arXiv subjects

Leon Balents

Publications and source records attributed to Leon Balents.

At least 199 records · Page 11Linked to original sources

arXiv2004

Spin Relaxation in a Two-Dimensional Electron Gas in a Perpendicular Magnetic Field

We consider the problem of spin relaxation in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field. We assume that the spin relaxation is induced by the Rashba spin-orbit (SO) interaction, which appears due to the inversion asymmetry of the confining potential. Our solution is based on a microscopic evaluation of the spin density response function of the 2DEG with impurities and SO interaction. We derive explicit expressions for the transverse and longitudinal spin relaxation rates. Our analysis shows, in particular, that the spin relaxation rates exhibit {\it magnetoquantum oscillations}, which are analogous to the Shubnikov-de Haas oscillations of the electrical resistivity. These oscillations can be observed, for example, in time-resolved optical experiments.

cond-mat.mes-hall↗

arXiv2003

Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm

We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice antiferromagnet between the Neel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second order quantum phase transition. The critical theory is not expressed in terms of the order parameters characterizing either state (as would be the case in Landau-Ginzburg-Wilson theory) but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half-filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z_2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.

cond-mat.str-el↗

arXiv2003

Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems

We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the field theory reveals the glassy nature of the dynamics, in particular divergent barriers and barrier distributions controling the spectrum of relaxation times. A naive single relaxation time approximation for each wavevector is found to be unsatisfactory. A second approximation based on a random friction model, yields a size (L) dependent log-normal distribution of relaxation times (mean barriers ~L^θand variance ~ L^{θ/2}) and a procedure to estimate dynamical scaling functions. Finally, we study the full structure of the running dynamical effective action within the field theory. We find that relaxation time distributions are non-trivial (broad but not log-normal) and encoded in a closed hierarchy of FRG equations. A thermal boundary layer ansatz (TBLA) appears as a consistent solution. It extends the one discovered in the statics which was shown to embody droplet thermal fluctuations. Although perturbative control remains a challenge, the structure of the dynamical TBLA which encodes barrier distributions opens the way for deeper understanding of the field theory approach to glasses.

cond-mat.dis-nn↗

arXiv2003

Charge accumulation on a Luttinger liquid

The average charge Q on a quantum wire, modeled as a single-channel Luttinger liquid, connected to metallic leads and coupled to a gate is studied theoretically. We find that the behavior of the charge as the gate voltage V_G varies depends strongly on experimentally adjustable parameters (length, contact transmission, temperature,...). When the intrinsic backscattering at the contacts is weak (i.e. the conductance is close to 2e^2/h at high temperature), we predict that this behavior should be described by a universal function. For short such wires, the charge increases roughly linearly with V_G, with small oscillations due to quantum interference between electrons scattered at the contacts. For longer wires at low temperature, Coulomb blockade behavior sets in, and the charge increases in steps. In both limits $\partial Q/\partial V_G$, which should characterize the linear response conductance, exhibits periodic peaks in V_G. We show that due to Coulomb interactions the period in the former limit is twice that of the latter, and describe the evolution of the peaks through this crossover. The study can be generalized to multi-channel Luttinger liquids, and may explain qualitatively the recent observation by Liang et al (Phys. Rev. Lett. 88, 126801) of a four-electron periodicity for electron addition in single-walled carbon nanotubes.

cond-mat.str-el↗

arXiv2003

Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet

We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z-axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground state wavefunction with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a novel fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing S^z = 0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as novel U(1) topological order. This state is stable to ALL zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wavefunction. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.

cond-mat.str-el↗

arXiv2003

"Deconfined" quantum critical points

The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or more phases and usually breaks a symmetry of the Hamiltonian. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. In this paper we show that near second order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm. We present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional `confining' order parameters. Nevertheless, the critical theory contains a new emergent gauge field, and `deconfined' degrees of freedom associated with fractionalization of the order parameters. We suggest that this new paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems.

