List of Papers
Kristine M. Lang

Practical Implementation of Dynamic Methods for Measuring Atomic Force Microscope Cantilever Spring Constants

S.M. Cook, T.E. Schäffer, K.M. Chynoweth, M. Wigton, R.W. Simmonds, and K.M. Lang

Nanotechnology March 2006 vol. 17 2135-2145
Measurement of atomic force microscope cantilever spring constants (k) is essential for many of the applications of this versatile instrument.  Numerous techniques to measure k have been proposed.  Of these, the thermal noise and Sader methods, stand out as being widely applicable and relatively user-friendly, providing an in situ, non-destructive, fast measurement of k for a cantilever independent of its material or coating.  Such advantages recommend these methods for widespread use.  An impediment thereto are the significant complications involved in the initial implementation of the methods.  Some details of the implementation are discussed in publications, while others are left unsaid.   Here we present a complete, cohesive, and practically-oriented discussion of implementation of both the thermal noise and Sader methods of measuring cantilever spring constants.  We review relevant theory and discuss practical experimental means for acquiring the required quantities.  We then present results which compare measurements of k by these two methods over nearly two orders of magnitude, and we discuss likely origins of both statistical and systematic error for both methods.  In conclusion, we find the two methods agree to within an average of 4 % over the wide range of cantilevers measured.  Given that the methods originate in distinct physics we find the agreement a compelling argument in favor of the accuracy of both, suggesting them as practical standards for the field.
Coincidence of Checkerboard Charge Order and Antinodal State Decoherence in Strongly Underdoped Superconducting Bi2Sr2CaCu2O8+d K. McElroy, D.-H. Lee, J. E. Hoffman, K.M. Lang, J. Lee, E.W. Hudson, H. Eisaki, S. Uchida, and J. C. Davis Physical Review Letters May 2005 vol. 94, no. 19 197005/1-4
The doping dependence of nanoscale electronic structure in superconducting Bi2Sr2CaCu2O8+d is studied by scanning tunneling microscopy. At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local ‘‘checkerboard’’ charge ordering of high energy states, with a wave vector of Q  = (+/-2p/4.5a0, 0); (0 ; +/-2p/4.5a0) +/- 15%. Surprisingly, this spatial ordering of high states coexists with the low energy Bogoliubov quasiparticle states.
Josephson Junction Materials Research Using Phase Qubits R.W. Simmonds, D.A. Hite, R. McDermott, M. Steffen, K.B. Cooper, K.M. Lang, John M. Martinis, D.P. Pappas Quantum Computation: solid state systems by P. Delsing, C. Granata, Y. Pashkin, B. Ruggiero and P. Silvestrini December 2004 Kluwer Academic Plenum Publishers
At present, the performance of superconducting qubits is limited by decoherence. Strong decoherence of phase qubits is associated with spurious microwave resonators residing within the Josephson junction tunnel barrier. In this work, we investigate three different fabrication techniques for producing tunnel junctions that vary the properties of the superconductor-insulator interface. Through experimental measurements, we characterize the junction and corresponding qubit quality. We find that there is a strong correlation between the morphology of oxidized base electrodes and the lowering of subgap currents in the junction I-V characteristics, while there is no noticeable improvement in the performance of fabricated phase qubits. Thus, “traditional” indicators of junction performance may not be enough to determine qubit performance. However, truly crystalline insulating barriers may be the key to improving Josephson junction based qubits.
Decoherence in Josephson Phase Qubits from Junction Resonators R.W. Simmonds, K.M. Lang, D. A. Hite, S. Nam, D. P. Pappas, and John M. Martinis Physical Review Letters August 2004 vol. 93, no. 7 077003/1-4
Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose ‘‘coherence amplitude’’ is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.
Conducting atomic force microscopy for nanoscale tunnel barrier characterization K.M. Lang, D. A. Hite, R.W. Simmonds, R. McDermott, D.P. Pappas, John M. Martinis Review of Scientific Instruments August 2004 vol. 75, no. 8 2726-2731
Increasing demands on nanometer-scale properties of oxide tunnel barriers necessitate a consistent means to assess them on these length scales. Conducting atomic force microscopy (CAFM) is a promising technique both for understanding connections between nanoscale tunnel barrier characteristics and macroscopic device performance as well as for rapid qualitative evaluation of new fabrication methods and materials. Here we report CAFM characterization of aluminum oxide (AlOx) barriers to be used in Josephson-junction qubits, with a particular emphasis on developing reproducible imaging conditions and appropriate interpretation. We find that control of the imaging force is a critical factor for reproducibility. We imaged the same sample on the same day with the same cantilever varying only the imaging force between scans. Statistical properties compiled from the resulting current maps varied approximately exponentially with imaging force, with typical currents increasing by two orders of magnitude for only a factor of 5 increase in imaging force. Given appropriate control of the imaging force, scan to scan variation of the current recorded at the same location was approximately ±0.5 Iavg, which establishes a criterion for statistical reproducibility of CAFM measurements. We further find that the appropriate interpretation for CAFM (under most imaging conditions), is as a probe of local propensity for insulator breakdown. Samples stored in air for weeks before study showed current features with oxidation times of order minutes. This indicates that these features were created by the scanning of the tip, and thus represent local pinhole susceptible regions. We finally present results for several AlOx samples showing that under appropriate imaging conditions significant sample to sample variation is observed, thus demonstrating the potential of this technique to qualitatively assess and facilitate understanding of potential qubit tunnel barrier devices.
