Benjamin Ezekiel Feldman
Assistant Professor of Physics
Web page: https://sites.stanford.edu/feldman
Honors & Awards

Dicke Postdoctoral Fellow, Princeton University (Dept. of Physics) (20132016)

Kavli Frontiers of Science Fellow, US National Academy of Sciences, Kavli Foundation (2018)

Terman Faculty Fellow, Stanford University (H&S) (20182020)

Sloan Research Fellow, Alfred P. Sloan Foundation (20192021)
Professional Education

M.S., Haverford College, Physics (2007)

Ph.D., Harvard University, Physics (2013)
Current Research and Scholarly Interests
How do material properties change as a result of interactions among electrons, and what is the nature of the new phases that result? What novel physical phenomena and functionality (e.g., symmetry breaking or topological excitations) can be realized by combining materials and device elements to produce emergent behavior? How can we leverage nontraditional measurement techniques to gain new insight into quantum materials? These are some of the overarching questions we seek to address in our research.
We are interested in a variety of quantum systems, especially those composed of twodimensional flakes and heterostructures. This class of materials has been shown to exhibit an incredible variability in their properties, with the further benefit that they are highly tunable through gating and applied fields.
202223 Courses
 Thermodynamics, Kinetic Theory, and Statistical Mechanics I
PHYSICS 170 (Aut)  Thermodynamics, Kinetic Theory, and Statistical Mechanics II
PHYSICS 171 (Win) 
Independent Studies (5)
 Curricular Practical Training
PHYSICS 291 (Sum)  Directed Studies in Applied Physics
APPPHYS 290 (Aut, Win, Spr, Sum)  Independent Research and Study
PHYSICS 190 (Aut, Spr)  Research
PHYSICS 490 (Aut, Win, Spr, Sum)  Senior Thesis Research
PHYSICS 205 (Aut, Win, Spr)
 Curricular Practical Training

Prior Year Courses
202122 Courses
 Thermodynamics, Kinetic Theory, and Statistical Mechanics I
PHYSICS 170 (Aut)  Thermodynamics, Kinetic Theory, and Statistical Mechanics II
PHYSICS 171 (Win)
202021 Courses
 Thermodynamics, Kinetic Theory, and Statistical Mechanics I
PHYSICS 170 (Aut)  Thermodynamics, Kinetic Theory, and Statistical Mechanics II
PHYSICS 171 (Win)
201920 Courses
 Thermodynamics, Kinetic Theory, and Statistical Mechanics I
PHYSICS 170 (Aut)  Thermodynamics, Kinetic Theory, and Statistical Mechanics II
PHYSICS 171 (Win)
 Thermodynamics, Kinetic Theory, and Statistical Mechanics I
Stanford Advisees

Doctoral Dissertation Reader (AC)
Vladimir Calvera, Sanyum Channa, Joe Finney, Zhaoyu Han, Connie Hsueh, Aidan O'Beirne, Tiffany Paul, Winston Pouse, Jonathan San Miguel, Daniel Wennberg, Charles Zheng 
Doctoral Dissertation Advisor (AC)
Ben Foutty, Jesse Hoke, Carlos Kometter, Yifan Li, Jiachen Yu 
Doctoral Dissertation CoAdvisor (AC)
Alana Gudinas
All Publications

Quantum Hall valley nematics.
Journal of physics. Condensed matter : an Institute of Physics journal
2019
Abstract
Twodimensional electron gases subject to strong magnetic fields provide a canonical platform to explore a variety of exotic electronic phenomena. Here we review the physics of one intriguing example: quantum Hall valley nematics. In these phases of matter, the formation of a topologically insulating integer quantum Hall state is accompanied by the spontaneous breaking of a pointgroup symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantum Hall physics links charge conduction to topological defects of this order. We discuss how these combine to yield a rich and intricate phase structure, and their implications for transport and spectroscopy measurements. We provide a brief survey of several relevant experimental systems and close with an outlook on future directions. .
View details for PubMedID 30743251

Interacting multichannel topological boundary modes in a quantum Hall valley system.
Nature
2019
Abstract
Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), twodimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct brokensymmetry QHFM phases are predicted to host gapless onedimensional modesthat is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials38, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equalenergy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valleypolarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting onedimensional quantum wires.QHFM domain walls can be realized in different classes of twodimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.
View details for PubMedID 30728501

