arXiv subjects

Vijay B. Shenoy

Publications and source records attributed to Vijay B. Shenoy.

At least 37 records · Page 2Linked to original sources

arXiv2016

Phases of Attractive Fermi Gases in Synthetic Dimensions

A novel way to produce quantum Hall ribbons in a cold atomic system is to use M hyperfine states of atoms in a 1D optical lattice to mimic an additional "synthetic dimension". A notable aspect here is that the SU(M) symmetric interaction between atoms manifests as "infinite ranged" along the synthetic dimension. We study the many body physics of fermions with attractive interactions in this system. We use a combination of analytical field theoretic and numerical density matrix renormalization group (DMRG) methods to reveal the rich ground state phase diagram of the system, including novel phases such as squished baryon fluids. Remarkably, changing the parameters entails unusual crossovers and transitions, e. g., we show that increasing the magnetic field (that produces the Hall effect) may convert a "ferrometallic" state at low fields to a "squished baryon superfluid" (with algebraic pairing correlations) at high fields. We also show that this system provides a unique opportunity to study quantum phase separation in a multiflavor ultracold fermionic system.

cond-mat.quant-gas↗

arXiv2016

The tenfold way redux: Fermionic systems with $N$-body interactions

We provide a systematic treatment of the tenfold way of classifying fermionic systems that naturally allows for the study of those with arbitrary $N$-body interactions. We identify four types of symmetries that such systems can possess, which consist of one ordinary type (usual unitary symmetries), and three non-ordinary symmetries (such as time reversal, charge conjugation and sublattice). Focusing on systems that possess no non-trivial ordinary symmetries, we demonstrate that the non-ordinary symmetries are strongly constrained. This approach not only leads very naturally to the tenfold classes, but also obtains the canonical representations of these symmetries in each of the ten classes. We also provide a group cohomological perspective of our results in terms of projective representations. We then use the canonical representations of the symmetries to obtain the structure of Hamiltonians with arbitrary $N$-body interactions in each of the ten classes. We show that the space of $N$-body Hamiltonians has an affine subspace (of a vector space) structure in classes which have either or both charge conjugation and sublattice symmetries. Our results can help address open questions on the topological classification of interacting fermionic systems.

cond-mat.mes-hall↗

arXiv2016

Boosted one dimensional superfluids on a lattice

We study the effect of a boost (Fermi sea displaced by a finite momentum) on one dimensional systems of lattice fermions with short-ranged interactions. In the absence of a boost such systems with attractive interactions possess algebraic superconducting order. Motivated by physics in higher dimensions, one might naively expect a boost to weaken and ultimately destroy superconductivity. However, we show that for one dimensional systems the effect of the boost can be to strengthen the algebraic superconducting order by making correlation functions fall off more slowly with distance. This phenomenon can manifest in interesting ways, for example, a boost can produce a Luther- Emery phase in a system with both charge and spin gaps by engendering the destruction of the former.

cond-mat.str-el↗

arXiv2015

Fractional Local Moment and High Temperature Kondo Effect in Rashba-Fermi Gases

We investigate the new physics that arises when a correlated quantum impurity hybridizes with Fermi gas with a generalized Rashba spin-orbit coupling produced via a uniform synthetic non-Abelian gauge field. We show that the impurity develops a {\it fractional} local moment which couples anti-ferromagnetically to the Rashba-Fermi gas. This results in a concomitant {\it Kondo effect with a high temperature scale} that can be tuned by the strength of the Rashba spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2015

Fluctuation Theory of Rashba Fermi Gases

Fermi gases with generalized Rashba spin orbit coupling inducedby a synthetic gauge field have the potential of realizing many interesting states such as rashbon condensates and topological phases. Here we develop a fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature ($T_c$) of a weakly attracting superfluid to the order of Fermi temperature, paving a pathway towards high $T_c$ superfluids.

cond-mat.quant-gas↗

arXiv2015

Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields

We investigate few body physics in a cold atomic system with synthetic dimensions (Celi et al., PRL 112, 043001 (2014)) which realizes a Hofstadter model with long-ranged interactions along the synthetic dimension. We show that the problem can be mapped to a system of particles (with $SU(M)$ symmetric interactions) which experience an $SU(M)$ Zeeman field at each lattice site {\em and} a non-Abelian $SU(M)$ gauge potential that affects their hopping from one site to another. This mapping brings out the possibility of generating {\em non-local} interactions (interaction between particles at different physical sites). It also shows that the non-Abelian gauge field, which induces a flavor-orbital coupling, mitigates the "baryon breaking" effects of the Zeeman field. For $M$ particles, the $SU(M)$ singlet baryon which is site localized, is "deformed" to be a nonlocal object ("squished" baryon) by the combination of the Zeeman and the non-Abelian gauge potential, an effect that we conclusively demonstrate by analytical arguments and exact (numerical) diagonalization studies. These results not only promise a rich phase diagram in the many body setting, but also suggests possibility of using cold atom systems to address problems that are inconceivable in traditional condensed matter systems. As an example, we show that the system can be adapted to realize Hamiltonians akin to the $SU(M)$ random flux model.

