Session L54: Supersolids and Band Structure in Strongly Correlated Systems

Re-investigating Solid Helium under DC Rotation with a Rigid Torsional Oscillator

The resonant period drop observed in a torsional oscillator (TO) containing solid helium first interpreted as the signature of supersolid is now generally accepted as the shear modulus change of solid helium at low temperature. However, there are still several aspects in solid helium that remain unresolved. For instance, the striking DC rotation effect on the TO experiments was observed without altering the shear modulus of solid helium. The DC rotation is not expected to change the elastic property of solid helium while it can destroy superfluidity. Therefore, the DC rotation effect was considered as the strong evidence of superfluidity in solid helium. Here, we re-examine the effect of DC rotation by utilizing a rigidly constructed TO. Previous DC rotation experiments were performed with a TO exhibiting high reduction ratio of the period, which can be attributed to non-ideal construction of the TO. It is plausible that the resonance period and dissipation of non-ideal TO can be more susceptible to environmental vibration caused by the DC rotation. The response of the rigid TO under DC rotation will be reported to test the validity of the previous interpretation thoroughly.   

Mass Flux Measurements in Solid $^4$He

There has been considerable attention given to solid helium over the past decade. Our approach to study the solid has been to sandwich solid helium between two reservoirs of superfluid helium. With this approach, we found and explored the characteristics of mass flux that takes place from one reservoir to the other\footnote{M.W. Ray and R.B. Hallock, Phys. Rev. Letters 100, 235301 (2008); 105, 145301 (2010); Phys. Rev. B 79, 224302 (2009).}. We observed flow that has the characteristics of one-dimensional conductivity\footnote{Ye. Vekhov and R.B. Hallock, Phys. Rev. Letters 109, 045303 (2012); Phys. Rev. B 90, 134511 (2014).} and we have documented the effects that various concentrations of $^3$He impurity have on the temperature dependence of the flow\footnote{Ye. Vekhov, W.J. Mullin and Hallock, Phys. Rev. Letters 113, 035302 (2014); Ye. Vekhov and R.B Hallock, Phys. Rev. B 92, 104509 (2015).} These experiments continue and we will report on this work and new results that may be available.   

Mass flow in bulk solid $^4$He

Experiments with solid $^4$He and liquid confined in vycor pores have shown an unexpected mass flow in both “liquid-solid-liquid” and “solid-liquid-solid” junctions. In both configurations, non-thermally activated flow emerges below 600 mK. The flow rate increases as the temperature decreases, then drops suddenly at a temperature around 100 mK. This drop in flow rate is related to the $^3$He impurity concentration in the samples and prevents us from studying the flow’s intrinsic behavior at the lowest temperatures. We have now modified our measurement technique, in which solid helium is compressed at one end of a cell and flow is observed as a pressure response at the opposite end. By removing the vycor from our cell, we have eliminated liquid $^4$He and the liquid-solid interfaces which complicated the interpretation of earlier experiments. We find that similar mass flow occurs with only bulk solid $^4$He present. When we reduced the $^3$He concentration to the level of a few parts per trillion, we were able to measure the intrinsic flow rate down to lower temperatures, with no evidence of a drop in flow down to at least 25 mK.   

Superclimbing instability in solid Helium-4

The accumulation of matter in solid $^4$He observed in the UMASS group and dubbed as the syringe effect is discussed within the model of dislocations with superfluid core beyond the linear approximation. Such dislocations are found to be unstable with respect to the syringe effect if biased by chemical potential above a threshold $\mu_c \approx Gb^4/L$, where $G$ is the shear modulus, $b$ - Burgers vector and $L$ - free length of a dislocation. In almost perfect crystals, where $L$ can be as long as several $\mu$m or even longer, the threshold is $macroscopically$ small - corresponding to overpressures smaller than few mbar. This effect for edge dislocations has its high temperature analog - Bardeen-Herring instability of dislocations due to diffusive high temperature vacancy transport. For screw dislocations the instability develops through helix formation first observed in Si at high temperatures by W. C. Dash (1958). In solid $^4$He the vacancy diffusion is replaced by the supertransport along dislocation cores. The instability should cause formation of the superfluid dislocation forest leading to the superflow-through-solid effect first observed in the UMASS group. Several testable predictions with respect to the bias and time dependence for the syringe dynamics are made.   

