Current Research

Condensed Matter Physics is very broadly, the search for new phases of matter and ways to describe them. I am interested in phases of matter where interactions between the constituent particles (like the electrons in certain solids) are so strong, that the appropriate description of the system is in terms of entirely new objects. Such phases may occur in strongly correlated electronic systems and cold atomic gases. I am also interested in frustrated quantum magnetism, and the physics of thermally fluctuating superconductors.

(i) Unconventional Quantum Criticality:
In [1] we studied the physics of 2D quantum magnets when certain space-time defects (hedgehog defects - see figure) are absent. This lack of "topological disorder" completely changes the physics of the model, in particular, even when the spins are fluctuating, the system possesses a hidden order that manifests itself in the form of an emergent photon excitation (light!) and excitations with fractional quantum numbers. Also, continuous phase transitions in these models turn out to be very different in character; and in one situation even turns out to be self-dual.
Interestingly, these deconfined critical points may actually occur quite naturally in certain quantum magnets [2] where quantum interference effects help to a suppress hedgehog defects. Moreover, they can control `Landau Forbidden' continuous transition - that is, transitions between two states of different symmetry that according to Landau's theory of phase transitions (and common sense) would be continuous without special fine tuning.
We are currently engaged in searching for microscopic models where such phenomena arise, and looking to generalize these results to three dimensions.

[1] Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
O. I. Motrunich, A. Vishwanath
Phys. Rev. B 96, 207202 (2004)
[2] Deconfined quantum critical points
T. Senthil, Ashvin Vishwanath, Leon Balents, Subir Sachdev, M. P. A. Fisher
Science 303,1490 (2004).
{Perspective - by R. B. Laughlin.}
TALK: Emerging Photons and Decaying Electrons

(ii) Novel Phases in Metallic Heli-magnets ( B. Binz )
Under pressure, MnSi a metal with a tendency to form helical magnetic structures, undergoes a transition into an unusual phase that shows "partial order" and non-Fermi liquid electrical transport. We have developed a theory of helical magnetic crystals - a coherent multi-spiral state (depicted in the figure), that agrees well with existing data on the magnetic structure. Moreover, it makes several predictions for unusual electrical transport arising from the presence of non-trivial magnetic structures [3].

[3] Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
B. Binz, A. Vishwanath, V. Aji
Phys. Rev. Lett. 96, 207202 (2006)
TALK: MnSi-Theory of the Helical Spin Cystal

(iii) Frustrated Magnetism (with Fa Wang)
Many magnetic systems display "frustration", competing interactions that lead to multiple ground states at the classical level. The system is then poised to realize a variety of phases, including, it is believed, exotic spin liquid states that possess an unusual "topological order" arising from the expulsion of certain topological defect configurations. The different flavors of spin liquid states were studied in [4], for the triangular and Kagome magnets. Symmetries are realized in a subtle way for these states, which severely constrains them. Finding all possible phases consistent with these constraints led us to new spin-liquid states (see figure) with enhanced stability.

Thermal and quantum fluctuations, which are generally associated with their disordering effects, can paradoxically select ordered states in frustrated magnets ("order by disorder"). These have been studied in the context of two spin 1/2 frustrated magnets on a distorted kagome (volborthite [5]) lattice and on the hyper-kagome lattice [6] (NaIrO), a new three dimensional frustrated lattice.

[4] Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis
Fa Wang and A. Vishwanath.
Phys. Rev. B, 74, 174423 (2006)
[5] Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite
Fa Wang, A. Vishwanath and Y. B. Kim
cond-mat/07040933. Submitted to Phys. Rev.B.
[6] Topological spin liquid on the hyper-kagome lattice of Na4Ir3O8
M. J. Lawler, H.-Y. Kee, Y. B. Kim and A. Vishwanath
cond-mat/07050990. Submitted to Phys. Rev. Lett.