cond-mat.quant-gas↗

arXiv2012

Feshbach Resonance in a Synthetic Non-Abelian Gauge Field

We study the Feshbach resonance of spin-1/2 particles in the presence of a uniform synthetic non-Abelian gauge field that produces spin orbit coupling along with constant spin potentials. We develop a renormalizable quantum field theory that includes the closed channel boson which engenders the Feshbach resonance, in the presence of the gauge field. By a study of the scattering of two particles in the presence of the gauge field, we show that the Feshbach magnetic field, where the apparent low energy scattering length diverges, depends on the conserved centre of mass momentum of the two particles. For high symmetry gauge fields, such as the one which produces an isotropic Rashba spin orbit coupling, we show that the system supports two bound states over a regime of magnetic fields for a negative background scattering length and resonance width comparable to the energy scale of the spin orbit coupling. We discuss the consequences of these findings for the many body setting, and point out that a broad resonance (width larger than spin orbit coupling energy scale) is most favourable for the realization of the rashbon condensate.

cond-mat.quant-gas↗

arXiv2012

Flow enhanced pairing and other novel effects in Fermi gases in synthetic gauge fields

Recent experiments on fermions in synthetic gauge fields result in systems with a spin-orbit coupling along one spatial axis, a detuning field, and a Zeeman field. We show theoretically that the presence of all three results in interesting and unusual phenomena in such systems in the presence of a contact singlet attraction between the fermions (described by a scattering length). For two particles, bound states appear over certain range of the centre of mass momenta when a critical positive scattering length is attained, with the deepest bound state appearing at a nonzero centre of mass momentum. For the centre of mass momenta without a bound state, the gauge field induces a resonance like feature in the scattering continuum resulting in a large scattering phase shift. For many particles, we demonstrate that the system, in a parameter range, shows flow enhanced pairing, i.e., a more robust superfluid at finite centre of mass momentum. Yet another regime of parameters offers the opportunity to study strongly interacting normal states of spin-orbit coupled fermionic systems utilizing the resonance like feature induced by the synthetic gauge field.

cond-mat.quant-gas↗

arXiv2012

Sensory organ like response determines the magnetism of zigzag-edged honeycomb nanoribbons

We present an analytical theory for the magnetic phase diagram for zigzag edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter U . We show that the edge magnetic moment varies as ln U and uncover its dependence on the width W of the ribbon. The physics of this owes its origin to the sensory organ like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first order magnetic transition from an anti-parallel orientation of the moments on opposite edges to a parallel orientation occurs upon doping with holes or electrons. The critical doping for this transition is shown to depend inversely on the width of the ribbon. Using variational Monte-Carlo calculations, we show that magnetism is robust to fluctuations. Additionally, we show that the magnetic phase diagram is generic to zigzag edge terminated nanostructures such as nanodots. Furthermore, we perform first principles modeling to show how such magnetic transitions can be realized in substituted graphene nanoribbons.

cond-mat.mes-hall↗

arXiv2012

Fermionic Superfluid from a Bilayer Band Insulator in an Optical Lattice

We propose a model to realize a fermionic superfluid state in an optical lattice circumventing the cooling problem. Our proposal exploits the idea of tuning the interaction in a characteristically low entropy state, a band-insulator in an optical bilayer system, to obtain a superfluid. By performing a detailed analysis of the model including fluctuations and augmented by a variational quantum Monte Carlo calculations of the ground state, we show that the superfluid state obtained has high transition temperature of the order of the hopping energy. Our system is designed to suppress other competing orders such as a charge density wave. We suggest a laboratory realization of this model via an orthogonally shaken optical lattice bilayer.

cond-mat.quant-gas↗

arXiv2012

Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural boundary conditions valid for such systems. Our formulation is particularly suited to develop a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modeled by the Bernevig-Hughes-Zhang (BHZ) hamiltonian, we show that the continuum theory with the natural boundary condition provides an appropriate description of the low energy physics. As a spin-off, we find that in a certain parameter regime, the gap that arises in topological insulator ribbons of finite width due to the hybridization of edges states from opposite edges, depends non-monotonically on the ribbon width and can nearly vanish at certain "magic widths".

cond-mat.mes-hall↗

arXiv2012

Collective excitations across the BCS-BEC crossover induced by a synthetic Rashba spin-orbit coupling