Analysis of recent observations of ultrasound propagation in solid $^4$He

Extensive measurements have been made on the propagation of 10 MHz ultrasound in solid $^4$He. When the sound excitation level is low, sudden shifts in both the sound propagation velocity and attenuation are observed below 100 mK but the sudden shifts disappear when the excitation level is sufficiently high. The detailed response depends on the ultrasound excitation level and thermal history. The observations are analyzed in terms of the Granato-L\"{u}cke theory on the effects of dislocation line motion on the propagation of sound. The effects of pinning of dislocation lines by $^3$He impurities are included in the analysis. Parameters such as the average dislocation length, the dislocation line density, the dissipation coefficient and the impurity binding energy that are extracted by fitting the data to theory will be discussed.   

$^{\mathrm{4}}$He adsorption on a $^{\mathrm{3}}$He-plated graphite surface

Path-integral Monte Carlo (PIMC) calculations have been performed for $^{\mathrm{4}}$He atoms on top of the $^{\mathrm{3}}$He first layer on graphite. For this we ignore Fermi statistics of solidified $^{\mathrm{3}}$He adatoms while Bose statistics of $^{\mathrm{4}}$He atoms are fully incorporated. We first find that the first $^{\mathrm{3}}$He layer exhibits a 7/12 commensurate solid structure at the areal density of 0.111 {\AA}$^{\mathrm{-2}}$, which turns out to be identical to the experimental value for its completion density. Additional adsorption of $^{\mathrm{4}}$He atoms above the complete first $^{\mathrm{3}}$He layer is found to sustain the underlying $^{\mathrm{3}}$He commensurate structure and the second $^{\mathrm{4}}$He layer is observed to display the 4/7 commensurate structure with respect to the first-layer commensurate $^{\mathrm{3}}$He solid at the areal density of 0.0636 {\AA}$^{\mathrm{-2}}$. Furthermore, it is found that the 4/7 commensurate structure of the second-layer $^{\mathrm{4}}$He atoms can be formed above a mixture of the first-layer $^{\mathrm{3}}$He and $^{\mathrm{4}}$He atoms on graphite. These PIMC results suggest that the 4/7 commensurate structure of the second-layer $^{\mathrm{4}}$He atoms on graphite, whose existence on top of the first $^{\mathrm{4}}$He layer has long been in dispute, may be realized on a $^{\mathrm{3}}$He-plated graphite surface. This could lead to a new approach to observe two-dimensional supersolidity in $^{\mathrm{4}}$He on graphite.   

Thermodynamics of the Noninteracting Bose Gas in a Two-Dimensional Box

Bose-Einstein condensation (BEC) of a noninteracting Bose gas of $N$ particles in a two-dimensional (2D) box with Dirichlet boundary conditions is studied. Confirming previous work, we find that BEC occurs at finite $N$ at low temperatures $T$ without the occurrence of a phase transition. We further show that the crossover temperature between weak and strong increases in BEC upon cooling is $T_{\rm E} \sim 1/\log(N)$ at fixed area per boson, so in the thermodynamic limit there is no significant BEC in 2D at finite $T$. Calculations of thermodynamic properties versus $T$ and area $A$ are presented, including Helmholtz free energy, entropy $S$, pressure $p$, ratio of $p$ to the energy density $U/A$, heat capacity at constant area $C_{\rm V}$ and at constant pressure $C_{\rm p}$, isothermal compressibility $\kappa_{\rm T}$ and thermal expansion coefficient $\alpha_{\rm p}$, obtained using both the grand canonical ensemble (GCE) and canonical ensemble (CE) formalisms. The GCE formalism gives acceptable predictions for $S$, $p$, $p/(U/A)$, $\kappa_{\rm T}$ and $\alpha_{\rm p}$ at large $N$, $T$ and $A$, but fails when $N$ is small or BEC is significant, whereas the CE formalism gives accurate results even at low $T$ and/or $A$ where BEC occurs.   