(iv) Fluctuating Superconductivity ( D. Podolsky)
When a superconductor is warmed above its transition temperature, the proximate superconductivity can influence a number of physical properties. This is especially marked if the superconductivity is destroyed by phase fluctuations, while the local amplitude remains finite. This is expected to be the case in the underdoped cuprates - and Nernst effect and magnetization are believed to be sensitive probes of this effect. We have computed these quantities within an XY model with thermally diffusing phase variables and find reasonable agreement with existing data. A remarkable outcome, that remains to be fully understood, is that the Nernst effect (specifically alpha_xy) closely tracks the magnetization (M/T) as shown [7]. We have also developed a vortex approach to fluctuating superconductivity, which allows one to directly access the effects of core energy, multiple vortex species etc. on the Nernst effect and magnetization.

[7] Nernst effect and diamagnetism in phase fluctuating superconductors
D. Podolsky, S. Raghu and A. Vishwanath
cond-mat/0612096. Submitted to Phys. Rev. Lett.

(v) Transport near Quantum Critical Points (D. Podolsky )
Matter near a quantum critical point can display properties very different from that in conventional phases, due to the presence of gapless critical modes. For example, the Widemann Franz law, a fundamental relation between the electrical and thermal conductivity of a metal, was found to break down on approaching a superconducting quantum critical point [8]. The theory developed there describes the onset of superconductivity in the overdoped cuprates, and in thin-film superconductors in a parallel field.
While several experimental systems show quantum phase transitions out of the superconducting state, a proper theoretical understanding is still lacking, partly because of a lack of distinct probes. We have calculated thermal and thermoelectric transport properties at quantum critical points [8], as well as current noise, which is characteristic of a quantum critical point driven out of equilibrium [9].

[8] Thermoelectric transport near the pair breaking quantum phase transition out of a d-wave superconductor.
D. Podolsky, A. Vishwanath, J. Moore and S. Sachdev
Phys. Rev. B 75, 014520 (2007).
[9] Current noise in the vicinity of the 2D superconductor-insulator quantum critical point
A. G. Green, J. Moore, S. Sondhi and A. Vishwanath
Phys. Rev. Lett. 97, 227003 (2006).
Transport of heat and charge at a Quantum Critical point.

(vi) New Probes and Orders in cold atomic gases
Although cold quantum gases present an exciting new class of condensed matter systems, probing their properties presents both a theoretical and experimental challenge. We have studied the non-equilibrium dynamics in the BCS-BEC crossover regime [10], and how this may be used to probe pairing on the BCS side. Shot noise measurements of one dimensional gases was shown [11] to contain information on the Luttinger parameters, that are usually hard to access.
Novel orders, such a supersolidity in a model of bosons on the triangular lattice [12] as well as biaxial and uniaxial nematic states in spin-2 condensates [13] were established. In both cases, these elusive ordered states have been much sought after in other contexts, but seem to be naturally realizable in cold atom systems. Interestingly, the theoretical mechanism stabilizing both these phases is "order-by-disorder", discussed in the frustrated magnetism paragraph.

[10] Dynamic projection on Feshbach molecules: a probe of pairing and phase fluctuations
E. Altman and Ashvin Vishwanath
Phys. Rev. Lett. 95, 110404 (2005).
[11] Noise Correlations in one-dimensional systems of ultra-cold fermions.
L. Mathey, E. Altman and A. Vishwanath.
cond-mat/0507108. Submitted to Phys. Rev. Lett.
[12] Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice
R. Melko, A. Paramekanti, A. Burkov, A. Vishwanath, D. Sheng and L. Balents
Phys. Rev. Lett. 95, 127207 (2005).
[13] Nematic Order by Disorder in Spin-2 BECs
A. Turner, R. Barnett, E. Demler and Ashvin Vishwanath
cond-mat/0702057. To be published in Phys. Rev. Lett.
TALK: Non-equilibrium Dynamics at the BCS-BEC Crossover

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