Squeezing strong correlations from graphene.
Science (New York, N.Y.)
2019; 363 (6431): 1035–36
View details for PubMedID 30846582

Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference
NATURE PHYSICS
2018; 14 (8): 796+
View details for DOI 10.1038/s4156701801482
View details for Web of Science ID 000440583300011

Visualizing heavy fermion confinement and Paulilimited superconductivity in layered CeCoIn5
NATURE COMMUNICATIONS
2018; 9: 549
Abstract
Layered material structures play a key role in enhancing electronelectron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasitwodimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in crosssection the quasitwodimensional electronic states of the heavy fermion superconductor CeCoIn5. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layerbylayer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the dwave order parameter determines whether ingap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical inplane magnetic field, consistent with a Paulilimited firstorder phase transition into a pseudogap phase.
View details for PubMedID 29416021

Highresolution studies of the Majorana atomic chain platform
NATURE PHYSICS
2017; 13 (3): 286?
View details for DOI 10.1038/NPHYS3947
View details for Web of Science ID 000395814000022

Observation of a nematic quantum Hall liquid on the surface of bismuth
SCIENCE
2016; 354 (6310): 316321
Abstract
Nematic quantum fluids with wave functions that break the underlying crystalline symmetry can form in interacting electronic systems. We examined the quantum Hall states that arise in high magnetic fields from anisotropic hole pockets on the Bi(111) surface. Spectroscopy performed with a scanning tunneling microscope showed that a combination of singleparticle effects and manybody Coulomb interactions lift the sixfold Landau level (LL) degeneracy to form three valleypolarized quantum Hall states. We imaged the resulting anisotropic LL wave functions and found that they have a different orientation for each brokensymmetry state. The wave functions correspond to those expected from pairs of hole valleys and provide a direct spatial signature of a nematic electronic phase.
View details for DOI 10.1126/science.aag1715
View details for PubMedID 27846563

Electronhole asymmetric integer and fractional quantum Hall effect in bilayer graphene
SCIENCE
2014; 345 (6192): 5557
View details for DOI 10.1126/science.1250270
View details for Web of Science ID 000338284400046

Fractional Quantum Hall Phase Transitions and FourFlux States in Graphene
PHYSICAL REVIEW LETTERS
2013; 111 (7)
Abstract
Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of brokensymmetry states arising from electronelectron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=1/2 and 1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches 1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of manybody states observed in graphene and demonstrate substantial control over their order parameters.
View details for DOI 10.1103/PhysRevLett.111.076802
View details for Web of Science ID 000323333800007
View details for PubMedID 23992076

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
SCIENCE
2012; 337 (6099): 11961199
Abstract
Graphene provides a rich platform to study manybody effects, owing to its massless chiral charge carriers and the fourfold degeneracy arising from their spin and valley degrees of freedom. We use a scanning singleelectron transistor to measure the local electronic compressibility of suspended graphene, and we observed an unusual pattern of incompressible fractional quantum Hall states that follows the standard composite fermion sequence between filling factors ν = 0 and 1 but involves only evennumerator fractions between ν = 1 and 2. We further investigated this surprising hierarchy by extracting the corresponding energy gaps as a function of the magnetic field. The sequence and relative strengths of the fractional quantum Hall states provide insight into the interplay between electronic correlations and the inherent symmetries of graphene.
View details for DOI 10.1126/science.1224784
View details for Web of Science ID 000308414000029
View details for PubMedID 22955829

Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
PHYSICAL REVIEW LETTERS
2010; 105 (25)
Abstract
Bilayer graphene has attracted considerable interest due to the important role played by manybody effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors ν= ± 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zerofield ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of brokensymmetry states at ν=0, ± 1, and ± 2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.
View details for DOI 10.1103/PhysRevLett.105.256806
View details for Web of Science ID 000286752100005
View details for PubMedID 21231612

Brokensymmetry states and divergent resistance in suspended bilayer graphene
NATURE PHYSICS
2009; 5 (12): 889893
View details for DOI 10.1038/NPHYS1406
View details for Web of Science ID 000273086700016