Characterizing Featureless Mott Insulating State by Quasiparticle Interferences - A DMFT Prospect

In this talk we discuss the quasiparticle interferences (QPIs) of a Mott insulator using a T-matrix formalism implemented with the dynamical mean-field theory (T-DMFT). In the Mott insulating state, the DMFT predicts a singularity in the real part of electron self energy s (w) at low frequencies [1], which completely washes out the QPI at small bias voltage. However, the QPI patterns produced by the non-interacting Fermi surfaces can appear at a critical bias voltage in Mott insulating state. The existence of this non-zero critical bias voltage is a direct consequence of the singular behavior of Re[s (w)] /sim n/w with n behaving as the 'order parameter' of Mott insulating state. We propose that this reentry of non-interacting QPI patterns could serve as an experimental signature of Mott insulating state, and the 'order parameter' can be experimentally measured [2]. [1] A. Georges et al, Rev. Mod. Phys. 68, 13 (1996). [2] Shantanu Mukherjee, and Wei-Cheng Lee, Arxiv: 1504.05214 (2015).   

Band Theory for the Electronic and Magnetic Properties of VO$_{2}$ Phases

VO$_{2}$ is widely studied for the insulator-metal transition between the monoclinic M1 (insulator) and rutile R (metal) phases. Recent experiments show that in addition to the M1 and R phases, VO$_{2}$ has a rich phase diagram including a recently identified metallic monoclinic phase, making the material particularly intriguing. The origin of the band gap in the insulating phase of VO$_{2}$ has been a subject of debate. It was suggested that the insulating phase cannot be described by band theory and thus strong correlations must be invoked. However, recent band calculations using density functional theory (DFT) with a hybrid functional and standard pseudopotentials correctly obtains a band gap for the M1 insulating phase. Subsequent calculations, however, found that the magnetic properties of VO$_{2}$ phases are not correctly described by such calculations. Here we present DFT calculations using a tuned hybrid functional and hard pseudopotentials that reproduce both the band gaps and the magnetic properties of the known VO$_{2}$ phases. Thus, it is appropriate to use band theory to describe VO$_{2}$ phases without invoking strong correlations. Furthermore, using the band theory treatment, we identify a candidate for the metallic monoclinic phase.   

A minimal model for the structural energetics of VO$_2$

Resolving the structural, magnetic, and electronic structure of VO$_2$ from the first-principles of quantum mechanics is still a forefront problem despite decades of attention. Hybrid functionals have been shown to qualitatively ruin the structural energetics. While density functional theory (DFT) combined with cluster extensions of dynamical mean-field theory (DMFT) have demonstrated promising results in terms of the electronic properties, structural phase stability has not yet been addressed. In order to capture the basic physics of the structural transition, we propose a minimal model of VO$_2$ based on the one dimensional Peierls-Hubbard model and parameterize this based on DFT calculations of VO$_2$. The total energy versus dimerization in the minimal mode is then solved numerically exactly using density matrix renormalization group (DMRG) and compared to the Hartree-Fock solution. We demonstrate that the Hartree-Fock solution exhibits the same pathologies as DFT+U, and spin density functional theory for that matter, while the DMRG solution is consistent with experimental observation. Our results demonstrate the critical role of non-locality in the total energy, and this will need to be accounted for to obtain a complete description of VO$_2$ from first-principles.   