cond-mat.str-el↗

arXiv2003

Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime

We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity $σ_{xy}^{AH}$. We show that $σ_{xy}^{AH}$ is proportional to the first derivative of the density of states $\varrho(ε)$ and thus can be expected to change sign as a function of impurity band filling. We also show that $σ_{xy}^{AH}$ depends on temperature as the longitudinal conductivity $σ_{xx}$ within logarithmic accuracy.

cond-mat.mes-hall↗

arXiv2003

The Roton Fermi Liquid

We introduce and analyze a novel metallic phase of two-dimensional (2d) electrons, the Roton Fermi Liquid (RFL), which, in contrast to the Landau Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a re-formulation of 2d electrons consisting of fermionic quasiparticles and $hc/2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e. roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable new quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order (ODQLRO) at zero temperature (T=0), but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance {\it vanishes} as $T \to 0$ with a power of temperature (and frequency), $R(T) \sim T^γ$ (with $γ>1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau Fermi liquid. Electrons can, however, scatter anomalously from rotonic "current fluctuations'' and "superconducting fluctuations'', leading to "hot" and "cold" spots. Fermionic quasiparticles dominate the Hall electrical transport. We also discuss instabilities of the RFL to a conventional Fermi liquid and a superconductor. Precisely {\it at} the instability into the Fermi liquid state, the exponent $γ=1$, so that $R(T) \sim T$. Upon entering the superconducting state the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phenomenology might apply to the cuprates.

cond-mat.str-el↗

arXiv2003

Phase Diagram for Quantum Hall Bilayers at $ν=1$

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at total filling factor $ν=1$, based on exact numerical calculations of the topological Chern number matrix and the (inter-layer) superfluid density. We find three phases: a quantized Hall state with pseudo-spin superfluidity, a quantized Hall state with pseudo-spin ``gauge-glass'' order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.

cond-mat.mes-hall↗

arXiv2003

Fabry-Perot interference and spin filtering in carbon nanotubes

We study the two-terminal transport properties of a metallic single-walled carbon nanotube with good contacts to electrodes, which have recently been shown [W. Liang et al, Nature 441, 665-669 (2001)] to conduct ballistically with weak backscattering occurring mainly at the two contacts. The measured conductance, as a function of bias and gate voltages, shows an oscillating pattern of quantum interference. We show how such patterns can be understood and calculated, taking into account Luttinger liquid effects resulting from strong Coulomb interactions in the nanotube. We treat back-scattering in the contacts perturbatively and use the Keldysh formalism to treat non-equilibrium effects due to the non-zero bias voltage. Going beyond current experiments, we include the effects of possible ferromagnetic polarization of the leads to describe spin transport in carbon nanotubes. We thereby describe both incoherent spin injection and coherent resonant spin transport between the two leads. Spin currents can be produced in both ways, but only the latter allow this spin current to be controlled using an external gate. In all cases, the spin currents, charge currents, and magnetization of the nanotube exhibit components varying quasiperiodically with bias voltage, approximately as a superposition of periodic interference oscillations of spin- and charge-carrying ``quasiparticles'' in the nanotube, each with its own period. The amplitude of the higher-period signal is largest in single-mode quantum wires, and is somewhat suppressed in metallic nanotubes due to their sub-band degeneracy.

cond-mat.mes-hall↗

arXiv2003

XY ring-exchange model on the triangular lattice

We study ring-exchange models for bosons or XY-spins on the triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbour exchange, fluctuations select a four-fold ferrimagnetically ordered ground state with a small spin/superfluid stiffness which breaks the global U(1) and translational symmetry. We explore consequences for phase transitions at finite temperature and in an in-plane magnetic field.

cond-mat.supr-con↗

arXiv2002

Spin Precession and Oscillations in Mesoscopic Systems

We compare and contrast magneto-transport oscillations in the fully quantum (single-electron coherent) and classical limits for a simple but illustrative model. In particular, we study the induced magnetization and spin current in a two-terminal double-barrier structure with an applied Zeeman field between the barriers and spin disequilibrium in the contacts. Classically, the spin current shows strong tunneling resonances due to spin precession in the region between the two barriers. However, these oscillations are distinguishable from those in the fully coherent case, for which a proper treatment of the electron phase is required. We explain the differences in terms of the presence or absence of coherent multiple wave reflections.