Synthetic non-Abelian gauge fields in cold atom systems produce a Rashba spin-orbit interaction described by a vector $\blam = (λ_x, λ_y, λ_z)$. It was recently shown [Phys. Rev. B 84, 014512 (2011)] that on increasing $λ= |\blam|$, fermions at a finite density $ρ\approx\kf^3$ evolve to a BEC like state even in the presence of a weak attractive interaction (described by a scattering length $\as$). The BEC obtained at large spin-orbit coupling ($λ\gg k_F$) is a condensate of rashbons -- novel bosonic bound pairs of fermions whose properties are determined solely by the gauge field. Here we study the collective excitations of such superfluids by constructing a Gaussian theory using functional integral methods. We derive explicit expressions for superfluid phase stiffness, sound speed and mass of the Anderson-Higgs boson that are valid for any $\blam$ and scattering length. We find that at finite $λ$, the phase stiffness is always lower than that set by the density of particles, consistent with earlier work[arXiv:1110.3565] which attributed this to the lack of Galilean invariance of the system at finite $λ$. We show that there is an emergent Galilean invariance at large $λ$, and the phase stiffness is determined by the rashbon density and mass, consistent with Leggett's theorem. We further demonstrate that the rashbon BEC state is a superfluid of anisotropic rashbons interacting via a contact interaction characterized by a rashbon-rashbon scattering length $a_R$. We show that $a_R$ goes as $λ^{-1}$ and is essentially {\em independent} of the scattering length between the fermions as long as it is nonzero. Analytical results are presented for a rashbon BEC obtained in a spherical gauge field with $λ_x = λ_y = λ_z = \fracλ{\sqrt{3}}$.

cond-mat.quant-gas↗

arXiv2011

Synchronous and Asynchronous Mott Transitions in Topological Insulator Ribbons

We address how the nature of linearly dispersing edge states of two dimensional (2D) topological insulators evolves with increasing electron-electron correlation engendered by a Hubbard like on-site repulsion $U$ in finite ribbons of two models of topological band insulators. Using an inhomogeneous cluster slave rotor mean-field method developed here, we show that electronic correlations drive the topologically nontrivial phase into a Mott insulating phase via two different routes. In a synchronous transition, the entire ribbon attains a Mott insulating state at one critical $U$ that depends weakly on the width of the ribbon. In the second, asynchronous route, Mott localization first occurs on the edge layers at a smaller critical value of electronic interaction which then propagates into the bulk as $U$ is further increased until all layers of the ribbon become Mott localized. We show that the kind of Mott transition that takes place is determined by certain properties of the linearly dispersing edge states which characterize the topological resilience to Mott localization.

cond-mat.str-el↗

arXiv2011

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength ($λ$) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density $ρ\sim \kf^3$ undergoes a change at a critical value, $λ_T \approx \kf$ [Phys. Rev. B {\bf 84}, 014512 (2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-$\half$ fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulae for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a {\em characteristic fashion with increasing $λ$}. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud for all gauge field configurations, which are anisotropic in general. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling $λ$. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians (eg. quantum hall spherical geometry) by using a non-Abelian gauge field in conjunction with another potential.

cond-mat.quant-gas↗

arXiv2011

Rashbons: Properties and their significance

In presence of a synthetic non-Abelian gauge field that induces a Rashba like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a BCS ground state to a BEC ground state when the strength of the gauge field is increased [Phys. Rev. B {\bf 84}, 014512 (2011)]. The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion-pairs whose properties are solely determined by the Rashba gauge field -- hence called rashbons. In this paper, we conduct a systematic study of the properties of rashbons and their dispersion. This study reveals a new qualitative aspect of the problem of interacting fermions in non-Abelian gauge fields, i.e., that the rashbon state induced by the gauge field for small centre of mass momenta of the fermions ceases to exist when this momentum exceeds a critical value which is of the order of the gauge coupling strength. The study allows us to estimate the transition temperature of the rashbon BEC, and suggests a route to enhance the exponentially small transition temperature of the system with a fixed weak attraction to the order of the Fermi temperature by tuning the strength of the non-Abelian gauge field. The nature of the rashbon dispersion, and in particular the absence of the rashbon states at large momenta, suggests a regime of parameter space where the normal state of the system will be a dynamical mixture of uncondensed rashbons and unpaired helical fermions. Such a state should show many novel features including pseudogap physics.

cond-mat.quant-gas↗

arXiv2011

The Nature and Properties of a Repulsive Fermi Gas in the "Upper Branch"

We generalize the Noziéres-Schmitt-Rink (NSR) method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch". We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.

cond-mat.quant-gas↗

arXiv2011

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-$\half$ fermions (3D) at a finite density ($ρ\sim \kf^3$) in the presence of a uniform non-Abelian gauge field. The gauge field configuration (GFC) described by a vector $\blam \equiv (λ_x, λ_y, λ_z)$, whose magnitude $λ$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $(\kf |\as| \lesssim 1)$, the ground state in the absence of the gauge field ($λ=0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) ground state of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum. For large gauge couplings $(λ/\kf \gg 1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the gauge field (and not by the scattering length so long as it is non-zero) -- we call these bosons "rashbons". In the absence of interactions ($\as = 0^-$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling $λ_T$. For high symmetry gauge field configurations we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $λ$ near $λ_T$. In the context of cold atomic systems, this work makes an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

cond-mat.quant-gas↗

arXiv2011

How does a synthetic non-Abelian gauge field influence the bound states of two spin-$\half$ fermions?

We study the bound states of two spin-$\half$ fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in 3D space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba type spin-orbit interaction is described by three coupling parameters $(λ_x, λ_y, λ_z)$. For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is {\em negative}, i.e. shifts to the "BCS side" of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., $λ_x = λ_y = λ_z$) for which there is a two body bound state for {\em any} scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid $^3$He. Our results show that the BCS-BEC crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

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