Ab Initio Infrared Spectra and Electronic Response Calculations for the Insulating Phases of VO$_2$

Previous studies have shown\footnote{J. H. Park et al., Nature {\bf 500}, 431 (2013).} that, under doping or tensile strain and upon heating, the well-known vanadium dioxide (VO$_2$) transition from an insulating monoclinic (M1) to a metallic rutile (R) phase progresses through a triclinic symmetry (T) phase and a magnetic monoclinic phase (M2), both of which are insulating. Structurally, this progression from M1 to R through T and M2 can be characterized by the progressive breaking of the V dimers. Investigation of the effect of these structural changes on the insulating phases of VO$_2$ may help resolve questions surrounding the long-debated issue of the respective roles of electronic correlation and Peierls mechanisms in driving the MIT. We investigated electronic and vibrational properties of the insulating phases of VO$_2$ in the framework of DFT+U. We will present {\em ab initio} calculations of infrared spectra and optical electronic responses for the insulating phases and compare these to available experimental measurements \footnote{T. J. Huffman et al., PRB {\bf 87}, 115121 (2013).}\footnote{A. S. Barker et al., PRL {\bf 17}, 1286 (1966).}\footnote{H. W. Verleur et al., PR {\bf 172}, 788 (1968).}\footnote{J. M. Tomczak and S. Biermann, PRB {\bf 80}, 085117 (2009).}.   

Role of non-local exchange in the electronic structure of correlated oxides

Transition-metal oxides (TMO) with partially filled d or f shells are a prototype of correlated materials. They exhibit very interesting properties, like metal-insulator phase transitions (MIT) [1]. In this work we consider several TMO insulators in which Kohn-Sham LDA band structures are metallic: VO2, V2O3, Ti2O3, LaTiO3 and YTiO3. In the past, this failure of LDA has been explained in terms of its inadequacy to capture the strong interactions taking place between correlated electrons. In the spirit of the Hubbard model, possible corrections to improve onsite correlation are the LDA$+$U [2] and LDA$+$DMFT [3] approaches. Here we make use of the HSE06 hybrid functional [4]. We show that, without invoking strong-correlation effects, the contribution of the non-local Fock exchange is essential to correct the LDA results, by curing its delocalization error. In fact, HSE06 provides insulating band structures and correctly describes the MIT in all the considered compounds [5]. We further discuss the advantages and the limitations of the HSE06 hybrid functional in correlated TMO [1] M. Imada et al., Rev. Mod. Phys. 70, 1039 (1998) [2] V.I. Anisimov, et al.,Phys. Rev. B 44, 943 (1991). [3] A. Georges et al., Rev. Mod. Phys. 68, 13 (1996). [4] J. Heyd et al., J. Chem. Phys. 118, 8207 (2003); J. Heyd et al., J. Chem. Phys. , 219906(E) (2006). [5] F. Iori, M. Gatti, and A. Rubio Phys. Rev. B , 115129 (2012)   

The electronic structure of the Mott insulator VO$_{\mathrm{2}}$: the strongly correlated metal state is screened by impurity band.

