K. S. D. Beach

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

Abstract We describe a general procedure to calibrate the detection of a nano/micro-mechanical resonator’s displacement as it undergoes thermal Brownian motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function, which is identical in all situations aside from a system-dependent effective mass value. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.

Determining Intrachain Diffusion Coefficients for Biopolymer Dynamics from Single-Molecule Force Spectroscopy Measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.

High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers

We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1/2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete bilayer), each with intra- and inter-plane couplings J and J_perp. We discuss the ground-state finite-size scaling properties of three different quantities--the Binder moment ratio, the spin stiffness, and the long-wavelength magnetic susceptibility--which we use to extract the critical value of the coupling ratio g=J_perp/J. The individual estimates of g_c are consistent provided that subleading finite-size corrections are properly taken into account. In the case of the complete bilayer, the Binder ratio leads to the most precise estimate of the critical coupling, although the subleading finite-size corrections to the stiffness are considerably smaller. For the incomplete bilayer, the subleading corrections to the stiffness are extremely small, and this quantity then gives the best estimate of the critical point. Contrary to predictions, we do not find a universal prefactor of the 1/L spin stiffness scaling at the critical point, whereas the Binder ratio is consistent with a universal value. Our results for the critical coupling ratios are g_c=2.52181(3) (full bilayer) and g_c=1.38882(2) (incomplete bilayer), which represent improvements of two orders of magnitude relative to the previous best estimates. For the correlation length exponent we obtain nu = 0.7106(9), consistent with the expected 3D Heisenberg universality class.

Field-induced antiferromagnetism in the Kondo insulator.

The Kondo lattice model, augmented by a Zeeman term, serves as a useful model of a Kondo insulator in an applied magnetic field. A variational mean field analysis of this system on a square lattice, backed up by quantum Monte Carlo calculations, reveals an interesting separation of magnetic field scales. For Zeeman energy comparable to the Kondo energy, the spin gap closes and the system develops transverse staggered magnetic order. The charge gap, however, remains robust up to a higher hybridization energy scale, at which point the canted antiferromagnetism is exponentially suppressed and the system crosses over to a nearly metallic regime. Quantum Monte Carlo simulations support this mean field scenario. An interesting rearrangement of spectral weight with magnetic field is found.

Mean Field study of the heavy fermion metamagnetic transition

We investigate the evolution of the heavy fermion ground state under application of a strong external magnetic field. We present a richer version of the usual hybridization mean field theory that allows for hybridization in both the singlet and triplet channels and incorporates a self-consistent Weiss field. We show that for a magnetic field strength B ⋆ , a filling-dependent fraction of the zerofield hybridization gap, the spin up quasiparticle band becomes fully polarized—an event marked by a sudden jump in the magnetic susceptibility. The system exhibits a kind of quantum rigidity in which the susceptibility (and several other physical observables) are insensitive to further increases in field strength. This behavior ends abruptly with the collapse of the hybridization order parameter in a first-order transition to the normal metallic state. We argue that the feature at B ⋆ corresponds to the “metamagnetic transition” in YbRh2Si2. Our results are in good agreement with recent experimental measurements.

Some formal results for the valence bond basis

Abstract In a system with an even number of SU ( 2 ) spins, there is an overcomplete set of states—consisting of all possible pairings of the spins into valence bonds—that spans the S = 0 Hilbert subspace. Operator expectation values in this basis are related to the properties of the closed loops that are formed by the overlap of valence bond states. We construct a generating function for spin correlation functions of arbitrary order and show that all nonvanishing contributions arise from configurations that are topologically irreducible. We derive explicit formulas for the correlation functions at second, fourth, and sixth order. We then extend the valence bond basis to include triplet bonds and discuss how to compute properties that are related to operators acting outside the singlet sector. These results are relevant to analytical calculations and to numerical valence bond simulations using quantum Monte Carlo, variational wavefunctions, or exact diagonalization.

SU(N) Heisenberg model on the square lattice: A continuous-N quantum Monte Carlo study

A quantum phase transition is typically induced by tuning an external parameter that appears as a coupling constant in the Hamiltonian. Another route is to vary the global symmetry of the system, generalizing, e.g., SU(2) to SU(N). In that case, however, the discrete nature of the control parameter prevents one from identifying and characterizing the transition. We show how this limitation can be overcome for the SU(N) Heisenberg model with the help of a singlet projector algorithm that can treat N continuously. On the square lattice, we find a direct, continuous phase transition between Neel-ordered and crystalline bond-ordered phases at Nc=4.57(5) with critical exponents z=1 and beta/nu=0.81(3).

High-Q Gold and Silicon Nitride Bilayer Nanostrings

Low-mass, high-Q, silicon nitride nanostrings are at the cutting edge of nanomechanical devices for sensing applications. Here we show that the addition of a chemically functionalizable gold overlayer does not adversely affect the Q of the fundamental out-of-plane mode. Instead the device retains its mechanical responsiveness while gaining sensitivity to molecular bonding. Furthermore, differences in thermal expansion within the bilayer give rise to internal stresses that can be electrically controlled. In particular, an alternating current (AC) excites resonant motion of the nanostring. This AC thermoelastic actuation is simple, robust, and provides an integrated approach to sensor actuation.

Coherence and metamagnetism in the two-dimensional Kondo lattice model

We report the results of dynamical mean field calculations for the metallic Kondo lattice model subject to an applied magnetic field. High-quality spectral functions reveal that the picture of rigid, hybridized bands, Zeeman-shifted in proportion to the field strength, is qualitatively correct. We find evidence of a zero-temperature magnetization plateau, whose onset coincides with the chemical potential entering the spin up hybridization gap. The plateau appears at the field scale predicted by (static) large-N mean field theory and has a magnetization value consistent with that of x=1-n_c spin-polarized heavy holes, where n_c < 1 is the conduction band filling of the noninteracting system. We argue that the emergence of the plateau at low temperature marks the onset of quasiparticle coherence.

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

High-stress silicon nitride nanostrings are a promising system for sensing applications because of their ultra-high mechanical quality factors (Qs). By performing thermomechanical calibration across multiple vibrational modes, we are able to assess the roles of the various dissipation mechanisms in these devices. Specifically, we possess a set of nanostrings in which all measured modes fall upon a single curve of peak displacement versus frequency. This allows us to rule out bulk bending and intrinsic loss mechanisms as dominant sources of dissipation and to conclude that the most significant contribution to dissipation in high-stress nanostrings occurs at the anchor points.