cond-mat.mes-hall↗

arXiv2002

Andreev current in finite sized carbon nanotubes

We investigate the effect of interactions on Andreev current at a normal-superconducting junction when the normal phase is a Luttinger liquid with repulsive interactions. In particular, we study the system of a finite sized carbon nanotube placed between one metallic and one superconducting lead. We show that interactions and finite size effects give rise to significant deviations from the standard picture of Andreev current at a normal- superconductor junction in the nearly perfect Andreev limit.

cond-mat.str-el↗

arXiv2002

Field theory of statics and dynamics of glasses: rare events and barrier distributions

We study thermally activated dynamics using functional renormalization within the field theory of randomly pinned elastic systems, a prototype for glasses. It appears through an essentially non-perturbative boundary layer in the running effective action, for which we find a consistent scaling ansatz to all orders. We find that in the statics the boundary layer describes the physics of rare low energy metastable states as suggested by a phenomenological droplet picture. The extension to equilibrium dynamics mandates a non-trivial broad distribution of relaxation times for the large scale modes, hitherto neglected in analytic calculations.

cond-mat.dis-nn↗

arXiv2002

Ring exchange, the Bose metal, and bosonization in two dimensions

Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase which underlies the spin-charge separation scenario for high-T_c superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the *Bose metal*. The Bose metal is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the Bose metal with the aid of an exact plaquette duality transformation, which motivates a universal low energy description of the Bose metal. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well-known one-dimensional bosonization approach. We verify the validity of the low energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-T_c superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two dimensional fermionic ring model.

cond-mat.str-el↗

arXiv2002

Quantum entanglement in carbon nanotubes

With the surge of research in quantum information, the issue of producing entangled states has gained prominence. Here, we show that judiciously bringing together two systems of strongly interacting electrons with vastly differing ground states - the gapped BCS superconductor and the Luttinger liquid, - can result in quantum entanglement. We propose three sets of measurements involving single-walled metallic carbon nanotubes (SWNT) which have been shown to exhibit Luttinger liquid physics, to test our claim and as nanoscience experiments of interest in and of themselves.

cond-mat.str-el↗

arXiv2001

Spin Transport in a Quantum Wire

We study the effect of electron-electron backscattering interactions on spin transport in a quantum wire. Even if these interactions have no significant effect on charge transport, they strongly influence the transport of spin. We use the quantum Boltzmann equation in the collision approximation to derive equations of motion for spin current and magnetization. In the limit of small perturbations from equilibrium, we explain the existence of `precessional' and `diffusive' behaviors. We also discuss the low-temperature non-linear decay of an uniform spin current outside the hydrodynamic regime.

cond-mat.str-el↗

arXiv2001

Field theory for generalized Shastry-Sutherland models

We consider the bosonic dimer representation for Generalized Shastry-Sutherland models that have the same symmetries as the original Shastry-Sutherland model and preserve the exact dimer eigenstate. Various phases with differing types of magnetic order are found within mean-field theory for the corresponding low-energy effective dimer field theory. Transitions are allowed between any of these mean-field phases, which are dimer bose condensates, and with the dimer phase, which is the dimer bose vacuum. The Neel state, absent from this mean-field study, is described as a bosonic Mott insulator induced by the coupling to the underlying lattice. Moreover, dimer bose condensates with local Neel order are found to be unstable to spiral states. Instead of a direct phase transition between the dimer and the Neel phases, we propose an intermediate weakly incommensurate spin-density wave (WISDW) phase. The stability of the mean-field transitions is studied by renormalization techniques in d=2, the upper critical dimension. While the transition from the Neel phase is found to be stable, the transition point from the dimer phase is not perturbatively accessible. We argue that the latter renormalization results point to the possibility of an intermediate phase of a different kind.

cond-mat↗