A Mott insulator VO$_{\mathrm{2}}$ (3$\mathrm{d}^{1})$ has a direct gap ($\Delta_{direct}\propto V_{direct})$ of 0.6 eV and an indirect gap of $\Delta_{act}\propto V_{direct}\approx $0.15 \textit{eV} coming from impurity indirect band. At $\mathrm{T}_{c}$, $\Delta_{direct}=\Delta_{act}=$ O is satisfied and the insulator-to-metal transition (IMT) occurs. The metallic carriers near core region can be trapped when a critical onsite Coulomb $U_{c}$ exists. Then, a potential energy is defined as \[ V_{g}=\left( V_{direct}+U_{c} \right)+V_{indirect} \] \begin{equation} \label{eq1} \thinspace \thinspace \thinspace \thinspace \thinspace =-(2 \mathord{\left/ {\vphantom {2 {3)E_{F}(1+e(N_{tot} \mathord{\left/ {\vphantom {N_{tot} {n_{tot})(1-\mathrm{exp}({-\Delta }_{act} \mathord{\left/ {\vphantom {{-\Delta }_{act} {k_{B}T)))+U_{c}}}} \right. \kern-\nulldelimiterspace} {k_{B}T)))+U_{c}}}}} \right. \kern-\nulldelimiterspace} {n_{tot})(1-\mathrm{exp}({-\Delta }_{act} \mathord{\left/ {\vphantom {{-\Delta }_{act} {k_{B}T)))+U_{c}}}} \right. \kern-\nulldelimiterspace} {k_{B}T)))+U_{c}}}}}} \right. \kern-\nulldelimiterspace} {3)E_{F}(1+e(N_{tot} \mathord{\left/ {\vphantom {N_{tot} {n_{tot})(1-\mathrm{exp}({-\Delta }_{act} \mathord{\left/ {\vphantom {{-\Delta }_{act} {k_{B}T)))+U_{c}}}} \right. \kern-\nulldelimiterspace} {k_{B}T)))+U_{c}}}}} \right. \kern-\nulldelimiterspace} {n_{tot})(1-\mathrm{exp}({-\Delta }_{act} \mathord{\left/ {\vphantom {{-\Delta }_{act} {k_{B}T)))+U_{c}}}} \right. \kern-\nulldelimiterspace} {k_{B}T)))+U_{c}}}}, \end{equation} where $V_{direct}=-(2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3)E_{F}$ is the screened Coulomb pseudopotential at K $=$ 0. $\mathrm{\Delta \rho =}N_{tot} \mathord{\left/ {\vphantom {N_{tot} {n_{tot}\approx 0.018\% }}} \right. \kern-\nulldelimiterspace} {n_{tot}\approx 0.018\% }$ [\underline {1}] is defined as the critical doping quantity, where $n_{tot}$ is the carrier density in the direct band and $N_{tot}$ is the carrier density in the impurity band. In $U_{c}<(2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3)E_{F}$ case, it sustains the insulator state. However, when both $U_{c}>(2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3)E_{F}$ and $\Delta_{act}\mathrm{=}$ 0 by excitation are satisfied, the IMT occurs in V$_{\mathrm{g}}\ge $ 0. This indicates that the excitation ($\Delta_{act}=$ 0) breaks the Coulomb equilibrium (V$_{\mathrm{g}}$\textless 0 and insulator sustaining $U_{c})$ in \textit{Eq.} ($\mathrm{1})$; the Coulomb energy changes from $U_{c}$ to a $U{ [Preview Abstract]

Two-dimensional quantum percolation with binary non-zero hopping integrals

In a previous work [Dillon and Nakanishi, Eur.Phys.J B 87, 286 (2014)], we calculated the transmission coefficient of the two-dimensional quantum percolation problem and mapped out in detail the three regimes of localization, i.e., exponentially localized, power-law localized, and delocalized which had been proposed earlier [Islam and Nakanishi, Phys.Rev. E 77, 061109 (2008)]. We now consider a variation on quantum percolation in which the hopping integral (V$_{diluted}$) associated with bonds that connect to at least one diluted site is non-zero but a fraction of the hopping integral (V$_{full}$=1) between non-diluted sites. We study the latter model by calculating quantities such as the transmission coefficient and the inverse participation ratio and find the original quantum percolation results to be stable over a wide range of energy. In particular, except in the immediate neighborhood of the band center (where increasing V$_{diluted}$ to just 0.02*V$_{full}$ appears to eliminate localization effects), increasing V$_{diluted}$ only shifts the boundaries between the 3 regimes but does not eliminate them until the V$_{diluted}$ reaches 20%-50% of V$_{full}$.   

Angle resolved photoemission study of the strongly correlated metal V$_2$O$_3$

V$_2$O$_3$ is often considered as the textbook example for the Mott metal-insulator transition. It has been the playground for multiple theoretical approaches and attempts to describe its metallic ground state for half a century. However, the experimental electronic structure is still unknown because of difficulties related to the three-dimensional character of the Fermi surface and the inhomogeneous cleavage of single crystals. Here we reveal for the first time the band structure of V$_2$O$_3$ using angle resolved photoemission spectroscopy. Direct comparison with theory is presented highlighting the important role of electron correlation for the physics of this material.