Banishing quasiparticles from Josephson-junction qubits: why and how to do it. K.M. Lang, S. Nam, J. Aumentado,
C. Urbina, John M. Martinis
IEEE Transactions on Applied Superconductivity June 2003 vol.13, no.2 989-993
Current-biased Josephson junctions are prime candidates for the realization of quantum bits; however, a present limitation is their coherence time. In this paper it is shown qualitatively that quasiparticles create decoherence. We can decrease the number of quasiparticles present in the junctions by two methods - reducing the creation rate with current shunts and increasing the depletion rate with normal-metal traps. Experimental data demonstrate that both methods are required to significantly reduce the number of quasiparticles and increase the system's coherence. We conclude that these methods are effective and that the design of Josephson-junction qubits must consider the role of quasiparticles.
STM study of novel resonances in Bi2Sr2CaCu2O8+d E.W. Hudson, V. Madhavan, K. McElroy, J.E. Hoffman, K.M. Lang, H. Eisaki,
S. Uchida, J.C. Davis
Physica B May 11, 2003 vol.329-333, pt.2 1365-1366
Low temperature scanning tunneling microscopy (STM) of various samples of the high temperature superconductor Bi2Sr2CaCu2O8+d consistently reveals the presence of quasi-particle scattering resonances, similar both spectro-scopically and spatially to those observed around Zn atoms in Zn-doped BSCCO. As the resonances appear at energies indicative of nearly unitary scattering (~0.5 meV) and are always accompanied by topographic depression of the surface Bi atom around which they are centered, we postulate that the source of scattering may be Cu vacancies in the CuO2 plane, Such resonances should thus provide a simpler test case for theoretical models than those created by Zn or Ni substitution.
Vortex-induced quasi-particle 'checkerboard' in Bi2Sr2CaCu2O8+d J.E. Hoffman, E.W. Hudson, K.M. Lang, H. Eisaki, S. Uchida, J.C. Davis Physica C May 2003 vol. 388-389 703-704
Scanning tunneling microscopy is used to image the additional quasi-particle states generated by quantized vortices in the high-Tc superconductor Bi2Sr2CaCu2O8+d. They exhibit a Cu–O bond oriented 'checkerboard' pattern, with (4.2± 0.4) a0 periodicity and ~30 Å decay length.
Incommensurate, dispersive, density of states modulations in Bi2Sr2CaCu2O8+d K. McElroy , J.E. Hoffman, D.-H. Lee, K.M. Lang, H. Eisaki, S. Uchida, J.C. Davis Physica C May 2003 vol. 388-389 225-226
Scanning tunneling spectroscopy of Bi2Sr2CaCu2O8+d reveals weak, incommensurate, spatial modulations in the tunneling conductance. When images of these energy-dependent modulations are Fourier analyzed the dispersion of their wave vectors can be determined. Comparison of the dispersions with angle-resolved photoemission indicates that quasiparticle interference, due to elastic scattering between specific regions of the Fermi surface, provides a consistent explanation for the conductance modulations.
Decoherence of a superconducting qubit due to bias noise John M. Martinis, S. Nam, J. Aumentado, K.M. Lang, C. Urbina Physical Review B Mar 1, 2003 vol. 67 94510/1-10
We calculate for the current-biased Josephson junction the decoherence of the qubit state from noise and dissipation. The effect of dissipation can be entirely accounted for through a semiclassical noise model that appropriately includes the effect of zero-point and thermal fluctuations from dissipation. The magnitude and frequency dependence of this dissipation can be fully evaluated with this model to obtain design constraints for small decoherence. We also calculate decoherence from spin echo and Rabi control sequences and show they are much less sensitive to low-frequency noise than for a Ramsey sequence. We predict small decoherence rates from 1/f noise of charge, critical current, and flux based on noise measurements in prior experiments. Our results indicate this system is a good candidate for a solid-state quantum computer.
Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+d J.E. Hoffman, K. McElroy,D.-H. Lee,
K.M. Lang, H. Eisaki, S. Uchida, J.C. Davis
Science Aug 16, 2002 vol. 297 1148-1151
Scanning tunneling spectroscopy of the high-Tc superconductor Bi2Sr2CaCu2O8+d reveals weak, incommensurate, spatial modulations in the tunneling conductance. Images of these energy-dependent modulations are Fourier analyzed to yield the dispersion of their wavevectors. Comparison of the dispersions with photoemission spectroscopy data indicates that quasiparticle interference, due to elastic scattering between characteristic regions of momentum-space, provides a consistent explanation for the conductance modulations, without appeal to another order parameter. These results refocus attention on quasiparticle scattering processes as potential explanations for other incommensurate phenomena in the cuprates. The momentum-resolved tunneling spectroscopy demonstrated here also provides a new technique with which to study quasiparticles in correlated materials.
Imaging the granular structure of high Tc superconductivity in underdoped Bi2Sr2CaCu2O8+d K.M. Lang, V. Madhavan, J.E. Hoffman, E.W. Hudson, H. Eisaki, S. Uchida,
J.C. Davis
Nature Jan 24, 2002 vol. 415 412-416
Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions; Josephson tunnelling between the grains establishes the macroscopic superconducting state. Although crystals of the copper oxide high-transition-temperature (high-Tc) superconductors are not granular in a structural sense, theory suggests that at low levels of hole doping the holes can become concentrated at certain locations resulting in hole-rich superconducting domains. Granular superconductivity arising from tunnelling between such domains would represent a new view of the underdoped copper oxide superconductors. Here we report scanning tunnelling microscope studies of underdoped Bi2Sr2CaCu2O8+d that reveal an apparent segregation of the electronic structure into superconducting domains that are ~3 nm in size (and local energy gap <50 meV), located in an electronically distinct background. We used scattering resonances at Ni impurity atoms as 'markers' for local superconductivity; no Ni resonances were detected in any region where the local energy gap Delta >50 +or- 2.5 meV. These observations suggest that underdoped Bi2Sr2CaCu2O8+d is a mixture of two different short-range electronic orders with the long-range characteristics of a granular superconductor.
A four unit cell periodic pattern of quasiparticle states surrounding vortex cores in Bi2Sr2CaCu2O8+d J.E. Hoffman, E.W. Hudson, K.M. Lang,
V. Madhavan, H. Eisaki, S. Uchida,
J.C. Davis
Science Jan 18, 2002 vol. 295 466-469
Scanning tunneling microscopy is used to image the additional quasi-particle states generated by quantized vortices in the high critical temperature superconductor Bi2Sr2CaCu2O8+d. They exhibit a copper-oxygen bond-oriented "checkerboard" pattern, with four unit cell (4a0) periodicity and a ~30 angstrom decay length. These electronic modulations may be related to the magnetic field-induced, 8a0 periodic, spin density modulations with decay length of ~70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength lambda should be associated with a corresponding electronic modulation of wavelength lambda /2, in good agreement with our observations.
Nanoscale one-dimensional scattering resonances in the CuO chains of YBa2Cu3O6+x D.J. Derro, E.W. Hudson, K.M. Lang,
S.H. Pan, J.C. Davis, J.T. Markert,
A.L. de Lozanne
Physical Review Letters 2002 vol. 88 097002/1-4
Wepresent scanning tunneling spectroscopy measurements of the CuO chain plane in YBa2Cu3O6 + x, showing a ~25  meV gap in the local density of states (LDOS) filled by numerous intragap resonances: intense peaks in LDOS spectra associated with one-dimensional, Friedel-like oscillations. We discuss how these phenomena shed light on recent results from other probes, as well as their implications for phenomena in the superconducting CuO2 plane.
Scanning Tunneling Spectroscopy Study of Inhomogeneity, Granularity, and Segregation in the Electronic Structure of Bi2Sr2CaCu2O8+d  (27 MB) Kristine Michelle Lang Ph.D. Thesis,
U.C. Berkeley
Fall 2001
Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x S.H. Pan, J.P. O’Neal, R.L. Badzey, C. Chamon, H. Ding, J.R. Engelbrecht, Z. Wang, H. Eisaki, S. Uchida, A.K. Gupta, K.-W. Ng, E.W. Hudson, K.M. Lang, J.C. Davis. Nature Sep. 20, 2001 vol. 413 282-285
The parent compounds of the copper oxide high-transition-temperature (high-Tc) superconductors are unusual insulators (so-called Mott insulators). Superconductivity arises when they are 'doped' away from stoichiometry. For the compound Bi2Sr2CaCu2O8+x, doping is achieved by adding extra oxygen atoms, which introduce positive charge carriers ('holes') into the CuO2 planes where the superconductivity is believed to originate. Aside from providing the charge carriers, the role of the oxygen dopants is not well understood, nor is it clear how the charge carriers are distributed on the planes. Many models of high-Tc superconductivity accordingly assume that the introduced carriers are distributed uniformly, leading to an electronically homogeneous system as in ordinary metals. Here we report the presence of an electronic inhomogeneity in Bi2Sr2CaCu2O8+x, on the basis of observations using scanning tunnelling microscopy and spectroscopy. The inhomogeneity is manifested as spatial variations in both the local density of states spectrum and the superconducting energy gap. These variations are correlated spatially and vary on the surprisingly short length scale of 14 Å. Our analysis suggests that this inhomogeneity is a consequence of proximity to a Mott insulator resulting in poor screening of the charge potentials associated with the oxygen ions left in the BiO plane after doping, and is indicative of the local nature of the superconducting state.
Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+d E.W. Hudson, K.M. Lang, V. Madhavan, S.H. Pan, H. Eisaki, S. Uchida, J.C. Davis Nature June 21, 2001 vol. 411 920-924
Magnetic interactions and magnetic impurities are destructive to superconductivity in conventional superconductors. By contrast, in some unconventional macroscopic quantum systems (such as superfluid 3He and superconducting UGe2), the superconductivity (or superfluidity) is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high-temperature superconductivity. Within this context, the fact that magnetic Ni impurity atoms have a weaker effect on superconductivity than non-magnetic Zn atoms in the high-Tc superconductors has been put forward as evidence supporting a magnetic mechanism. Here we use scanning tunnelling microscopy to determine directly the influence of individual Ni atoms on the local electronic structure of Bi2Sr2CaCu2O8+d. At each Ni site we observe two d-wave impurity states of apparently opposite spin polarization, whose existence indicates that Ni retains a magnetic moment in the superconducting state. However, analysis of the impurity-state energies shows that quasiparticle scattering at Ni is predominantly non-magnetic. Furthermore, we show that the superconducting energy gap and correlations are unimpaired at Ni. This is in strong contrast to the effects of non-magnetic Zn impurities, which locally destroy superconductivity. These results are consistent with predictions for impurity atom phenomena derived from a magnetic mechanism.
A Detailed Scanning Tunneling Microscopy Study o f the CuO chains in YBa2Cu3O7-x D. J. Derro, E. W. Hudson, K. M. Lang,  S. H. Pan, J. C. Davis, K. Mochizuki, J. T. Markert, A. L. de Lozanne Physica C Nov 2000 vol. 341-348 425-428
We have previously reported a 1.36-nm DOS modulation in the CuO chains on the surface of cold- cleaved, atomically-resolved YBCO. We have recently completed new experiments in which we obtained detailed spectroscopic data on the same crystal plane, thereby confirming and extending our earlier work. Here we present data showing twin boundaries and steps, and focusing on the effects of these structures on the CuO chain DOS modulations.
Imaging the Effects of Individual Zinc Impurity Atoms on Superconductivity in Bi2Sr2CaCu2O8+d S.H. Pan, E.W. Hudson, K.M. Lang,
H. Eisaki, S. Uchida, J.C. Davis
Nature Feb 17, 2000 vol. 403 746-750
Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu2O8+d. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within 15 Å of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle 'cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.
STM of quasiparticle scattering resonances in Bi2Sr2CaCu2O8+d E.W. Hudson, S.H. Pan, K.M. Lang, A.K. Gupta, K.-W. Ng, J.C. Davis, Physica B Feb 2000 vol. 284-288 969-970
High-resolution, low-temperature scanning tunneling microscopy and spectroscopy on Bi2Sr2CaCu2O8+d reveal the existence of large numbers of scattering centers in this material. The spatial and spectroscopic characteristics of these features are consistent with theories of quasiparticle scattering from atomic scale impurities in a d-wave superconductor. These characteristics include breaking of local particle-hole symmetry and an inverse square dependence of their local density-of-states (LDOS) on distance from the scattering center. Furthermore, these observations identify a source for the anomalously high levels of low-energy excitations in Bi2Sr2CaCu2O8+d at low-temperatures.
Search for superconductivity in lithium K. M. Lang, A. Mizel, J. Mortara, E.W. Hudson, J. Hone, M.L. Cohen, A. Zettl, J.C. Davis Journal of Low Temperature Physics March 1999 vol. 114,     no. 5-6 445-454
We report on the results of a search for superconductivity in Li. We find no evidence for the predicted transition to superconductivity at any temperature down to 5 mK in magnetic fields down to 0.4 microT. However, an unexpected Curie- Weiss temperature dependence in the magnetic susceptibility is observed. We discuss the possibility that this signal arises from the Li itself, the possibility that it arises from Kondo behavior, and the implications of the effect for the predicted Tc of Li.