as well as to non-centrosymmetric systems. The application to chiral liquid crystals is briefly discussed.

EPL (Europhysics Letters), 2009

Very diluted Bose gas placed into a disordered environment falls into a fragmented localized stat... more Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.

Physical Review Letters, 2014

The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytica... more The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

The European Physical Journal B-Condensed …, 1999

Abstract: In pure anisotropic or layered superconductors thermal fluctuations induce a van der Wa... more Abstract: In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order ...

Physical Review Letters, 2006

A long one-dimensional wire with a finite density of strong random impurities is modelled as a ch... more A long one-dimensional wire with a finite density of strong random impurities is modelled as a chain of weakly coupled quantum dots. At low temperature T and applied voltage V its resistance is limited by "breaks": randomly occuring clusters of quantum dots with a special length distribution pattern that inhibits the transport. Due to the interplay of interaction and disorder effects the resistance can exhibit T and V dependences that can be approximated by power laws. The corresponding two exponents differ greatly from each other and depend not only on the intrinsic electronic parameters but also on the impurity distribution statistics.

The zero temperature phase diagram of Cooper pairs exposed to disorder and magnetic field is foun... more The zero temperature phase diagram of Cooper pairs exposed to disorder and magnetic field is found to exhibit four distinct phases: a Bose and a Fermi insulating, a metallic and a superconducting phase, respectively. The results explain the giant negative magneto-resistance found experimentally in In-O, TiN, Bi and high-$T_c$ materials.

Physica A: Statistical Mechanics and its Applications, 2004

The position of an interface (domain wall) in a medium with random pinning defects is not determi... more The position of an interface (domain wall) in a medium with random pinning defects is not determined unambiguously by a current value of the driving force even in average. Based on general theory of the interface motion in a random medium we study this hysteresis, different possible shapes of domain walls and dynamical phase transitions between them. Several principal characteristics of the hysteresis, including the coercive force and the curves of dynamical phase transitions obey scaling laws and display a critical behavior in a vicinity of the mobility threshold. At finite temperature the threshold is smeared and a new range of thermally activated hysteresis appears. At a finite frequency of the driving force there exists a range of the non-adiabatic regime, in which not only the position, but also the average velocity of the domain wall displays hysteresis.

Comptes Rendus de l'Académie des Sciences - Series IV - Physics, 2001

Bose-Einstein condensates confined in traps exhibit unique features which have been the object of... more Bose-Einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. In this paper I will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems.

AIP Conference Proceedings, 2009

ABSTRACT The localization-disorder paradigm is analyzed for a specific system of weakly repulsive... more ABSTRACT The localization-disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that, at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long-range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes non-ergodic at very low density. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose-systems.This article is an extended version of a presentation delivered by one of the authors (V.L.P.) at a Conference on Modern Trends in Theoretical Physics dedicated to the Lev Landau Centenary (Chernogolovka, Russia, June 2008).

Physical Review B, 1992

ABSTRACT

Bulletin of the American Physical Society, 2010

A theory of the hysteresis loop in ferromagnets controlled by the domain wall motion is presented... more A theory of the hysteresis loop in ferromagnets controlled by the domain wall motion is presented. Domain walls are considered as plane or linear interfaces moving in a random medium under the action of the external ac magnetic field H = H0 sin ωt. We introduce important characteristics of the hysteresis loop, such as dynamic threshold fields, reversal field etc. together with well known characteristics as coercive field and hysteresis loop area (HLA) A. We show that all these characteristics are regulated by two dimensionless combinations of the H0 and ω and intrinsic characteristics of the ferromagnet. The moving domain wall can create magnetic bubbles playing the role of pre-existing nuclei of the reversed magnetization. We discuss a simple model of this process. For magnetization reversal determined by domain inflation we predict that HLA scales as A ∝ ω β H α 0 with α = 1/2 and β = 1/2. Numerical simulations confirm this result.

Physical Review B, 2018

An asymptotically exact theory of spectrum and transverse distribution of magnetization in long-w... more An asymptotically exact theory of spectrum and transverse distribution of magnetization in long-wave magnons is presented. It is based on exact analytical solution of linearized Landau-Lifshitz equation in a film. The quantization of the transverse wave vector and role of evanescent waves at different values of parameters and wave vectors is studied.

Zeitschrift f�r Physik B Condensed Matter, 1991

We analyze the influence of thermal and frozen-in disorder on the flux line (FL) density p oc(H-H... more We analyze the influence of thermal and frozen-in disorder on the flux line (FL) density p oc(H-H~)~ close to the lower critical field H~ 1. Arguments which consider the steric repulsion of fluctuating FLs give/7= (d-1)~/ 2(1-~) with ~ the roughness exponent of a single FL and d the space dimensionality. We show by a phenomenological scaling approach and a renormalization group treatment, that this is correct only for d<d~-2/~-1, i.e. for/7< 1. For d > dc the steric FL repulsion at scales more than some critical one is irrelevant and fi= 1. For disordered superconductors d~=2 and /7= 1 for d=2, 3. We also found the melting line for a FL lattice in the presence of frozen-in impurities close to

Series on Directions in Condensed Matter Physics, 1997

A review is given on some recent developments in the theory of the Ising model in a random field.... more A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

Physical Review Letters, 2008

Le Journal de Physique IV, 1999

Physical Review Letters, 1998

Physical Review Letters, 2006

It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects... more It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects as twin or grain boundaries. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher

EPL (Europhysics Letters), 2014

PACS 75.10.-b-General theory and models of magnetic ordering PACS 75.60.-d-Domain effects, magnet... more PACS 75.10.-b-General theory and models of magnetic ordering PACS 75.60.-d-Domain effects, magnetization curves, and hysteresis PACS 75.70.Kw-Domain structure (including magnetic bubbles and vortices) Abstract-Recently completely new types of domain walls (DWs) have been discovered in helical magnets, consisting generically of a regular array of pairs of magnetic vortex lines [1]. Only for special orientations DWs are free of vortices. In this article we calculate their elastic and pinning properties, using the pitch angle θ as a small parameter. In particular we show that vortex free DWs exhibit long range elasticity which makes them very stiff and suppresses their pinning by impurities. Their roughening transition temperature is of the order of the Néel temperature. DWs including vortices (either by orientation or due to step formation above their roughening transition) show short range elasticity and strong pinning by impurities. These results apply both to centro-symmetric as well as to non-centrosymmetric systems. The application to chiral liquid crystals is briefly discussed.

EPL (Europhysics Letters), 2009

Very diluted Bose gas placed into a disordered environment falls into a fragmented localized stat... more Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.

Physical Review Letters, 2014

The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytica... more The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

The European Physical Journal B-Condensed …, 1999

Abstract: In pure anisotropic or layered superconductors thermal fluctuations induce a van der Wa... more Abstract: In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order ...

Physical Review Letters, 2006

A long one-dimensional wire with a finite density of strong random impurities is modelled as a ch... more A long one-dimensional wire with a finite density of strong random impurities is modelled as a chain of weakly coupled quantum dots. At low temperature T and applied voltage V its resistance is limited by "breaks": randomly occuring clusters of quantum dots with a special length distribution pattern that inhibits the transport. Due to the interplay of interaction and disorder effects the resistance can exhibit T and V dependences that can be approximated by power laws. The corresponding two exponents differ greatly from each other and depend not only on the intrinsic electronic parameters but also on the impurity distribution statistics.